UNIVERSITY OF CAMBRIDGE
INSTITUTE OF ASTRONOMY
THE ADAPTIVE OPTICS LUCKY IMAGER:
COMBINING ADAPTIVE OPTICS
AND LUCKY IMAGING
STEPHEN JONATHAN CRASS
ST EDMUND’S COLLEGE
Supervisor:
PROF. CRAIG MACKAY
This dissertation is submitted for the degree of Doctor of Philosophy
May 2014
Cambridge, United Kingdom

“The purpose of life is to contribute in
some way to making things better.”
Robert F. Kennedy
For my parents:
My biggest supporters no matter
how much (or little) they understand
my work!

Declaration
I hereby declare that my thesis entitled The Adaptive Optics Lucky Imager: Combining adaptive optics
and lucky imaging is not substantially the same as any that I have submitted, or, is being
concurrently submitted for a degree or diploma or other qualification at the University of
Cambridge or any other University or similar institution except as declared in the Preface and
specified in the text. I further state that no substantial part of my thesis has already been
submitted, or, is being concurrently submitted for any such degree, diploma or other qualification
at the University of Cambridge or any other University of similar institution except as declared in
the Preface and specified in the text. I also declare that this thesis is the result of my own work and
includes nothing which is the outcome of work done in collaboration except where specifically
indicated in the text. Various figures in the thesis are reproduced from the work of other authors
for illustration or discussion. Such figures are clearly credited in the text.
Figures showing optical designs have been produced by David King unless otherwise specified.
The following parts have been published or accepted for publication:
• Sections of Chapters 4, 5 and 6 were published as part of
The AOLI low-order non-linear curvature wavefront sensor: a method for high sensitivity wavefront
reconstruction
Crass, J., Aisher, P.L., Femenia Castella´, B., King, D.L., Mackay, C., Rebolo-Lo´pez, R., Labadie,
L., Pe´rez Garrido, A., Balcells, M., et al., 2012, Proceedings of the SPIE, Volume 8447, 84470T
and
The AOLI Non-Linear Curvature Wavefront Sensor: High sensitivity reconstruction for low-order
AO
Crass, J., King, D.L., Mackay, C., 2013, Proceedings of the Third AO4ELT Conference
• Sections of Chapters 4 and 5 were published as part of
Wavefront phase retrieval with non-linear curvature sensors
i
Aisher, P.L., Crass, J., Mackay, C., 2013, MNRAS 429, 2019-2031
• Sections of Chapters 3 and 6 were published as part of
AOLI: Adaptive Optics Lucky Imager: diffraction limited imaging in the visible on large ground-based
telescopes
Mackay, C., Rebolo-Lo´pez, R., Femenia Castella´, B., Crass, J., King, D.L., Labadie, L., Aisher,
P.L., Pe´rez Garrido, A., Balcells, M., et al., 2012, Proceedings of the SPIE, Volume 8446, 844621
This dissertation contains fewer than the limit of 60,000 words.
S.J. Crass
Cambridge, May 2014
ii
Summary
One of the highest resolution astronomical images ever taken in the visible were obtained by
combining the techniques of adaptive optics and lucky imaging. The Adaptive Optics Lucky
Imager (AOLI), being developed at Cambridge as part of a European collaboration, combines
these two techniques in a dedicated instrument for the first time. The instrument is designed
initially for use on the 4.2 m William Herschel Telescope (WHT) on the Canary Island of La Palma.
This thesis describes the development of AOLI, in particular the adaptive optics system and a new
type of wavefront sensor, the non-linear curvature wavefront sensor (nlCWFS), being used within
the instrument. The development of the nlCWFS has been the focus of my work, bringing the
technique from a theoretical concept to physical realisation at the WHT in September 2013.
The non-linear curvature wavefront sensor is based on the technique employed in the
conventional curvature wavefront sensor where two image planes are located equidistant either
side of a pupil plane. Two pairs of images are employed in the nlCWFS providing increased
sensitivity to both high- and low- order wavefront distortions. This sensitivity is the reason the
nlCWFS was selected for use with AOLI as it will provide significant sky-coverage using natural
guide stars alone, mitigating the need for laser guide stars.
This thesis is structured into three main sections; the first introduces the non-linear curvature
wavefront sensor, the relevant background and a discussion of simulations undertaken to
investigate intrinsic effects. The iterative reconstruction algorithm required for wavefront
reconstruction is also introduced. The second section discusses the practical implementation of
the nlCWFS using two demonstration systems as the precursor to the optical design used at the
WHT and includes details of subsequent design changes. The final section discusses data from
both the WHT and a laboratory setup developed at Cambridge following the observing run.
The long-term goal for AOLI is to undertake science observations on the 10.4 m Gran Telescopio
Canarias, the world’s largest optical telescope. The combination of AO and lucky imaging, when
used on this telescope, will provide resolutions a factor of two higher than ever before achieved at
visible wavelengths. This offers the opportunity to probe the Cosmos in unprecedented detail and
has the potential to significantly advance our understanding of the Universe.
iii
iv
Acknowledgements
There are many people who have contributed, not only to making this thesis possible but, to making
my last four years in Cambridge truly unforgettable. To list them all here would significantly
lengthen this document and so, for those who get bulked together or I forget to mention, I apologise
in advance!
Firstly my thanks must go to my supervisor, Craig Mackay, for all of his support and guidance
through this project. I think it speaks volumes of his experience that AOLI has gone from a concept
to an on-sky instrument within such a short period of time (even with a lot of kicking and screaming
in the process!). Thanks go to David King for helping to ‘cross each bridge as we came to it’ and
providing invaluable discussion and insight into optical design. Several other members of the
AOLI team also deserve a mention - Bruno Femenı´a for keeping me on the straight and narrow
when it comes to adaptive optics and both Marta Puga Antolı´n and Victor Gonza´lez Escalera for
their work and troubleshooting at the WHT.
Thanks go to several other people at the IoA for keeping me moving forward with my research.
I am particularly grateful to Paul Hewett for making sure I’m progressing in the right direction
and, perhaps more importantly, ensuring only the best wine and cheese is consumed at IoA tasting
events! Thanks go to Richard McMahon for his feedback and guidance with my work and making
sure computing problems always got in the way. I would also like to take this opportunity to thank
Roderick Johnstone for putting up with my sometimes odd computing ideas, over-specification of
projects and perhaps, most importantly, his excellent sense of humour... To all my other friends at
the IoA, past and present, I also say a huge thank you.
This academic year has proved to be particularly challenging for several reasons and the support of
three people within the IoA has been invaluable in getting this thesis completed. Firstly, Margaret
Harding - by far the best graduate student administrator anyone could ever hope for; I don’t know
what this department will do when you finally retire but your support this year has been far beyond
the call of duty. Secondly, Aime´e Hall - for giving me the kick I sometimes needed, hearing me rant
and for her sterling efforts in proof reading this thesis! Finally, Carolin Crawford - for giving me
the platforms to teach, communicate science and most importantly, how to (safely!) blow things up
v
in a room full of people.
Elsewhere, there are many people who have made this happen. All my friends in Cambridge and
St Edmund’s College who have provided an escape from work, whether sober or otherwise. To my
supervisees over the last four years for providing an escape from research into something where the
answers are known! I hope that you have actually learnt something during all those supervisions
and that you won’t just remember the cake... Further afield, specific mentions go to Alice Chaytow
and Tom Abell for giving me the chance to escape from the bubble of Cambridge which, as any
student here will tell you, is most definitely needed. And lastly, but by no means least in this
group, my thanks go to Dan Wilkins for his support, whether here or far, and for everything else
that is still to come.
My final and most heartfelt thanks must go to my family who have always been there to encourage
and support me whether academically or otherwise. I owe my deepest gratitude to my parents
for pushing me to think the sky’s the limit - a Ph.D. from Cambridge is certainly heading in that
direction.
And now on with the story!
vi
Contents
Declaration i
Summary iii
Acknowledgements v
1 Introduction 1
2 Background 3
2.1 Imaging from the ground: The theoretical limit . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Light: A brief introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Describing light: A mathematical introduction . . . . . . . . . . . . . . . . . . 4
2.2.2 The propagation of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Imaging planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 The Kolmogorov model of turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Layers of turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Short and long exposure images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Characterising turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.1 The Fried parameter r0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.2 Seeing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.3 Strehl ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.4 Isoplanatic patch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
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CONTENTS
2.5.5 Zernike polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 Correcting for atmospheric turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6.1 Adaptive optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6.2 Lucky imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 The Adaptive Optics Lucky Imager 25
3.1 Combining adaptive optics and lucky imaging . . . . . . . . . . . . . . . . . . . . . . 25
3.2 An introduction to AOLI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 The science case for AOLI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 An introduction to wavefront sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.1 Wavefront sensing basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Wavefront sensing techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.1 The Shack-Hartmann wavefront sensor . . . . . . . . . . . . . . . . . . . . . . 30
3.4.2 The conventional curvature wavefront sensor . . . . . . . . . . . . . . . . . . 33
3.4.3 The pyramid wavefront sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4.4 Evaluation of wavefront sensing techniques . . . . . . . . . . . . . . . . . . . 37
3.5 Wavefront correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 Low- and high-order correction . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 An introduction to the non-linear curvature wavefront sensor 43
4.1 Reconstruction basics: The Gerchberg-Saxton method . . . . . . . . . . . . . . . . . . 43
4.1.1 Improvements beyond the Gerchberg-Saxton technique . . . . . . . . . . . . . 44
4.2 Reconstruction for the nlCWFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 Wavefronts and their propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.1 Propagation regimes and techniques . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3.2 Selecting the correct propagation technique . . . . . . . . . . . . . . . . . . . . 50
viii
CONTENTS
4.3.3 Numerical propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Constraining the wavefront estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Phase unwrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.6 Speed of reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5 Investigation and simulation of the nlCWFS 59
5.1 Simulation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1.1 Verifying the suitability of Arroyo . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2 Chromatic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2.1 Strategies to minimise chromatic effects . . . . . . . . . . . . . . . . . . . . . . 65
5.3 Beam scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3.1 Plane positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4 Developing the wavefront reconstruction algorithm . . . . . . . . . . . . . . . . . . . 68
5.4.1 Low photon number reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 70
5.4.2 Defining a prior for reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6 The AOLI instrument: Optical design 81
6.1 Development systems and verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.1.1 Thorlabs AO kit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.1.2 AOLI development system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.2 Deformable mirror selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3 Optical layout for the William Herschel Telescope . . . . . . . . . . . . . . . . . . . . 85
6.3.1 Common optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3.2 Lucky imaging science camera . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3.3 Wavefront sensor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.4 Calibration system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
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CONTENTS
6.5 Mechanisms and software control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.5.1 Pickoff mirror mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.5.2 Camera mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.5.3 Camera control and software . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.6 Current optical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.6.1 Improvements to the AOLI calibration system . . . . . . . . . . . . . . . . . . 109
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7 Observing at the William Herschel Telescope 113
7.1 Instrument commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.1.1 The commissioning process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.1.2 Commissioning challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.1.3 Installation in the GHRIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.2 Challenges during observing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.2.1 Weather conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.2 Wavefront sensor camera dewar . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.3 Wavefront sensor gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.3 Calibration system data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.3.1 Beam sizes of the nlCWFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.3.2 Phase plate data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.4 On-sky data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.4.1 On-sky wavefront sensor data . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.4.2 On-sky science camera data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.4.3 Magnitude values of the calibration system . . . . . . . . . . . . . . . . . . . . 128
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
8 nlCWFS laboratory data 131
8.1 Reconstructing AOLI in Cambridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
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CONTENTS
8.1.1 Pickoff mirror stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
8.1.2 Alignment and commissioning of the laboratory setup . . . . . . . . . . . . . 132
8.2 Calibration system chromaticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.2.1 Throughput and reference star spectral types . . . . . . . . . . . . . . . . . . . 136
8.2.2 Beam sizes with the nlCWFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.3 Limited bandwidth data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.3.1 Recovering the pupil mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.4 Wavefront reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.4.1 Initialising the algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.4.2 Results of the reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.5 Comparison with the SHWFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
9 Conclusions 151
9.1 Current status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
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CONTENTS
xii
“Equipped with his five senses, man
explores the universe around him and
calls the adventure Science.”
Edwin Powell Hubble
1
Introduction
Since the invention of the telescope in the 1600s, the effects of atmospheric turbulence have been
observed on astronomical images:
“If the Theory of making Telescopes could at length be fully brought into Practice, yet
there would be certain Bounds beyond which Telescopes could not perform. For
the Air through which we look upon the Stars, is in a perpetual Tremor; as may be
seen by ... the twinkling of the fix’d Stars.”
Newton, Opticks, 1730
The random motions of the Earth’s atmosphere limit the resolution of all large ground-based
telescopes to a fraction of their theoretical diffraction limit. Astronomers have found two possible
ways to overcome this: by rising above the atmosphere into the vacuum of space or correcting for
the effects of the atmosphere on the ground. One of the most famous space-based examples is the
Hubble Space Telescope, now approaching its 24th year of operation. It has provided some of the
most deep and stunning images of the Universe and has been a vital tool revolutionising our
understanding of the Cosmos. With the retirement of the Space Shuttle fleet however, it is almost
impossible to maintain and will likely come to the end of its lifetime in the upcoming decade.
1
In addition to the retirement of the Hubble Space Telescope, astronomers always strive for higher
resolution and better sensitivity of observations to allow them to study deeper into the Universe
with ever more detail. The next stage in this ongoing story is the development of the Extremely Large
Telescopes which will provide both large collecting areas and the potential to provide high resolution
imaging. These instruments have the potential to revolutionise observational astronomy however
to achieve their full potential, they must have effective atmospheric correction. With this in mind,
it is prudent to continue to investigate ground-based techniques to correct for these atmospheric
effects.
My research has focused on developing ground-based solutions to the problem of atmospheric
turbulence, in particular the combination of two, adaptive optics (AO) and lucky imaging. Using
the combination of these two techniques has produced some of the highest resolution images in
astronomy, and a new instrument, the Adaptive Optics Lucky Imager (AOLI) combines these
together into a dedicated instrument for the first time. It is the development of AOLI which has
been the focus of my work, in particular, the adaptive optics component of the instrument. The
AO system employs a new technology, the non-linear curvature wavefront sensor (nlCWFS) to
measure optical distortions imparted on light by the atmosphere, and this method has been
shown to be significantly more sensitive than currently implemented technologies.
The work in this thesis is structured into three main sections; Chapters 2 and 3 introduce the
relevant background regarding optical imaging, atmospheric conditions and correction and
provide an introduction to AOLI. Chapters 4 and 5 are a discussion of the nlCWFS and simulation
work I have undertaken in Cambridge to develop this method from its theoretical basis to a
practical implementation. Chapter 6 follows on from this discussion, presenting the optical design
of AOLI, in particular the specific design requirements highlighted by the work in Chapter 5.
Finally in Chapter 7, I present results from the first on-sky observing run with AOLI and
follow-up on this with laboratory work which is presented in Chapter 8.
2
“In physics, you dont have to go
around making trouble for yourself
nature does it for you.”
Frank Wilczek
2
Background
When designing optical ground-based telescopes it is important to understand the effects limiting
the capabilities of any such system. These can be controllable effects e.g. optical component
quality, fundamental limits imposed by physics e.g. the diffraction limit of optics, or changeable
and transient phenomena e.g. atmospheric changes. In this chapter, I present an introduction to
the background of ground-based telescope imaging with a focus on the strongest effect,
atmospheric turbulence.
2.1 Imaging from the ground: The theoretical limit
The resolution of any imaging system is limited by the quality of optics within the system. Even
with ‘perfect’ optics however (if only there was such a thing!), there is an upper limit on resolution
for any imaging system due to intrinsic diffraction effects. In this diffraction limited regime, the
highest resolution obtainable i.e. the angular separation θ (in radians), is given by the Rayleigh
criterion
θ = 1.22
λ
D
(2.1)
3
2.2 Light: A brief introduction
where λ is the optical wavelength and D is the diameter of the aperture in the system (for
telescopes, the diameter of the primary mirror). To obtain higher resolution images of a scientific
source, this means either a shorter wavelength of light (which is challenging as it’s not currently
possible to change the spectral output from distant stars or launch a telescope towards them at
relativistic speeds) or a telescope with a larger diameter must be used.
When working with a diffraction limited system with a single point source, an ‘Airy Disk’ pattern
should be visible at an imaging plane as shown in Figure 2.1 (although as every optical engineer
knows, this can take many hours of alignment to achieve and a single tap to undo...). The resolution
limit is set when two Airy patterns overlap and are still discernible as individual objects. At a
smaller angular separation, it is impossible to identify them as two distinct objects.
2.2 Light: A brief introduction
Before proceeding further, it is useful to give a brief introduction to the ideas of light and the
methodologies used to describe it within this thesis. Theories of light can be crudely broken into
two very different approaches; those using quantum mechanics where light is comprised of
elementary particles called photons or classical electromagnetism in which interlinked oscillating
electric and magnetic fields produce the radiation we see. I will predominantly adopt the
electromagnetism description in this thesis as it is most applicable to the overall structure of light
when working with optical systems.
2.2.1 Describing light: A mathematical introduction
In classical optics theory, light can be considered to be a complex scalar field, U [P (r), t], with
separable spatial and temporal components:
U [P (r), t] =
{
U [P (r)] exp
(−2ipict
λ
)}
(2.2)
where r is the position vector, t is the time and c is the speed of light. The spatial component is
given by
U [P (r)] = A(r) exp(ik · r) (2.3)
where k is the wavevector.
For astronomical applications, the spatial element is the component of interest and comprises a
position dependent amplitude component, A, which describes the brightness and an exponential
4
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(a) The Airy disk pattern.
(b) Intensity distribution of diffraction from a circular
aperture.
(c) The Rayleigh criterion: two apertures, each
generating an Airy disk pattern, are separated by the
minimum angular distance to still allow each to be
individually resolved. The vertical lines show the
location of the two sources.
Figure 2.1: The Airy disk pattern and characteristics generated by a circular aperture (Goodman, 2005).
5
2.2 Light: A brief introduction
term which encompases the phase of the wave to describe the propagation direction. When taking
measurements of the spatial extent of the wave, only the square of the amplitude, i.e. the intensity,
can be measured. No direct measurements of the phase are possible and any such information
must be recovered from the intensity information.
2.2.2 The propagation of light
The propagation of light can be considered in several ways (e.g. Fermat’s principle, Huygen’s
principle), however many of these return to the principle of ‘wavefronts’. These wavefronts are
lines of constant phase in the spatial component of the complex scalar field (Equation 2.3) and the
propagation of light is perpendicular to them. Plane wavefronts will map out straight lines of
constant phase and the light these wavefronts represent will travel perpendicularly in a straight
line. If the wavefronts are spherical across their extent, this will cause the light to converge to a
focus. Wavefronts however can be much more complex in shape with distortions on scales much
smaller than their overall size. This means that as light propagates perpendicular to the distortions,
it can create localised regions of increased and decreased amplitude (i.e. higher and lower intensity
regions when recorded) due to this focusing effect.
The phase of an optical field can be changed principally by entering a medium of differing
refractive index. If a collimated light beam in vacuum (which would propagate in a straight line)
enters a lens, the controlled change in phase brings the beam to a focal point. Unlike this system
however, many changes in phase are not undertaken in such a controlled manner which can lead
to overall optical distortions in image quality.
Of course, the propagation of light is not only affected by differing refractive indices, but also when
passing through apertures giving rise to the effects of diffraction. Diffractive effects are of particular
importance when dealing with apertures similar in size to the wavelength of light propagating
through them and must be accounted for when propagating light in this regime.
2.2.3 Imaging planes
Conventionally, optical imaging is undertaken at a ‘focal plane’ as shown in Figure 2.2. When
considering telescopes, this is the point where light from across the full aperture is brought
together to a single location, increasing the signal-to-noise ratio at any imaging detector. Imaging
at this location however is not the only possibility and imaging away from this focal plane allows
additional information regarding the optical field to be determined. In particular, it is often of
interest to image at a ‘pupil plane’ when dealing with telescope systems. The pupil plane is
defined at the entrance plane of the telescope (i.e. where light enters from the imaging source)
however imaging at this location would be unhelpful as no light would then reach an scientific
6
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Figure 2.2: The location of pupil and focal/imaging planes within an optical system. Planes can be
interchanged by the use of a lens with focal length f as shown.
instrument in the telescope. We can reimage the pupil as shown in Figure 2.2 to a ‘conjugate pupil
plane’ which has the same characteristics as the entrance pupil. Indeed, by choosing an
appropriate combination of lenses, it is possible to reduce the pupil size down while still
maintaining phase and amplitude information.
2.3 The Kolmogorov model of turbulence
The most significant limitation on the resolution of ground-based telescopes is their need to image
through the turbulent atmosphere. This turbulence is conventionally described by the Kolmogorov
model developed in the 1960s by Tatarski and based upon the studies of turbulence undertaken by
Andrei Kolmogorov in the 1940s (Kolmogorov, 1941a,b; Tatarski, 1961).
As light enters the Earth’s atmosphere, it can be considered to be made up of plane wavefronts
propagating from a vacuum of refractive index 1.0 to a medium of close to, but not exactly 1. The
refractive index of the atmosphere is dependent upon temperature, pressure and density, all of
which fluctuate on scales ranging from the largest weather systems through to small pockets of air,
just millimetres in size.
The Kolmogorov model of turbulence describes how energy transfers through a system by entering
on the largest scales, where the majority of the energy is located, and only being dissipated on the
smallest scales. The energy propagates from these ‘inner’ and ‘outer’ scales through a cascade
process where kinetic energy is conserved and the turbulent fluid sub-divides into smaller and
7
2.3 The Kolmogorov model of turbulence
Figure 2.3: The von Karman three dimensional power spectrum of refractive index variations within a
turbulent atmosphere (Hardy, 1998).
smaller vortices as shown in Figure 2.3. Finally, the energy is dispersed though viscosity. The
continual evolution of the atmosphere leads to an inhomogeneous refractive index which changes
over time. This manifests itself as distortions when using large telescopes for research or simply
the twinkling of stars when observing with the naked eye (Tyson, 2000).
The scales of these small scale air cells is important when considering the effects of atmospheric
turbulence on telescopes image quality; as they are smaller than the ground-based telescopes in
use today, many turbulent ’cells’ are above a telescope aperture at any one time, each with different
physical properties and therefore differing refractive indices. This leads to an unequal wavefront
distortion across the telescope aperture causing a degradation of image quality. The variations
in refractive index on these different scales manifests itself as phase variations across incoming
wavefronts, φ(r), where r is a spatial vector denoting position on the wavefront.
In the Kolmogorov model, the structure function (i.e. the mean-square difference in phase) between
a point r’ and a point a displacement r from it on a wavefront is given by:
Dφ(r) =
〈|φ(r’)− φ(r’− r)|2〉 = 6.88( |r|
r0
) 5
3
(2.4)
8
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where r0 is the Fried parameter, defined in Section 2.5.1. Experimental measurements from many
observatory sites widely support this model (Buscher et al., 1995; Short et al., 2003) however in
recent years measurements from some sites have been shown to differ from this Kolmogorov
model, particularly at high and low frequencies (Lazorenko, 2002; Di Folco et al., 2003). It is still
common practice however to assume the Kolmogorov model to simulate turbulence and has been
the technique employed throughout this work.
2.3.1 Layers of turbulence
In fluid dynamics, the strongest turbulent effects occur at the boundary between layers of
differing density or at the interface between layers of moving fluids. In the atmosphere, several
different layers and motions are known, for example the jet stream. When studying the structure
of the atmosphere with techniques such as SLODAR (SLOpe Detection And Ranging) and
SCIDAR (SCIntillation Detection And Ranging), these layers are clearly visible as shown in Figure
2.4. The strongest turbulent effects are located at the boundary between land and air i.e. in the
so-called ground layer.
2.4 Short and long exposure images
In the Kolmogorov turbulence model, there is a continuous evolution of the atmospheric structure
due to air motions. This leads to a spatially and temporally varying refractive index above the
telescope aperture causing distortions in the wavefront at the telescope pupil plane and in-turn
reducing image quality recorded. Changes in the atmospheric structure take place on fraction of
a second timescales and this imposes two imaging regimes: exposures taken on timescales shorter
than the atmospheric changes and exposure taken over longer periods. The effect of these two
timescales on images can be seen in Figure 2.5.
Individual ‘short’ exposure images taken on timescales less than that of changes in the
atmosphere are an instantaneous snapshot of the atmospheric structure and refractive index
variations affecting the telescope. They have a particularly variable point spread function (PSF)
due to the rapid variations within the atmosphere. Individual exposures take the form of a speckle
pattern which consists of multiple distorted copies of the diffraction limited PSF which are
overlaid upon each other. As such, these short exposure images retain information about the PSF
of the object being observed however it is usually strongly distorted (Law, 2006). In addition, the
more turbulent cells above a telescope aperture (i.e. the larger the telescope) the more ‘speckles’
are visible within a short exposure image.
Traditionally, to achieve the levels of sensitivity required in their data, astronomers have taken
9
2.4 Short and long exposure images
(a) Atmospheric profiling at the 1 m Jacobus Kapteyn Telescope (JKT) on La
Palma. The profile plots atmospheric turbulence against altitude and shows
the ground layer and two independent layers around 4 km in height.
(b) The optical turbulence profile at the JKT, May 2013. The plots show how the turbulence
profile varies with time. The turbulence intensity is represented by the colour bar with the
lower figure also showing the wind vectors at the time of the measurements.
Figure 2.4: The atmospheric turbulence profile on La Palma (Osborn et al., 2013).
10
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images on ground based telescopes of seconds or longer in exposure time. These ‘long’ exposures
are simply the collection of short exposures time averaged together. The averaging effect leads to
a highly blurred and extended PSF compared to both the short and diffraction limited exposures.
The resolution is typically at least an order of magnitude worse than the diffraction limit of the
telescope with even outstanding observing sites only obtaining resolution of 0.5 arcsec at best. The
trade-off in resolution however is to obtain high signal-to-noise data due to the limitation in current
imaging technology and faintness of many science sources.
2.5 Characterising turbulence
The effect of the atmosphere on wavefronts is to induce a phase error, typically of the order of a
few wavelengths due to the varying refractive index. To characterise the effect of these distortions,
several parameters are used.
2.5.1 The Fried parameter r0
The Fried parameter, or Frieds coherence length, is a single parameter which describes the spatial
extent of a turbulent cell over an aperture. First defined by Fried (1966), the parameter gives a
value for the length over which the RMS wavefront phase difference is less than 1 radian, the value
beyond which seeing-effects begin to limit resolution. The parameter is defined as
r0 =
[
0.423k2secβ
∫
Path
Cn
2(z)dz
]
(2.5)
where k is the wavenumber, β is the zenith angle and Cn2 is the atmospheric structure constant
along the propagation path dz. The value of r0 is usually given in centimetres and can be thought of
as the largest diameter of telescope which is limited by diffraction effects, rather than atmospheric
turbulence.
2.5.2 Seeing
Seeing is the atmospherically limited angular resolution of a telescope system, given by the ratio of
the optical wavelength λ and r0:
 = 0.98
λ
r0
. (2.6)
11
2.5 Characterising turbulence
Figure 2.5: The simulated effect of atmospheric turbulence on images with telescopes of differing
diameter as discussed in Section 2.3. The left hand column shows the output at an image plane with
no turbulence effects. The central column shows an image taken on a timescale less than that of the
coherence time with turbulent effects. The right hand column shows a long exposure image in the
same regime. Simulations performed with Kolmogorov turbulence profile at 650nm.
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 (given in radians) is the turbulence-limited resolution of a long exposure image for a telescope
with diameter much greater than r0 (Dierickx, 1992). Typically, the seeing is measured using the
full width at half maximum (FWHM) of the long-exposure PSF.
2.5.3 Strehl ratio
When determining the amount of distortion in an image, a comparison is typically made to the
diffraction limited equivalent. If this is done with a point source, the diffraction limited image
would produce an Airy disc. By comparing the power in the central peak of the Airy disc against
the maximum intensity in the measured PSF, the Strehl ratio R, can be measured. The values of R
range from 0 (no central maxima) to 1 (a perfect system with no turbulence). As such, when trying
to correct for the effects of turbulence, the higher the Strehl Ratio, the better the correction (Roddier,
1999).
2.5.4 Isoplanatic patch
As the light coming into the telescope is distorted randomly across the telescope aperture, the
distortion measured in one location will only be valid a finite distance away from the location
where it was measured. This region in which the measurement is valid, i.e. where the atmospheric
turbulence is unchanged, is called the isoplanatic patch and is usually quoted as an angle on the
sky - the isoplanatic angle. Typically, a reference star is being used to measure the distortions and
as such, the isoplanatic angle limits the distance you can observe from that object. This is often of
the order 4-20 arcsec (Law, 2006) while more recent work by (Mackay, 2013) has shown this can be
extended up to 1 arcmin in radius. If there are few reference objects, this can significantly limit the
sky coverage over which atmospheric distortions can be measured.
2.5.5 Zernike polynomials
As the entrance pupil of telescopes is typically circular (although with the next generation of
extremely large telescopes, this may not be entirely true), it can be useful to consider an
appropriate representation of amplitude and phase at the telescope aperture based upon a circular
co-ordinate system.
The phase of an electric field can be represented as a three-dimensional surface, the height of which
represents the advance or retardation of the phase. Much like Fourier series are used to describe
a function in one-dimension through its component parts, this phase surface can be described in
terms of Zernike Polynomials which perform a similar role.
13
2.5 Characterising turbulence
Figure 2.6: Visual representation of the first 28 Zernike modes (Shaw-McMinn, 2006).
Zernike Polynomials, are a basis set of functions which allow the representation of complex
wavefronts to be described. They are defined on a unit circle using polar coordinates (r,θ) with a
radial degree, n, and azimuthal frequency m by
Zmn (r, θ) =
√
n+ 1Rmn

√
2 cosmθ for n = even, m 6= 0√
2 sinmθ for n = odd, m 6= 0
1 (m = 0)
(2.7)
where
Rmn =
n−m
2∑
s=0
(−1)s(n− s)!)
s!
[
n+m
2 − s
]
!
[
n−m
2 − s
]
!
rn−2s (2.8)
and m ≤ n and n−m is even.
The lower order Zernike Polynomials (this is slightly subjective depending which expert you speak
to or book you read, but typically is a value n ≤ 3) relate to controllable wavefront distortions such
as tip, tilt, defocus and astigmatism. Higher order terms have more radial complexity and the first
28 terms are shown in Figure 2.6.
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Zernike Polynomial Removal Residual Turbulence Remaining
1 1.0299
2 0.582
3 0.134
4 0.111
5 0.0880
6 0.0648
7 0.0587
8 0.0525
9 0.0463
10 0.0401
11 0.0377
12 0.0352
13 0.0328
14 0.0304
15 0.0279
Table 2.1: Fractional residual turbulence remaining after removal of Zernike polynomials. Fractions
are relative to the incidence turbulence (Noll, 1976).
Zernike polynomials and Kolmogorov turbulence
In Section 2.3, I discussed the process by which energy transfer through the atmosphere from the
largest distortions through to smaller and smaller scales. As shown in Figure 2.3, the strongest
power is located in the largest scales of the atmospheric turbulence and from this, it is no surprise
that the strongest atmospheric distortions are on the largest scales i.e. in the lowest-order Zernike
Polynomial modes. Work undertaken by (Noll, 1976) determined the residual turbulence
remaining after the removal of each order of Zernike Polynomials (as shown in Table 2.1). By
removing up to the second order, 40% of atmospheric effects could be removed with higher orders
continuing to remove the distortion.
2.6 Correcting for atmospheric turbulence
Several methods are available today to correct for the effects of atmospheric turbulence including
adaptive optics, lucky imaging, tip/tilt correction systems and interferometry (Law, 2006). Only
two are covered in this thesis due to their relevance to this work: adaptive optics and lucky
imaging.
15
2.6 Correcting for atmospheric turbulence
Figure 2.7: A typical adaptive optics system. Distorted light enters the telescope after propagating
through the atmosphere and is corrected by a deformable mirror to provide high resolution imaging
at a science instrument.
2.6.1 Adaptive optics
Adaptive optics (AO) systems are designed to apply counter distortions to offset the effects of
atmospheric turbulence on wavefronts. The technique was proposed independently by Babcock
(1953) and Linnik (1957), however it wasn’t until the 1970s where suitable technology became
available to implement this on telescopes, originally being used for correcting laser transmission
and imaging satellites in orbit. Since then, the systems have rapidly developed to those having
over 1000 degrees of freedom in their corrections (Roddier, 1999). This section briefly introduces
the technique however there are many sources in the literature which provide further discussion
and information (Tyson, 1991; Beckers, 1993; Hardy, 1998; Tyson, 2000; Davies & Kasper, 2012).
The technique
Adaptive optics systems rapidly counteract the effects of turbulence by measuring the phase
distortions on the incoming wavefront and applying inverse phase shifts to the wave. This
effectively ‘hammers out’ the distortions, correcting the distorted light reaching the science
detector and increasing the resolution of the obtained image.
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As shown in Figure 2.7, AO systems comprise three principle components; the wavefront sensor
(WFS), real time control system (RTCS) and deformable mirror (DM). Distorted light with an
uncorrected wavefront enters the AO system from the telescope and is reflected off a deformable
mirror. After this, a reference object is selected for which the incoming undistorted image is
known (e.g. a star which should appear as an Airy disc) by either using a pick off mirror or beam
splitter. This light passes to a wavefront sensor which images the wavefront allowing the real time
control system to calculate the phase distortions. The control system then applies the inverse
phase corrections to the wave by driving the deformable mirror surface to the appropriate shape.
As AO systems typically determine the phase distortions on incoming wavefronts, apply a
correction and then observe the consequence of that correction, they are termed ‘closed loop’. This
is in contrast to a system where the distortion would be measured and blindly applied without
any feedback, termed an ‘open loop’ system.
To apply corrections at the appropriate speed, the rate at which the wavefront distortions change in
front of the telescope i.e. the coherence time, τ0 needs to be considered. In Section 2.3, the different
scales of atmospheric turbulence were discussed and when dealing with the shortest timescales on
which changes occur, the smallest scales of turbulent cells are most important.
If small turbulent cells are assumed to be ∼10 cm across and pass over an 8 m telescope with a
wind speed of 5 m s−1 , there are a total of 80 cells across the telescope diameter. The time taken for
each cell to move 10 cm across the telescope (so that there is a noticeable change in the observed
image) is around 20 ms. As such, this simple estimate suggests a control system needs to run at a
minimum of 50 Hz to be able to maintain an accurate correction and this rate should preferably be
at least a factor of two higher. This is consistent with the measured values of τ0 which range from
a few milliseconds up to tens of milliseconds (Roddier et al., 1990; Buscher, 1994).
Limitations of adaptive optics
Although successful at near- and mid-IR wavelengths on 8-10 m telescopes, AO systems are not yet
capable of the 100 nm RMS residual wavefront errors required for high quality diffraction limited
images at visible wavelengths (Guyon, 2010). This limits the resolution of any telescope by at least a
factor of two beyond what is theoretically possible with the instrument optical quality. In addition,
as corrections have to be applied on the order of milliseconds, this severely limits the number of
photons received by the wavefront sensor limiting sky-coverage with the technique. This issue is
discussed further in Section 3.3.
17
2.6 Correcting for atmospheric turbulence
2.6.2 Lucky imaging
The technique of lucky imaging is based upon the fact that although turbulent, the atmosphere
appears still when observed on millisecond timescales. The technique was first proposed by Fried
(1978) (although there was brief work published by Hufnagel (1966)) who undertook a quantitative
analysis of the probability of obtaining a diffraction limited image on a telescope with diameter D,
through an atmosphere characterised by r0. By using Monte Carlo techniques, the probability of
obtaining a diffraction limited image was found to be
Probability ≈ 5.6× exp
[
−0.1557 (D/r0)2
]
(2.9)
for D/r0 ≥ 3.5. This relation was was verified experimentally by Bensimon et al. (1981).
The probabilistic nature of the work by Fried assumed ‘instantaneous’ imaging through the
atmosphere. While this is impossible to implement practically, by imaging at high frame rates
(∼30 Hz) and taking short exposures, some of the recorded frames will be less affected by
turbulence than others as expected. By evaluating the quality of each of these recorded images
and ranking them in terms of image quality, a percentage of the least affected frames can be
combined in post processing (aligning images prior to co-adding to remove low-order tip-tilt
distortions) to produce milli-arcsecond resolution images. While this principle of imaging is
relatively simple, the technology required to image at these high frame rates with good signal to
noise (i.e. with short exposures comes a reduction in the number of recorded photons per image)
has not been easily accessible until recent years.
High speed imaging: Electron multiplying CCDs
Traditional CCDs have read out speeds (pixel rates) of around 30-500 kHz which minimises read
out noise caused by the amplifier on the CCD output. If frames are read out at speeds required for
lucky imaging, a pixel rate of 5-35 MHz is required, leading to a significant increase in the noise
floor of the image (Mackay et al., 2003).
In the last decade, the development of Electron multiplying CCDs (EMCCDs or Low Light Level
CCDs, L3CCDs, as they are sometimes known) has provided a method offering fast readout
speeds with sub-electron read out noise (Mackay et al., 2001). This low noise read out is achieved
by adding an additional section on the output register of the CCD which is held at high voltage.
Before electrons reach the output amplifier, they pass through this section causing an avalanche
multiplication effect. This effectively provides noiseless gain allowing high signal to noise with
individual photons being able to be detected.
The advances in this technology have allowed lucky imaging methods to be used at several
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Figure 2.8: A comparison of images taken of the same field of the globular cluster M13 with a field
of view of 2.0×1.5 arcsec. From left to right: ACS on board the Hubble Space Telescope, conventional
lucky imaging with 10% selection, high efficiency lucky imaging at 20% selection and 50% selection.
The lucky imaging data was taken with the 5.1 m Hale Telescope and its adaptive optics system
(Mackay, 2013).
research facilities around the world. Today, this technique has produced the highest resolution
optical images ever taken in astronomy, bettering even those of the Hubble Space Telescope as
shown in Figure 2.8.
Lucky imaging data processing
Lucky imaging has a key advantage over other correction techniques as it allows data to be
processed after collection rather than requiring real-time analysis. This allows the data to be
re-analysed on multiple occasions giving the possibility of identifying new and improved
techniques to maximise the usability of the data without needing additional telescope time.
Conventional processing Conventional lucky imaging requires each recorded frame to be ranked
in terms of quality. The simplest way to achieve this ranking is through a comparison of the same
reference object in each frame. By measuring the FWHM of this reference object, the recorded
images can then be ranked in order from sharpest (i.e. with the smallest FWHM value) to poorest.
Depending upon the sensitivity of observations required for the scientific goal, a fraction of the total
images, starting with the sharpest, can be combined together to produce the final image. Before
being combined, each frame must undergo standard processing techniques (debiasing, flat fielding
etc.) and then be co-aligned by comparing positions of objects in the field. This alignment process
removes the tip-tilt effects caused by both the atmosphere and telescope tracking limitations.
The fraction of images chosen depends upon the object being observed and the goal of the
observation. For systems where resolution is key, for example the centre of globular clusters
19
2.6 Correcting for atmospheric turbulence
where determining stellar dynamics is important, a smaller fraction of images will likely be used
as the objects being observed are bright and will provide sufficient signal-to-noise. For fainter,
more diffuse observations e.g. nebulae, a higher fraction of images needs to be used to provide a
useful output image however this is at the cost of decreasing the resolution of the image.
High efficiency lucky imaging For many years, one of the limitations of lucky imaging has been
the effective ‘discarding’ of images which are not used in the combining process. This process,
which provides high resolution, is at the cost of sensitivity and leads to longer observation times
being required to reach the same limiting magnitude.
By studying the lower quality images, it is clear that although overall they do not have good image
quality, typically the degradation is only in one direction which is unsurprising as the atmospheric
effects are typically caused by larger scale wind motion. With this knowledge, the question then is
‘how to recover usable information from this degraded image’?
The solution to the problem comes in the form of the Fourier domain as suggested by Garrel et al.
(2012). By considering the two dimensional Fourier transform of each image, the spatial
components in each direction can be identified. By co-aligning images before Fourier
transforming, a selection can be made in Fourier space to produce a final image when the best
frames are combined together. The key difference in Fourier space however is that the selection is
done on a pixel-by-pixel basis rather than assessing the quality of the image as a whole.
When Fourier transforming images obtained with the lucky imaging technique, a peak appears at
the four corners. It is simpler to understand and interpret this if these are moved so that the zero
frequency component is located at the centre of the Fourier plane. The characteristics of the peak
generated in this process is, not surprisingly, closely linked to the sharpness of the original image.
For a sharp image, this peak will be wider and circular while for a poorer quality image, the peak
will be sharper. The shape of the peak in the lower image quality situation depends however on
the atmospheric effects at the time; if they were relatively equal in each direction the peak will
appear to be circular however, as is often the case, if there are stronger effects in one direction,
the peak will be narrower in that direction. By ranking the same Fourier element in each image, a
fractional selection can then be done on that element, much in the same way the ranking process is
undertaken with the conventional technique. By combining all of these elements into a final Fourier
array, this can then be inversely transformed back to the image plane to produce a final scientific
image.
This Fourier transform method has only become possible in the last few years with increased
computing power, particularly memory and the development of graphics processing unit (GPU)
hardware. GPUs are well suited to this kind of Fourier transform work allowing a significant
reduction in the time taken for this selection process when compared to undertaking it on a
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conventional processor. Full details of this Fourier lucky imaging process and the caveats with it
can be found in Mackay (2013). It was demonstrated that a significant increase in selection fraction
can be achieved without degrading image quality and that the scientific integrity of the data e.g.
photometry is maintained.
Limitations of lucky imaging
The primary challenge with lucky imaging comes from its intrinsic basis upon probability. The
more atmospheric turbulence affecting the incoming wavefront, the smaller the probability that a
sharp image will be obtained. This limitation is in constant conflict with scientific imaging which
pushes for higher resolution and sensitivity i.e. larger telescope apertures.
Due to the exponential term in Equation 2.9, there is a severe limitation on the size of telescope
on which lucky imaging is effective. Fried placed a limit on the diameter of a telescope where
lucky imaging would be effective as a technique to 7 − 8r0 as at larger diameters the likelihood of
obtaining a usable image rapidly decreases. The effect of this is shown in Figure 2.9.
While the probability of lucky imaging may seem prohibitively small, the work done by Fried
assumed that the value of r0 would remain constant (and has been assumed in Figure 2.9) while
undertaking observations. As any observational astronomer will tell you, the seeing over a night of
observations is very rarely constant and as such, there are times when r0 will be significantly larger
than an average value. It is this variability which allows lucky imaging to work even in ‘average’
seeing conditions although there is still a limit on telescope diameter of approximately 2.5 metres
where is becomes ineffective.
2.7 Summary
The effects of atmospheric turbulence significantly limit the resolution of ground-based telescopes
to well below their theoretical diffraction limit. The constantly changing nature of the atmosphere
with its varying refractive index, causes incoming wavefronts of light from astronomical sources to
be distorted as they pass through the atmosphere. For several decades, astronomers have proposed
techniques to counter this effect and two, adaptive optics and lucky imaging, are now routinely
used on telescopes around the world.
Adaptive optics uses real-time correction to measure and counter the effects of the atmosphere.
While used successfully at infrared wavelengths, it is challenging to provide correction at optical
wavelengths and current wavefront sensors require bright reference objects. Lucky imaging on the
other hand works well in both the optical and with fainter sources however it becomes ineffective
on telescopes larger than around 2.5 m. To overcome the limitations of these techniques, the two
21
2.7 Summary
1 1.5 2 2.5 3 3.5 4
100
105
1010
1015
Telescope Diameter (m)
N
um
be
r o
f f
ra
m
es
 re
qu
ire
d 
to
 o
bt
ai
n 
a 
di
ffr
ac
tio
n 
lim
ite
d 
im
ag
e
 
 
r0 = 0.10
r0 = 0.15
r0 = 0.20
r0 = 0.25
r0 = 0.30
(a) The probability of obtaining a diffraction limited image at different values of r0.
1 1.5 2 2.5 3 3.5 4
10−2
100
102
104
106
108
Telescope Diameter (m)
M
in
ut
es
 o
f o
bs
er
vin
g 
tim
e 
to
 o
bt
ai
n 
a 
di
ffr
ac
tio
n 
lim
ite
d 
fra
m
e
 
 
r0 = 0.10
r0 = 0.15
r0 = 0.20
r0 = 0.25
r0 = 0.30
(b) The time taken to obtain a diffraction limited image with a frame rate of 25 Hz.
Figure 2.9: Probabilities of lucky imaging at different values of r0 ( m). The upper figure shows the
number of frames required to obtain a ‘lucky’ exposure while the lower figure shows the estimated
observing period assuming a frame rate of 25 Hz. The lucky imaging technique becomes challenging
on telescopes larger than ∼2.5 m in diameter as the required observing time rapidly increases even for
large values of r0.
22
Background
can be combined together to provide diffraction limited imaging of astronomical objects at optical
wavelengths.
23
2.7 Summary
24
“Science is always wrong. It never
solves a problem without creating ten
more.”
George Bernard Shaw
3
The Adaptive Optics Lucky Imager
The Adaptive Optics Lucky Imager (AOLI) instrument combines the techniques of adaptive optics
and lucky imaging in a dedicated single instrument for the first time. The instrument is designed
initially for use on the 4.2 m William Herschel Telescope (WHT) on the Canary Island of La Palma.
AOLI uses a novel type of wavefront sensor, the non-linear curvature wavefront sensor, as part of
its adaptive optics system to offer improved sensitivity over existing wavefront sensing methods.
In this chapter I present an introduction to the AOLI project and its science case as well as a
discussion about the choice of wavefront sensor for use within the instrument.
3.1 Combining adaptive optics and lucky imaging
As previously discussed in Sections 2.6.1 and 2.6.2, current methods for correcting atmospheric
distortions have limitations reducing their effectiveness when used alone. The particular challenge
with lucky imaging is that with increasing telescope diameter comes an increase in the number of
turbulence cells across the telescope aperture. However, if the effective number of turbulent cells
across the telescope aperture can be reduced, this once again increases the chance of obtaining a
sharp image. By using an adaptive optics system prior to a lucky imaging detector, this can be
25
3.2 An introduction to AOLI
Figure 3.1: The globular cluster M13 as imaged on the 5 metre Hale Telescope at Mount Palomar,
California. The image on the left shows the cluster when imaged using conventional techniques with
no correction and the right shows the cluster when imaged using combined adaptive optics and lucky
imaging (Law et al., 2008).
achieved to provide diffraction limited imaging in the visible on ground-based telescopes.
The combination of adaptive optics and lucky imaging has been previously demonstrated on the
200 inch Hale Telescope at Mount Palomar, California as shown in Figures 3.1 and 3.2. The images
obtained during this observing run are the highest resolution images ever taken at visible
wavelengths in astronomy with a resolution of 35 milli-arcsec.
3.2 An introduction to AOLI
The construction and development of AOLI is being undertaken as a collaboration between
several research institutions across Europe. These institutions have previous experience in
high-resolution imaging techniques, particularly lucky imaging, and the aim of the collaboration
is to expand the capabilities of this technique to provide diffraction limited imaging on large
ground-based telescopes (Oscoz et al., 2008; Law et al., 2008, 2009; Femenı´a et al., 2011). The
collaboration comprises the following institutions:
• Institute of Astronomy (IoA), University of Cambridge, UK
• Instituto de Astrofı´sica de Canarias (IAC), Tenerife, Spain
• Universita¨t zu Ko¨ln, Germany
• Universidad Polite´cnica de Cartagena (UPCT), Murcia, Spain
26
The Adaptive Optics Lucky Imager
Figure 3.2: The Cat’s Eye Nebula (NGC7543) - the left image shows the nebula with no image correction
and the right shows the improved image quality when adaptive optics and lucky imaging are used.
Oxygen emission is shown in green, hydrogen in red and blue is near-infrared.
• Isaac Newton Group of Telescopes (ING), La Palma, Spain
Work to date on AOLI has focused on the development of the instrument for use on the 4.2 m
William Herschel Telescope. The instrument use on the WHT is the first phase of development
with subsequent plans for modifications to facilitate use on the 10.4 m Gran Telescopio Canarias
(GTC). The primary purpose of the instrument however is to provide diffraction limited imaging
on both of these telescopes by combining adaptive optics and lucky imaging together into a single
instrument.
3.2.1 The science case for AOLI
With AOLI having the potential to significantly increase the resolution of ground-based telescopes,
there are several science cases and areas of research which can be observed by the instrument. The
following cases are initial research areas to be investigated and are principally led by researchers at
Cambridge. Additional research interests are being pursued by other members of the collaboration
at the Instituto de Astrofı´sica de Canarias and Universita¨t zu Ko¨ln.
Starforming regions at high redshift Current observations and theoretical models show the
importance of cold gas and its accumulation in the formation of distant galaxies. This process
results in unstable disks of gas, heavily characterised by massive clumps which play a pivotal role
in the evolution of the galaxy. AOLI will resolve UV emission from these galaxies (red-shifted to
visible wavelengths by the expansion of the Universe) on scales of 25 milli-arcsec, far exceeding
27
3.2 An introduction to AOLI
that possible with the HST. This will provide a key insight into the evolution of the clumps and
their effect on the galaxies and star formation in the early Universe.
Gravitational lens studies In recent decades, astronomers have used the magnifying effects of
gravitational lenses to probe distant objects within the Universe. In the night sky, objects are
continually moving and over time, nearby objects appear to pass infront of more distant objects. If
both these objects are galaxies, a significant magnification of the distant galaxy occurs due to light
being bent around the gravitational field of the foreground galaxy. This field is created by both the
matter and dark matter of the galaxy.
Often multiple images can be seen of the distant galaxy when magnification occurs e.g. the
Einstein Cross, however through computer modelling, a single image of the distant galaxy can be
reconstructed, allowing probes of their structure, star formation and evolution. In addition,
information about the nearby galaxy can be extracted including a probe of its dark matter
structure and any smaller galaxies bound to it.
Binary fraction in globular clusters The energy stored within binary star systems significantly
affects the dynamics and evolution of globular clusters, in particular the process of core collapse.
With these strong effects, having high resolution images of globular clusters will make it possible
to further probe the evolution of these systems.
By imaging the nearest globular clusters (at 2.2-6 kpc), AOLI can directly image binaries with a
resolution between 30-120 AU in V-band and 45-150 AU in I-band. This will allow the investigation
of the nearest neighbour separation distribution allowing the calculation of binary statistics within
a significant proportion of the cluster. In addition, with the high resolution technique, it will be
possible to observe binaries with components of unequal brightness which are often missed with
current photometric and spectroscopic surveys.
Supernova studies in Local Group galaxies A supernova is the final stage in the evolution of the
largest types of star. Due to runaway nuclear fusion, these stars explode at the end of their life,
releasing huge amounts of energy and creating some of the brightest visible sources in the sky. The
explosion leaves a remnant which provides information about the star’s life and physical processes
at work while the shockwave produced in the process propagates through space, providing a probe
into the material within in the interstellar medium of galaxies.
Recent surveys have identified relatively large numbers of supernovae in nearby galaxies such
as M31 and M33. While there are also supernovae within our own spiral galaxy, the Milky Way,
very few of these are directly observable due to obscuration by dust as they lie within the disk of
the galaxy. Present imaging techniques do not have the resolution to provide detailed observations
28
The Adaptive Optics Lucky Imager
about the supernovae we can see in M31 and M33. AOLI will provide the high resolutions required
to probe these targets and their supernova remnants.
Blackhole to bulge ratios in quasar host galaxies The high resolution visible/near infrared
capabilities of AOLI will provide the tools to probe the relationship between luminous quasars
and their massive host galaxies, thereby measuring their properties. At a redshift z∼1, quasar host
galaxies are only a few arcseconds in diameter and any images of them are dominated by the light
from the central quasar. By using AO-corrected lucky imaging on the WHT and GTC, AOLI will
provide near-diffraction-limited imaging enabling the separation of light from the quasar from
that of the underlying host galaxy. This will facilitate the investigation of the full range of host
galaxy colours, radio loud and radio quiet quasar classifications and other key physical
parameters.
3.3 An introduction to wavefront sensing
To meet the requirement of diffraction limited imaging on large ground-based telescopes, AOLI
employs a novel type of wavefront sensor as part of its adaptive optics system. In this section,
I provide a more in-depth discussion of wavefront sensing techniques in adaptive optics before
describing the system used in AOLI.
As described in Section 2.4, short exposure images taken on timescales less than the atmospheric
coherence time retain information about PSF and atmospheric distortions which created them. If
attempting to extract information about the distortions imparted by the atmosphere on incoming
wavefronts, it is important that any sensing method works both on these timescales and provides a
high signal-to-noise ratio in this regime. This imposes the requirement that for effective wavefront
sensing either a bright reference object or an efficient detector (or preferably both) be employed to
minimise uncertainty in any wavefront recovery.
There are many existing types of wavefront sensor in use on telescopes today which are able to
recover wavefront information. Many of the first techniques were originally developed for
observing military surveillance satellites from the ground.
3.3.1 Wavefront sensing basics
When attempting to measure wavefront distortions imparted by a particular system, it is vital to
have prior information regarding the wavefront which was incident on the system. This wavefront
is typically emitted from a ‘reference object’ and can be spherical or planar depending upon the
geometries involved. In astronomy, we conveniently have reference objects located at an ‘infinite’
29
3.4 Wavefront sensing techniques
distance away (at least optically) which, before entering the atmosphere, provide a plane incident
wavefront which can be considered to be our ‘control’ position. As the wavefront passes through
the atmosphere, it is imparted with phase distortions and by measuring the wavefront at ground
level, it is possible to calculate the effects of the atmosphere relative to the incident plane wave, the
effects of which can be calculated either by simulation or illumination from a laboratory source.
As discussed in Section, 2.2, it is only possible to record intensity measurements of any light wave.
When undertaking wavefront sensing, we wish to recover the phase and as such, reconstruction
techniques to obtain the phase from these intensity measurements must be employed.
3.4 Wavefront sensing techniques
There are several possible techniques to recover phase from intensity measurements. Historically,
these techniques have used linear reconstruction processes to maintain simplicity and minimise
the requirements for real-time computing. The common types of wavefront sensor in use today,
the Shack-Hartmann, curvature and pyramid wavefront sensors are discussed in this section.
3.4.1 The Shack-Hartmann wavefront sensor
A Shack-Hartmann wavefront sensor (SHWFS) is based upon the Hartmann screen test often used
in testing optical aberrations within a telescope system. A narrow beam of light from a small part
of a telescope aperture (typically created by using a small screen with holes) propagates through
the system. This is done by placing a mask over the telescope aperture, allowing rays to be traced
through the system traditionally using photographic plates, or more commonly nowadays a CCD
detector, at pre- and post-telescope focal plane locations.
On large telescopes, to maximise the amount of light incident on the detector, instead of using a
mask with small holes to create the beams to trace through the system, an array of lenses (i.e. a
‘lenslet array’) is used at the pupil plane. Each lenslet within the array, which can be considered
as a subaperture, produces an image of the reference object which is recorded on a CCD detector.
The location of the centroid of each image is then compared to a reference position i.e. the location
when an undistorted (either plane or spherical) wavefront is used to illuminate the sensor. This
provides the ‘slope’ of the wavefront at the location which the lenslet maps to on the telescope
aperture and by combining the slope from each lenslet, the wavefront from across the full aperture
can be recovered (Bely, 2003). This is shown in Figure 3.3 where an incoming wavefront is imaged
onto a CCD through a lenslet array.
The accuracy of any wavefront measurement using a SHWFS is governed by the number of
elements within the lenslet array used. For a low-order measurement, a small number of elements
30
The Adaptive Optics Lucky Imager
Figure 3.3: The principle of the Shack-Hartmann wavefront sensor. A distorted wavefront enters the
sensor and passes through a lenslet array located at a pupil plane. The centroid position from each
lenslet is recorded and measured relative to the positions recorded for an incoming plane wavefront.
By comparing the offset, the slope of the wavefront at this position can be calculated and then
combined with the other values to determine the incoming wavefront distortion (Murphy, 1992).
will be sufficient i.e. if you simply wanted to sample the wavefront in each quadrant of the
telescope aperture, a 2×2 array would be sufficient. For higher-order measurements, significantly
more elements will be required with systems now running on sky with 30×30 elements. For each
subaperture within the lenslet array, at least four pixels are required on the imaging detector to
allow to image position to be measured. This reduces the sensitivity of the overall detector as
often the beam will be spread across more than one pixel decreasing the signal-to-noise level.
As the incoming light from the reference object is used to create multiple images using the lenslet
array, Shack-Hartmann wavefront sensors require bright reference objects to provide high
signal-to-noise measurements. If using natural guide stars (NGS) i.e. bright stars in the field of
view of the telescope, this severely limits the sky-coverage of any instrument using this type of
wavefront sensor for any level of higher-order measurement. Because of this limitation, in the
1980s, the technique of laser guide stars was developed to allow bright reference ‘stars’ to be
artificially created in the Earth’s atmosphere.
Laser guide stars
There are two principal methods of creating artificial guide stars; Rayleigh scattering and sodium
layer excitation. The Rayleigh scattering technique focuses a laser beam to a point around an
31
3.4 Wavefront sensing techniques
altitude of 10-20 km in the atmosphere allowing back scattered photons to be observed while the
sodium layer method generates a reference object at approximately 90 km in altitude. Both
techniques are actively used in adaptive optics instruments today with a general preference
towards the use of the sodium laser guide star method due to its increased altitude.
Sodium laser guide stars are created by exciting the 2.104 eV fluorescence lines of sodium atoms in
the atmosphere (known as the sodium D lines). Created by meteors hitting the Earth’s atmosphere,
this 5-10 km thick layer containing sodium is located at an altitude of approximately 90 km above
the ground. When atoms in the layer are excited, they emit photons at a wavelength of 589.2 nm
which can be used as a reference object for wavefront sensing. By employing this technique, the
limitations of sky-coverage when using NGSs alone can be overcome.
To excite sufficient atoms to generate a bright enough reference object, high power pulsed lasers
are used with powers of tens of watts. This is a particular challenge technologically and it is only
in recent years that the technology has really come into its own to allow correction in the infrared
across the entire sky (Vidal et al., 2013).
Challenges using LGSs
Although very successful, the use of laser guide stars to provide significant sky coverage with
SHWFSs imposes limitations upon the accuracy of wavefront measurements and any correction
attempted. Due to path differences, the wavefront aberrations experienced by light from the LGS
differ from those experienced by the light reaching the telescope from the science target. This focal
anisoplanatism or ‘cone effect’ is due to the guide stars being formed at a finite distance from the
telescope meaning that the light propagation from the artificial source to telescope aperture passes
through a cone with a base size of the telescope diameter (van Dam et al., 2006). This contrasts
with light propagating from stars and science targets at effectively an infinite optical distance from
the telescope which propagates through a cylinder of the atmosphere. As such, the measured
distortions from the laser guide star differ slightly from the phase distortions experienced by the
science target wavefronts which in turn limits any potential correction to the science image.
An additional issue which arises when using LGS is that the laser beam emitted by the telescope
propagates up through the atmosphere and back to the telescope after re-emission along the same
optical path. This propagation effect means any wavefront sensing using a LGS is insensitive to
tip-tilt measurements (see Section 2.5.5) as any turbulent cell in the optical path will add this effect
and as the beam propagates upwards and have it removed as the beam propagated downwards
as shown in Figure 3.4. For this reason, a natural guide star must still be used to determine this
measurement although as this is a low-order distortion, a small lenslet array can be employed and
allows the use of a much fainter reference object for this measurement (Bely, 2003).
32
The Adaptive Optics Lucky Imager
Figure 3.4: The diagram above shows the lack of tip-tilt measurement sensitivity when using laser
guide stars. Any turbulent cell (or air wedge) is traversed both upwards and downwards leading to
any optical effects being cancelled out overall (Bely, 2003).
To date, these two challenges have limited the ability of AO with Shack-Hartmann wavefront
sensors to only providing effective corrections at infrared wavelengths. In the last few years
however, the use of multiple laser guide star systems (i.e. multi-conjugate adaptive optics) has
begun to come to fruition allowing the possibility to reduce the focal anisoplanatism effects. The
complexity and costs of these systems however mean they are limited to only the largest
telescopes e.g. the Gemini Multi-Conjugate Adaptive Optics System (GeMs) at the Gemini South
Telescope, which delivers diffraction limited image quality at near-infrared wavelengths (Neichel
et al., 2013).
3.4.2 The conventional curvature wavefront sensor
Although less common than Shack-Hartmann wavefront sensors, curvature sensors have been
shown to be ten times more sensitive (i.e. require a reference object 2.5 magnitudes fainter) than
their more common counterparts. In addition, they have been shown to be much more sensitive
when used for low order correction (Racine, 2006).
The principle
The curvature wavefront sensor (CWFS) was first proposed by Roddier (1988). The illumination of
a defocused reference object is measured at image planes on either side of the focal plane. Intensity
variations observed can be mapped to infer distortions on the incident wavefront as shown in
Figure 3.5. As any optical wave propagates at 90 degrees to its wavefront, if a small amount of
additional curvature is added to a selected region on the wavefront, this causes the wave in that
33
3.4 Wavefront sensing techniques
Figure 3.5: The principle of curvature wavefront sensing. Bright regions imaged at the intrafocal plane
are caused by additional curvature on the incoming wavefront bringing this region of the wavefront
to focus prior to the focal plane. After this location, the beam will diverge leading to a darker region
at the extrafocal plane (Bely, 2003).
region to converge as it propagates. This leads to a bright spot appearing before the focal plane
and once the wave has passed through this point, it diverges. This leads to a darker region in
an extrafocal plane. By subtracting the extrafocal and intrafocal images, it is possible to obtain
information about the phase aberrations as the measured intensity reflects variations in the total
curvature of the wavefront. The overall wavefront can be reconstructed with appropriate boundary
conditions which can be provided by measuring the slope at the edge of the aperture (Roddier,
1999; Tyson, 2000; Bely, 2003).
For curvature measurements, it is not a requirement to image around the focal plane. Instead
images at different distances from the pupil plane can be used. If the pupil plane is considered
to be made up of several separate sections, the curvature in neighbouring parts will cause light to
converge or diverge. As shown in Figure 3.6, if we consider a wavefront made purely from low-
or high-order curvature, as the wavefront propagates, regions with higher and lower intensity (i.e.
brighter and darker) appear. With higher-order distortions, these regions develop closer to the
telescope and are smaller in size as the localised curvature is greater. For low-order distortions
however, these modes only develop at a greater distance from the telescope as the regions take
longer to converge.
A specific example of different scales of phase distortion leading to intensity variations comes if a
sinusoidal phase (or any other periodic structure) and uniform amplitude is used as the input at
the pupil plane. Due to the phase at the aperture, as this wavefront propagates, it generates specific
regions of high contrast amplitude effects alternating with low contrast regions. This effect is called
the Talbot Effect, shown in Figure 3.7 and describes where it is possible to observe the effects from a
34
The Adaptive Optics Lucky Imager
Figure 3.6: Convergence of phase distortions leading to the development of high and low intensity
regions at different distances from an aperture. For low-order distortions, regions are located far from
the aperture (left) while for higher-order distortions, they are found closer to the aperture (right).
propagated wave with periodic phase distortion (Goodman, 2005; Guyon et al., 2008).
While the idea of curvature sensing is relatively simple, i.e. taking images at different distances
around a focal or pupil plane, it has been used less frequently than Shack-Hartmann sensors even
though it offers several advantages over them. Instead of the four or more pixels required for each
lenslet in a SHWFS, only one pixel is needed per equivalent subaperture. Curvature sensors are also
particularly effective in a closed-loop setup. Despite this, curvature sensors in their traditional form
have been shown to have increased wavefront errors at low spatial frequencies when compared to
Shack-Hartmann wavefront sensors (Guyon, 2007; Guyon et al., 2008).
3.4.3 The pyramid wavefront sensor
The pyramid wavefront sensor was proposed by Ragazzoni (1996) as an alternative to the SHWFS.
It is undergoing continued development by several research groups for use in AO systems,
particularly for use in Extremely Large Telescopes.
The principal of the pyramid wavefront sensor is, in some respects, similar to that of the Shack-
Hartmann Sensor. The key difference however is that instead of the wavefront being split into sub-
apertures at the pupil, it is split into four planes at a focal plane as shown in Figure 3.8. The light
from the reference object is focused onto the peak of a refractive pyramid optic. The light which
passes through this optic, due to the differing incident angles, is spread into four independent
35
3.4 Wavefront sensing techniques
Figure 3.7: Figure from Guyon et al. (2008) showing the effect of a period phase oscillation within an
aperture on amplitude as the wave propagates. The bottom panel shows the phase variation for an
8 m telescope while the upper panel shows the change in amplitude with distance from the aperture.
36
The Adaptive Optics Lucky Imager
Figure 3.8: The optical layout of the pyramid wavefront sensor. Light is focused from the
aperture/pupil plane of the telescope onto the peak of a pyramid optic. This process produces four
seperate beams which, when collimated can be recorded on a detector to recover the wavefront phase
at the pupil (Tyson & Frazier, 2004).
beams which are then re-collimated onto a detector. By comparing the intensity of equivalent pixels
in each of the four beams, it is possible to recover the slope in both the vertical and horizontal
directions. This allows the wavefront slope to be recovered which in turn allows the phase at the
aperture to be reconstructed (Tyson & Frazier, 2004). In addition, by rapidly rotating the pyramid
optic, the linearity of the wavefront reconstruction and dynamic range can be improved although
this is at the cost of sensitivity (Guyon, 2005).
The key advantage of the pyramid wavefront sensor over the Shack-Hartmann is that no lenslet
array is used. As such, the smallest scales which the reconstruction process is sensitive to is the
pixels on the detector rather than the physical size of the elements within the lenslet array.
3.4.4 Evaluation of wavefront sensing techniques
With each of the different types of wavefront sensors discussed, there are successes and
limitations. Depending upon the type of system being developed, one may be more suited than
others and as such, it is important to understand their relative strengths. Guyon (2005) undertook
an evaluation of the standard wavefront sensors with a particular focus on adaptive optics, high
contrast imaging and maximising the sensitivity of the sensor. As previously discussed (see
Section 3.4.1), the sensitivity of a wavefront sensor is important to maintain a high signal-to-noise
37
3.5 Wavefront correction
when using faint reference objects which in turn, allows increased sky-coverage using natural
guide stars.
Simulations undertaken by Guyon (2005) provided several key results, particularly regarding
improving sensitivity and wavefront reconstruction. This included recommending that the
wavelength range for the wavefront sensor matches that being used for science observations. This
was typically not the case in many systems where wavelength splitting was used to isolate light of
the reference object. The key result from the paper however was that the Shack-Hartmann sensor,
although widely used, had particularly poor sensitivity relative to the theoretical maximum.
Conventional curvature wavefront sensors were shown to offer near this theoretical maximum
however this was only for one scale of distortion i.e. spatial frequency.
Further work by Guyon et al. (2008) provided a solution to this spatial frequency limitation; instead
of simply using the two imaging planes which would limit you to one spatial scale, a total of
four should be used. This allows distortions of many frequencies to be recovered and helps limit
insensitivities from periodic effects i.e. low contrast regions of the Talbot effect. This technique has
now been termed the non-linear curvature wavefront sensor which is fully discussed in Chapter 4.
3.5 Wavefront correction
The image and data output by wavefront sensors is passed through a processing system which
calculates the distortions, often in terms of Zernike modes. When attempting to improve image
quality, the correction for these modes must then be applied to the incoming wave using either a
birefringent electro-optical material or, more commonly, a mirror with a deformable surface
(Roddier, 1999).
Deformable mirrors have properties well suited to astronomical adaptive optics. Their rapid
response times, large wavelength independent panoptical path differences and high uniform
reflectivity mean they allow for fast, efficient corrections over a broad wavelength range. There
are three different types; segmented, continuous faceplate and edge actuated as shown in Figure
3.9. Segmented mirrors have individual segments with either a single or 3 or more actuators
attached. Each actuator is individually controlled, typically by applying a voltage to the element.
Continuous faceplate mirrors have either force (electromechanical or hydraulic) or more
commonly displacement (piezoelectric or magnetostrictive) actuators which deform the reflective
flexible surface. Edge actuated mirrors use a lever system to generate curvature across the mirror.
It is vital that any deformable mirror providing wavefront correction is able to do so at rates similar
to those of atmospheric turbulence changes and with an accuracy required to provide diffraction
limited imaging. This sets the requirement for deformable mirrors to work at speeds of greater
than 100 Hz with a control accuracy on nanometre scales. This means any hysteresis effects can
38
The Adaptive Optics Lucky Imager
(a) Segmented mirrors (top left) have actuators with independent mirror segments
while the continuous faceplate (top right) has a similar actuator layout but this is bonded
to a sheet making up the mirror surface. As there is no separation, this leads to inter-
actuator effects. An edge actuated mirror (bottom) uses horizontal actuators to distort
the overall shape of the mirror although this is less common today (Tyson, 2000).
(b) Four different types of deformable mirrors: a) Phase-plate with piezoelectric
actuators, b) bimorph mirror in which the shape is controlled by applying different
voltages over the top and bottom layers, c) membrane mirror with electrostatic control,
and d) segmented mirror with actuators on each segment (Andersen & Enmark, 2011).
Figure 3.9: Types of deformable mirror. The upper figure shows the basic deformable mirror types
with continuous and segmented phase sheets. The lower figure shows different types of actuators for
distorting the mirror surface.
39
3.5 Wavefront correction
seriously limit their effectiveness. In addition, the amplitude of each actuator motion (typically
called the stroke) must be sufficient to provide correction for the typical wavefront distortions.
Although the first deformable mirrors had actuator numbers in single figures, the devices available
today have easily over one thousand allowing higher order Zernike modes to be corrected. Mirrors
with high number of actuators are principally continuous faceplate in design and come in different
sizes and technologies.
On the largest scales are fully deformable secondary mirrors which can be up to several metres
in diameter while their surface is only a few millimetres thick, hence the name thin shell mirrors.
The European Extremely Large Telescope deformable mirror (rather than a secondary, this will
be located as the fourth mirror) is 2.4 m in diameter, has a faceplate 1.95 mm thick and has 5910
voice coil actuators with 4974 being attached to the optical surface (Vernet et al., 2012). This allows
adaptive optics correction to be provided to all telescope instruments if required.
When building new telescopes, or indeed upgrading existing ones, providing a deformable
secondary mirror within the telescope optics can be attractive as it allows correction to all
instruments on the telescope. If however there is a specific instrument which requires
high-resolution imaging, it can often be more cost effective and less technologically challenging to
use smaller form factor deformable mirrors. These come in two main technologies:
Micro-Electro-Mechanical (MEMS) deformable mirror or classical deformable mirrors with
individually controlled actuators based on piezoelectric, electrostatic or solenoid based elements.
MEMS deformable mirrors are one of the most ubiquitous type of deformable mirror in use today
although their use is still growing within the AO community. While often being limited in stroke,
they provide a very large number of actuators into a very small area by using electrostatic
actuators. Currently available models from manufacturers such as Boston Micromachines can
have up to 4092 actuators in a square region 25 mm across with minimal or no hysteresis effects
and a rapid response time of ∼50µ s . With these mirrors, the manufacturing process does allow
the option of having a segmented optical surface with a variety of mirror coatings available
(Boston Micromachines Corporation, 2014).
Classical deformable mirrors have previously had challenges due to the actuators technology
available for use with them. Piezo-electric actuators can have significant hysteresis effects limiting
their correction accuracy although these can be run at speeds within the kHz range. Bimorph
mirrors, where two layers of piezoelectric material are bonded together as shown in Figure 3.9(b),
can help minimise this effect although can only run at slower bandwidths. In recent years, a new
actuator technology based upon solenoids has been developed by manufacturer ALPAO. These
mirrors allow significantly larger stroke than possible with MEMS or other actuator technologies,
have minimal hysteresis (less than 3%) and have a bandwidth of several hundred Hz (ALPAO,
2014).
40
The Adaptive Optics Lucky Imager
When applying any wavefront correction, it is important to consider the location where a
deformable mirror should be located within an optical system. Typically this should be well
matched with the location that the wavefront sensor is recovering the phase measurement i.e. if
the wavefront sensor is recovering the phase at a pupil plane, the deformable mirror should be
located at a conjugate pupil plane within the system. As previously discussed, atmospheric
turbulence often comes in discrete layers (see Section 2.3.1). Single deformable mirrors are
typically used to provide ground layer turbulence correction however this leaves higher altitude
turbulent layers uncorrected. If multiple deformable mirrors are used and positioned at the
correct conjugate altitudes to match the turbulence, it is possible to provide an improved
wavefront correction compared to a single ground layer correction.
3.5.1 Low- and high-order correction
When designing an AO system, it is important to keep in mind the level of correction which needs
to be applied for the defined scientific goals. As described in Section 2.5.5, the distortions on the
incoming wavefront are often described in terms of low- and high-order Zernike polynomials. The
higher the order of Zernike mode which is corrected, the better the removal of turbulent effects
in the science image as more turbulent power is removed (see Table 2.1). The lower-order modes
contain most of the distorting effects of the wavefront i.e. have the greatest amplitude and the
strongest power. This requires only a few actuators to correct but requires large stroke capabilities
of the mirror. As higher-order modes have finer structure across the wavefront surface, they require
a greater number of actuators on the deformable mirror so that they can be accurately generated
although the stroke requirements in this case however are less. Because of these two differing
levels of correction, often a ’woofer-tweeter’ configuration is used in a correction system with a
mirror with large stroke and smaller number of actuators being used to provide coarse correction
initially (i.e. the woofer) and a second higher-order mirror with more limited stroke correcting for
the higher-order effects.
3.6 Summary
The Adaptive Optics Lucky Imager, or AOLI, is a new instrument being developed for use
initially at the 4.2 m William Herschel Telescope. The instrument combines the techniques of
adaptive optics and lucky imaging into a dedicated instrument for the first time allowing
diffraction limited imaging at visible wavelengths to be achieved from the ground. To overcome
the problems of poor sky-coverage without using laser guide stars, a new type of wavefront
sensor, the non-linear curvature wavefront sensor, has been chosen for use with AOLI.
41
3.6 Summary
The non-linear curvature wavefront sensor offers several benefits over the current generation of
wavefront sensors. Based loosely on the principal of conventional curvature wavefront sensors,
the nlCWFS uses four, rather than the traditional two, imaging planes either side of the conjugate
pupil plane. These additional planes provide the sensor with increased sensitivity to both high-
and low-order wavefront distortions allowing fainter reference objects to be used for wavefront
reconstruction. Because of this, the nlCWFS within AOLI will be able to provide significant sky
coverage with natural guide stars alone.
42
“Only two things are infinite, the
universe and human stupidity, and I’m
not sure about the former.”
Albert Einstein
4
An introduction to the non-linear curvature
wavefront sensor
The non-linear curvature wavefront sensor (nlCWFS) uses an iterative reconstruction algorithm to
recover phase values from recorded intensity information. In this chapter, I introduce the
non-linear curvature wavefront sensor and the principles behind this technique of wavefront
reconstruction.
4.1 Reconstruction basics: The Gerchberg-Saxton method
The Gerchberg-Saxton algorithm was developed in 1971 to solve the problem of reconstructing
phase fluctuations from two intensity measurements for electron microscopy (although there was
a suggestion it may be useful for normal photographic methods) (Gerchberg & Saxton, 1972). As
shown in Figure 4.1, the algorithm consists of transforming from the object (spatial) domain to the
Fourier (image) domain repeatedly, each time applying known constraints to the values obtained
after the transform.
The generalised algorithm can be used for any problem in which partial constraints are known
43
4.1 Reconstruction basics: The Gerchberg-Saxton method
Figure 4.1: Schematic of the Gerchberg-Saxton Algorithm (Osherovich et al., 2009).
(either through measured data or other information known a priori) in both the Fourier and object
domains (Fienup, 1982). This method is often termed the ‘error-reduction (ER) algorithm’ as each
iteration should decrease the value of the error prior to the constraints being applied although this is
only true for noiseless data (which as any instrument scientist will tell you is impossible to obtain!).
Initial work by Guyon (2007) used the standard error-reduction algorithm for phase reconstruction
and was successful when using monochromatic light.
4.1.1 Improvements beyond the Gerchberg-Saxton technique
There are several variations on the Gerchberg-Saxton method as described by Fienup (1982), for
example the Input-Output method which uses an averaging process to determine a new
wavefront estimate. All of these additional algorithms have different speeds with which they
converge on the minimum error result, with some algorithms stagnating or even increasing in
error before they converge. Solutions to these problems have been proposed by many authors
leading to several different algorithms used today, however these are still based upon the
principle of the Gerchberg-Saxton method (Fienup & Wackerman, 1986; Guyon, 2010). Methods to
improve the algorithm include binning the data to quickly converge on an answer before using
the full set of data, as the majority of computational time is spent Fourier transforming arrays
which slows down with increasing size. Work in Cambridge has also investigated using an
averaging technique from previous iteration results to converge on an answer in an improved
manner (Aisher et al., 2012). It is however important to note that once an accurate phase value has
been obtained, the next wavefront phase measurement is unlikely to change significantly allowing
stronger constraints on the next iteration, leading to faster convergence.
44
An introduction to the non-linear curvature wavefront sensor
Figure 4.2: The non-linear curvature wavefront sensor uses pairs of imaging planes, one at ±z1 and
the other at ±z2 where z is the distance from the pupil plane. The images recorded at these planes
(p1 − p4) are used as part of an iterative reconstruction process to recover the phase information at the
pupil plane.
4.2 Reconstruction for the nlCWFS
The original Gerchberg-Saxton algorithm is based upon the propagation between two planes a
fixed distance apart. This configuration, due to the fixed distance, limits you to certain orders of
distortions within the pupil (or object) plane due to the Talbot effect as discussed in Section 3.4.2.
To improve the sensitivity of the algorithm to multiple orders, more image (or Fourier) planes are
used, some closer to the pupil to be sensitive to higher-order effects and some more distant to
record lower-order effects. In the case of the nlCWFS, these planes are positioned with an inner
pair and an outer pair equidistant from a conjugate pupil plane as shown in Figure 4.2.
From the intensity information recorded at these image planes, the phase at the pupil is retrieved
through an iterative wavefront reconstruction process based upon the Gerchberg-Saxton method.
This refined version of the technique propagates between the pupil plane and each image plane in
turn, constraining the propagated wavefront at each stage with known information about
amplitude and phase. The full reconstruction algorithm is shown in Figure 4.3.
The reconstruction process begins by making an initial estimate of the complex scalar field at the
pupil plane. It is hoped, after acting on this estimate with the algorithm, it will converge to the value
45
4.3 Wavefronts and their propagation
Figure 4.3: The reconstruction algorithm for the non-linear curvature wavefront sensor. The imaging
plane numbering corresponds to those shown in Figure 4.2.
of the actual phase (and amplitude) at the pupil plane i.e. what we want to recover. Initially, there
is little prior information available to make an ‘accurate’ estimate and as such, a best assumption
is to assume a flat wavefront i.e. a constant phase and illumination/amplitude (this is discussed
further in Section 4.3.3). The estimated field at the pupil is propagated to each image plane in turn,
starting initially with plane p1 as shown in Figure 4.2 (note with this initial estimate, a perfect Airy
disk pattern will be obtained after the propagation). At this point, any known information is used
to constrain the wavefront allowing convergence to the optical field at the pupil.
The version of the algorithm in Figure 4.3 is optimised to maximise the speed of convergence of the
wavefront estimate.
4.3 Wavefronts and their propagation
Up to this point, I have simply stated that during the reconstruction process the wavefronts are
propagated between the planes. This numerical process is dependent upon the optical regime in
which we are working and other constraints on the system. It is important to select the correct
technique to ensure that the amplitude and phase components of the input wavefront are
propagated appropriately.
46
An introduction to the non-linear curvature wavefront sensor
4.3.1 Propagation regimes and techniques
The selection of the correct propagation technique when simulating an optical system is of
importance to ensure the relevant effects are included while maintaining as simple a technique as
possible (summarised nicely by Albert Einstein: ”Everything should be made as simple as
possible, but not simpler”). There are three principal propagation methods (although there are
variants on each) which are described within this section; geometric optics which is based upon
ray-tracing methods and the Fraunhofer and Fresnel propagation techniques which are based
upon the Rayleigh-Sommerfeldt diffraction integral.
Geometric Optics
Geometric optics is the simplest of the propagation regimes and is used principally to describe
optical systems primarily comprising simple refractive and reflective components i.e. lenses and
mirrors. Conventionally, paraxial ray matrices describe how optical elements transform the
location and direction of light rays. Using this technique, rays are represented by their distance, y,
from the optical axis at a certain location, z, the slope of the ray y′ and the refractive index n. This
description is then operated upon by transform matrices allowing refraction and reflection to be
described. This method is used in many optics modelling programs e.g. Zemax, and allows the
optical quality of components to be tested before manufacture.
Geometric optics works well in the regime where the dimensions of the optical system are
significantly larger than wavelength i.e. where the effects of diffraction are not important. They
require a large number of rays to be traced through any system and assume a homogeneous
medium within each component or element of the system. This allows the assumption that light
will propagate in a predictable manner i.e. a straight line.
The assumptions used in geometric optics make it favourable for many system modelling
applications however, they limit the method from accounting for both diffractive effects and the
effects of an inhomogenous medium e.g. the turbulent atmosphere. Because of these limitations,
other techniques exist to work in this regime.
Rayleigh-Sommerfeldt diffraction integral
The Rayleigh-Sommerfeldt diffraction integral is the mathematical method for transforming the
complex scalar field describing light in one location to the field at another location after propagating
through space. While not a complete solution in itself, by using approximations to the equation, it
becomes possible to provide a numerical description of the optical field at another location subject
to the relevant conditions.
47
4.3 Wavefronts and their propagation
Figure 4.4: The coordinate system used to describe numerical optical propagation.
The coordinate system and positions used for describing the Rayleigh-Sommerfeldt diffraction
integral are shown in Figure 4.4. Light is propagated through an isotropic and homogenous
medium from an initial plane, constrained by an aperture, to an observation plane at a distance
∆z from the aperture. It is assumed that the wavelength of light, λ, is significantly greater than the
size of the aperture, D, allowing edge effects from the aperture to be ignored and the field incident
on the plane to simply be limited to the region inside the aperture. For the technique to be valid, it
is also assumed that ∆z  λ so that we are imaging away from the aperture.
The process is represented by two complex fields, U(x1, y1) at the initial plane and U(x2, y2) at the
observation plane. The process of transforming between them is given by taking the convolution
of the field in the aperture plane with the impulse response of free space (i.e. the effect the field
has when propagating in space). Mathematically, this can be written as the Rayleigh-Sommerfeldt
diffraction integral
U(x2, y2) =
∫∫
A
U(x1, y1)
1
iλ
exp (ikρ)
ρ
∆z
ρ
dx1dy1 (4.1)
where
ρ =
√
(x2 − x1)2 + (y2 − y1)2 + (∆z)2 (4.2)
and is the magnitude of the distance between a point in the aperture and imaging plane. In
Equation 4.1, the final term, ∆z/p is an obliquity factor between the planes as there has been no
assumption about the direction of the propagation of light.
48
An introduction to the non-linear curvature wavefront sensor
While Equation 4.1 may provide a rigorous mathematical description of the problem of light
propagation, it is challenging to solve analytically. By imposing that ∆z  r2 where
r2 = |−→r2| =
√
x22 + y
2
2 , we can use the paraxial approximation so that the light propagation is along
the optical axis, in this case z. This allows the final term in Equation 4.1, which can be considered
to be an inclination factor, to becomes unity and we can write
U(x2, y2) =
∫∫
A
U(x1, y1)
1
iλ
exp (ikρ)
ρ
dx1dy1 (4.3)
Fresnel Propagation
Even though Equation 4.3 contains approximations, it is still challenging to solve due to ρ including
a square root. To further simplify the equation, the binomial expansion can be used to expand ρ by
considering that (x2 − x1)2 + (y2 − y1)2  (∆z)2. This allows ρ to be written as
ρ ≈ ∆z + (x2 − x1)
2 + (y2 − y1)2
2∆z
−
[
(x2 − x1)2 + (y2 − y1)2
]2
8(∆z)3
+ ... . (4.4)
ρ in the denominator of Equation 4.3 is only sensitive to the first term in this expansion while the
exponential is sensitive to the first two terms. With these constraints on each term in the expansion,
ρ can be substituted into Equation 4.3 to give
U(x2, y2) =
∫∫
A
U(x1, y1)
1
iλ∆z
exp
(
ik
[
∆z +
(x2 − x1)2 + (y2 − y1)2
2∆z
])
dx1dy1
=
exp(ik∆z)
iλ∆z
∫∫
A
U(x1, y1) exp
[(
ik
2∆z
)
(x2 − x1)2 + (y2 − y1)2
]
dx1dy1
=
eik∆z
iλ∆z
e
ik
2∆z (x
2
2+y
2
2)
∫∫
A
{
U(x1, y1)e
ik
2∆z (x
2
1+y
2
1)
}
e
−ik
∆z (x1x2+y1y2)dx1dy1
(4.5)
which is the Fresnel diffraction integral.
The Fresnel diffraction integral is used in the regime close to the original aperture where the
amplitude of the complex field is changing as the wavefront propagates. It allows a wave to be
propagated to multiple distances and to examine the effect of this process.
Examining Equation 4.5 further, if we assume the integrand to be zero outside of the aperture (a safe
assumption for any sane telescope system), the limits of integration can be extended to [−∞,+∞].
This then, aside from the multiplicative factors, is simply the Fourier transform of the complex field
49
4.3 Wavefronts and their propagation
Optics Model / Algorithm Principle Applicable Regime
Geometric Optics Determination of the optical
pathlength along traced rays
Scale of components and rays
is significantly larger than
wavelength
Fresnel propagation Convolution with amplitude
transfer function
Near field where amplitude
distribution over light field
changes as light propagates
Fraunhofer propagation Fourier transform Far field where the overall
form of the amplitude
distribution does not change
when light propagates
Table 4.1: A summary of methods for modelling optical systems and propagation. Adapted from
Andersen & Enmark (2011)
at the aperture multiplied by a quadratic phase term which is possible to solve either analytically
for specific cases or numerically for any incident wavefront.
Fraunhofer Propagation
When observing a significant distance from the original aperture in the so called far field regime, the
quadratic phase term in Equation 4.5, e
ik
2∆z (x
2
1+y
2
1), tends to unity. This allows the Fresnel diffraction
integral to be simplified further giving
U(x2, y2) =
exp(ik∆z) exp
[
ik
2∆z (x
2
2 + y
2
2)
]
iλ∆z
∫∫
A
U(x1, y1) exp
(−ik
∆z
(x1x2 + y1y2)
)
dx1dy1 (4.6)
which is the Fraunhofer diffraction formula. In this regime, the diffraction pattern is fixed and simply
scales with distance, growing larger as it moves away from the aperture. To allow this
approximation to be valid, the conditions can be severe: for light at 600 nm and an aperture
diameter of 2.5 cm, the output plane must be at ∆z  1.6 km (Goodman, 2005).
4.3.2 Selecting the correct propagation technique
Given the constraints and approximations of the different propagation methods discussed, it is
important to understand when each is valid. A summary of the different techniques and their use
is shown in Table 4.1.
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An introduction to the non-linear curvature wavefront sensor
While it is clear that if the effects of diffraction are important geometric optics will be insufficient,
there is perhaps some ambiguity in the selection between the use of Fresnel and Fraunhofer
propagation. The solution to this comes in the form of the Fresnel Number, a value which describes
the type of diffraction effects expected in an optical system.
The Fresnel number, F is defined as
F =
a2
∆zλ
(4.7)
where a is the characteristic size of the aperture in the system e.g. radius, ∆z is the distance
between the aperture and imaging plane and λ is the wavelength. The value of F is indicative of
the propagation method required and effectively gives a measure of the strength of the second-
and higher-order terms in Equation 4.2. For F  1, the distance to the imaging plane is
significantly larger than the aperture and Fraunhofer propagation should be used. For F ∼ 1,
Fresnel propagation is the best approach while for larger values of F , diffraction effects become
decreasingly important and it is possible to turn to geometric optics techniques.
The Fresnel number, while indicative, does not always give a precise answer regarding which
technique is most appropriate to employ. If in doubt, it is always best to use the method with
fewest approximations, i.e. Fresnel propagation over Fraunhofer, however, this is not always
possible to solve analytically. If solving numerically, in the far field regime both techniques will
recover the same result although the Fresnel technique will take a slightly increased computing
resource.
Propagation for the nlCWFS
In light of the previous discussion regarding the nlCWFS and its techniques, it is clear that any
propagation within this system must be based upon Fresnel propagation. The development of
amplitude structure due to phase distortions fails to be described within the Fraunhofer and
geometric optics regimes. In addition, by using the Fresnel technique, beams can be simulated or
equivalents generated by maintaining the Fresnel number.
4.3.3 Numerical propagation
Several of the optical propagation techniques are based upon Fourier transforms. Today, discrete
Fourier transforms (DFT) are often implemented as standard functionality within computer
systems (or can be added from standard libraries) and as such, can be used to numerically model
optical systems and wavefront propagation within them. In the previous discussion of
propagation methods, the Fourier transforms have been analytical. It is important to note some of
51
4.3 Wavefronts and their propagation
the important limitations and differences between these and the numerical techniques,
particularly to ensure valid propagations are being performed. A full discussion can be found
within the literature (Schmidt, 2010; Andersen & Enmark, 2011).
DFTs are undertaken numerically on a finite sequence of numbers. This sequence of numbers can
be one dimensional, the simplest case, or extended to a two dimensional case. This array, due
to its limited size is only a small section of the infinite analytical solution and it is important to
ensure there are sufficient elements within the array to allow the recovery of the highest spatial
frequencies within the function. To correctly sample the data, it is important to identify the correct
spacing between grid elements, δ and the total number of grid points in one direction, N . These
values are set by the highest frequency element of the function being transformed - to recover this
frequency at least two measurements must be made per period. This sets the limit that the sampling
frequency, fs must obey
fs ≥ 2fmax (4.8)
where fmax is the highest frequency component to be recovered. The limit, fc = 1/δc, is the Nyquist
sampling criterion which is the lowest limit of the sampling frequency (and grid space δc) required
for accurate reconstruction from the discrete data.
A Fourier transform shows a representation of the frequency components of the function being
transformed. The resolution of the output from the Fourier transform process, δFourier, (i.e. the
spacing in frequency space) is linked to the grid spacing in the input plane by
δFourier =
1
Nδ
(4.9)
which, when undertaking Fresnel propagation using the coordinates in Figure 4.4, gives rise to the
grid spacing in the output plane of
δ2 = δFourierλ∆z =
λ∆z
Nδ1
. (4.10)
If performing a single DFT for Fresnel propagation, the output plane scaling is limited by Equation
4.10. This is particularly problematic as the scale at the imaging plane is often set by the physical
pixel scale of the detector.
Two step propagation
To overcome the limitation on the image plane grid spacing, there are multiple possible solutions.
Firstly, it is possible to simply adjust the number of elements within the input grid, N , to set the
52
An introduction to the non-linear curvature wavefront sensor
Figure 4.5: The two step propagation method. A wavefront is propagated from the aperture/input
plane via an intermediate plane to an imaging plane. The grid spacing in each plane is δ.
output scaling to be as desired. This however can significantly increase the computing time
required to undertake the DFT and as such, for the real-time nature of the nlCWFS is impractical.
An alternative solution, and the one adopted for the development of the nlCWFS, is to use a two-
step propagation process where the input plane is propagated to an intermediate plane before
then being propagated to the desired output location as shown in Figure 4.5 (Schmidt, 2010). The
required location of the intermediate plane to achieve this can be found by considering the ratio of
the scaling of the input and output planes, m = δ2/δ1.
Equation 4.10 gives a relation for the grid spacing at an imaging plane after propagation and as
such, we can use this to specify the spacing at the intermediate plane,
δint =
λ|∆z1|
Nδ1
where ∆z1 = zint − z1 . (4.11)
If we then consider propagating the wavefront from the intermediate plane to the imaging plane,
the grid spacing at this final plane will be
53
4.3 Wavefronts and their propagation
δ2 =
λ|∆z2|
Nδint
where ∆z2 = z2 − zint .
=
λ|∆z2|
N
(
λ|∆z1|
Nδ1
)
=
|∆z2|
|∆z2|δ1
(4.12)
By considering the definition of m, δ1 and δ2 from the above equations, we can write the relation
giving the position of the intermediate plane as
m =
δ2
δ1
=
|∆z2|
|∆z1| . (4.13)
The two step propagation technique is not the only method for managing the requirement to be
able to specify the imaging plane grid spacing. Methods based on the convolution theorem allow
a scaling factor to be added into the propagator. This allows the scale to be specified however this
has not been used for the nlCWFS development (Schmidt, 2010).
Additional numerical effects
When undertaking any discrete Fourier transform, individual frequency components are often re-
arranged within the output array due to only positive index notation being used for array elements.
This means that the origin of an input wavefront, which is conventionally located at the centre of
an image, is inconsistent with the first element of the array which is found at the top left. Many
standard numerical Fourier transform packages handle this effect by providing an additional ‘shift’
functionality both before and after propagation allowing the expected output to be recovered.
Numerically, performing a DFT on a two dimensional array returns an array with the same
number of elements. When DFTs are used as part of a Fresnel propagation integral, it is important
to remember that the wavefront will expand, particularly if propagating from an aperture. In this
instance, if the aperture occupies the full region of the input plane to the DFT, it is important that
the grid spacing in the output plane is larger to account for this beam expansion.
An alternative solution, which has been adopted for the nlCWFS development, is to include a
region of padding around the aperture so that the pixel scaling between planes can be maintained
while allowing accurate propagation. This technique also helps minimise any high-frequency
components due to boundary effects which are caused by DFTs implicitly assuming the input data
has a periodic continuation outside of the input plane. If there are data values at the edge of the
54
An introduction to the non-linear curvature wavefront sensor
array, this assumed continuation leads to discontinuities at the boundary creating spurious high
frequency components in the output.
4.4 Constraining the wavefront estimate
As we are dealing with a complex field, at each image plane, we can separate the propagated
wavefront into its amplitude and phase components. This makes it possible to constrain both the
amplitude and phase separately with any measurements (remembering amplitude2 ≡ intensity)
or knowledge about the light path (i.e. there will no contributions to the field from outside of the
telescope aperture).
In the nlCWFS reconstruction algorithm, at an image plane, the intensity is recorded and this
information is used to replace the amplitude component of the propagated estimate. This image
information must be normalised before being used to constrain the wavefront. No phase
information is replaced however as it is not possible to provide any constraints on it at this
location. The ‘new’ estimate (comprising the new amplitude and original phase) is then
propagated to the next image plane via the pupil plane (the next image plane is chosen ensuring
any propagation would pass through the pupil in the process). Propagating via the pupil plane
has been shown to significantly increase the rate of convergence of the algorithm towards the true
phase value at the pupil (Aisher et al., 2012), reducing the number of iterations required from
other orders of propagation. In addition, it takes minimal additional computing time to separate
the propagation between two images planes into two stages. This means any speed of
reconstruction is not adversely affected.
The known constraints at the pupil plane are more limited in some respects than those at an image
plane as no measurements are made. Saying that however, knowing the pupil shape (i.e. the pupil
mask of the telescope in this case), makes it possible to identify regions where the wavefront data is
valid i.e. within the telescope aperture, and invalid i.e. outside of the telescope aperture. Areas with
invalid data are set to zero amplitude and phase, while any data within the valid region remains
unchanged. The pupil plane is the only location where phase location can be constrained and it is
this information which significantly aids the speed of reconstruction.
4.5 Phase unwrapping
Phase values can mathematically take any value, however conventionally, these are restricted to a
range from −pi to pi (or 0 to 2pi depending upon which field you work in). When using numerical
techniques involving phase, this is also the case and as such, when performing wavefront
55
4.6 Speed of reconstruction
propagations, instead of phase values simply increasing linearly as the wavefront propagates
from the aperture, they become wrapped and maintain a value within their 2pi range.
While this wrapping process has no numerical effect on the amplitude of the wavefront after
propagation, the phase values can often appear as a ‘saw-tooth’ as the phase has integer numbers
of 2pi subtracted until the value lies within the valid region. The output from subsequent
propagations is unaffected by this phase wrapping process and as such, if it is only the intensity
(i.e. the only directly measurable property) which is important in the propagation, this effect can
be neglected.
For the nlCWFS, the aim is to recover the phase at the pupil plane and as such, the numerical
phase wrapping effect must be considered. This is particularly important as the ultimate aim of the
reconstruction is to provide a continuous value of the phase across the full pupil aperture to allow
for correction with a deformable mirror.
The simplest method of phase unwrapping is achieved by dealing with individual rows within
the pupil plane. By scanning along the row element by element, if it is assumed that there is a
maximum change between elements, for example (3/2)pi, a change greater than this would imply
a ‘phase wrap’ has occurred. By adding or subtracting integer values of 2pi, the phase can then be
unwrapped.
Unfortunately, this method of phase unwrapping, while working with ‘noiseless’ data, frequently
fails particularly with artefacts from numerical propagation. As such, other techniques need to be
employed to attempt to recover the unwrapped phase screen. Several exist to achieve this however
many struggle to work in real-time as required in this usage (Ghiglia & Pritt, 1998).
4.6 Speed of reconstruction
Any wavefront reconstruction technique must provide a recovered wavefront in a timescale similar
to that of the coherence time of the atmosphere. For the nlCWFS, the principle element of the
reconstruction process which utilises most time computationally is the propagation of wavefronts
between planes which, as previously discussed, is done by performing a Fourier transform.
Current computing technology allows several different ways to undertake DFTs. Conventionally
these have been done on CPU which allows flexibility but at the cost of a relatively slow process.
In recent years, there has been a steady increase in the use of numerical computing using Graphics
Processing Units (or GPUs). Traditionally these units are designed for rendering graphics from the
central processing systems within a computer but due to their functionality, they are structured in
a highly parallel manner allowing rapid manipulation of memory and numeric calculations. The
most recent GPUs from Nvidia are the GeForce GTX TITAN Black with 2880 cores and the Tesla
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An introduction to the non-linear curvature wavefront sensor
K40 with 2880 cores offering 5.1 Tflop/s and 4.29 Tflop/s respectively at single precision and 1.3
Tflops/s and 1.43 Tflop/s at double precision. This is significantly more than even the fastest
multicore CPUs today.
Work undertaken in Cambridge has shown the need for GPU acceleration when undertaking
Fresnel propagation to reach the speeds needed for real-time wavefront reconstruction. With this
high level of speed however does come particular challenges as GPUs are designed for longer
durations of calculation rather than short rapid operations. As the CPU of any computer governs
the interactions between all the hardware components, any data to be manipulated by the GPU
must first pass through the CPU before being transferred across the PCI express (PCIe) bus to the
GPU. This all has to occur prior to any GPU processing commencing and, due to the limited
bandwidth across the PCIe bus, a potential lag is introduced when compared to processing
commencing on the CPU.
As data from the imaging planes must pass through the CPU, there is currently a technical
challenge in pushing the boundaries of GPU acceleration. With faster processors and PCI lanes
within the computing hardware, the barriers to using GPUs in this real-time application are
rapidly decreasing. In addition, there is current work to develop the technology to allow data to
be transferred directly between PCIe devices. This would allow data from the imaging planes, if
captured with a PCIe device, to be placed straight into the GPU eliminating the need for any CPU
overheads.
4.7 Summary
The non-linear curvature wavefront sensor uses an iterative algorithm to recover the phase
information in the pupil plane from intensity measurements. The information recorded in two
pre- and two post-pupil imaging planes allows the amplitude of a Fresnel propagated wave to be
constrained in these planes. By propagating between the pupil and imaging planes and applying
these intensity measurements, an estimate of the wavefront at the pupil will converge to the actual
value. In addition, when propagating through the pupil plane, the pupil mask can be applied to
aid convergence.
Numerically, the reconstruction algorithm for the nlCWFS consists of two Fourier transforms per
propagation which allows the scaling at an output plane to be selected. These DFTs (which are
undertaken with GPUs to provide the required speed) have several numerical effects which must
be considered. Of principle concern to the nlCWFS are the high-frequency edge effects caused by
the assumed periodic continuation of the input array and the wrapping of phase values between
-pi and pi. This latter effect can cause a particular challenge when using the nlCWFS as an input for
wavefront correction. In the case of adaptive optics, any deformable mirror will require continuous
57
4.7 Summary
phase values and as such, strategies must be employed to unwrap the recovered phase.
58
“If your result needs a statistician then
you should design a better
experiment.”
Ernest Rutherford
5
Investigation and simulation of the nlCWFS
To implement and develop the non-linear curvature wavefront sensor, it was critical to develop a
good understanding of the technique, its intrinsic effects and strategies for optimisation. Through
the use of simulations, I have identified several key areas which need to be addressed within the
optical system of AOLI and nlCWFS reconstruction strategies. The simulations and analysis work
are presented in this chapter.
5.1 Simulation techniques
There are several simulation packages to model the propagation of light through a turbulent
atmosphere and telescope systems. Two such systems, Yao and Arroyo have previously been used
within the Optics Group at Cambridge as well as being used widely for research within the
adaptive optics community. Arroyo was selected to undertake simulation work for AOLI due to
its wide range of inbuilt propagation methods with the program being structured as a C++ library.
This allows a large amount of flexibility when modelling and developing optical systems.
59
5.1 Simulation techniques
5.1.1 Verifying the suitability of Arroyo
As previously discussed in Section 4.3.2, propagation within the nlCWFS is best described by
Fresnel propagation. While Arroyo has been used in several projects to date and has published
verification results, several simple verifications were completed to ensure the suitability of the
program for use in this regime. This testing was initially based on the sample codes provided with
Arroyo which were developed further to produce outputs similar to previously published work
on the nlCWFS.
To model an optical system, Arroyo creates and stores an incoming wave as an object. The
parameters are defined when the object is created, e.g. pixel scale, allowing the object to be passed
to functions to allow specific processes and phenomena to be applied to the wave (e.g. passing
through a turbulent layer or aperture). To allow Arroyo to model as diverse a range of systems as
possible, it provides several different functions for completing similar processes. For example,
when generating a power spectra to describe atmospheric turbulence, it is possible to use a
Kolmogorov, von Karmann or Greenwood spectrum while for propagating wavefronts, there are
nine different methods.
Atmospheric and propagation effects can be modelled in Arroyo using the following process:
1. Generate a wavefront with uniform illumination and amplitude simulating undistorted light
from a distant point source.
2. Pass the wavefront through a single turbulent atmospheric layer generated using
Kolmogorov turbulence model. This simulates the effects of passing through the
atmosphere.
3. Pass the wavefront through an aperture screen simulating the wavefront entering the
telescope and being constrained. Several shapes can be selected within Arroyo however a
circular or annular aperture was used.
4. Propagate the wavefront to a distance away from the telescope aperture where amplitude
and phase are recorded.
While the Kolmogorov modelling was selected for simulating turbulence due to its previous
verification during software development, the most suitable wavefront propagator required
further investigation. This was done using the modelling technique described and by examining
the imaging plane structure at different distances from the pupil plane. The outcome of these
investigations highlighted several important factors and are summarised in Table 5.1.
The results of the investigation showed features common to several of the propagators. Firstly, the
further the wavefront was propagated away from the telescope aperture with the far-field
60
Investigation and simulation of the nlCWFS
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1:
A
su
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m
ar
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of
pr
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ch
ni
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w
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d.
61
5.1 Simulation techniques
propagators, the smaller the image became. This makes it difficult at large distances from the
telescope (>3000 km for an 8 m aperture) to examine the structure without using significant
computing resources, however, this can be countered by using the Goertzel-Reinsch based
propagators which allow the user to specify an arbitrary sampling and array size of the final
wavefront. Secondly, all the far-field propagators at distances of less than around 150 km from the
telescope aperture have overlapping images due to the Fourier methods used in the propagation.
For generating images closer than this distance, the near-field propagators must be used which
preserve the pixel wavefront scale and do not suffer from this overlapping effect.
As perhaps expected, the most suitable techniques for simulating with the nlCWFS are the
techniques based upon ‘Far-field Fresnel’ propagation. These simulate the standard Fresnel
integral (Equation 4.5) using different numerical methods. Due to the challenge of decreasing
beam size with distance for the standard propagator, the Goertzel-Reinsch propagator was
selected for other simulation work as it allows the output pixel scale (and consequently physical
size of the image plane) to be specified.
Replication of previously published work
Guyon (2007) simulated the structure of wavefront intensity as a function of distance from the
telescope aperture as shown in Figure 5.1. The simulation method used involved the propagation
of a wavefront passed through a turbulent phase screen to varying distances from the aperture
using Fresnel propagation. To further verify the suitability of Arroyo for simulating the nlCWFS, a
similar technique was undertaken to reproduce the characteristics shown in the original paper.
The technique for generating the required image planes is as previously described with a
turbulence affected wavefront being propagated from the telescope aperture. The output from the
simulation can be seen in Figure 5.2. Slight differences in the telescope aperture used can be seen
between the original paper and the simulations (i.e. the inner radius of the annular aperture being
smaller) however the expected structure is clearly visible. As discussed in Section 3.4.2, low order
structure is visible at large distances from the aperture while the higher order structure should
only be visible within the first few hundred kilometres. This effect is clearly identifiable in both
figures.
The ability of Arroyo to produce propagated wavefronts with the same characteristics as those
previously published in the literature makes it an excellent tool for any optical system where
Fresnel propagation is important. By understanding the effects from each type of propagator, the
most appropriate can be chosen for different systems and this software has been used as the
principal tool when investigating propagated wavefronts within the nlCWFS system.
62
Investigation and simulation of the nlCWFS
Figure 5.1: Figure from Guyon (2007) showing the propagation of light from an aperture. The aperture
mask and phase distortions at the pupil are shown at the upper right. These distortions give rise to the
intensity fluctuations shown on the left. The difference between the beams propagated forward and
backwards from the pupil are shown on the bottom right.
63
5.1 Simulation techniques
Figure 5.2: Simulated wavefront propagation using Arroyo replicating the work in Guyon (2007).
64
Investigation and simulation of the nlCWFS
5.2 Chromatic effects
As discussed in Section 4.3.2, Fresnel propagation must be used to describe the propagation of
wavefronts within the nlCWFS. This propagation technique has a dependence upon wavelength
(see Equation 4.5) which leads to potential chromatic effects when using a broadband light source.
Previous simulation work by Guyon (2007, 2010) assumed monochromatic illumination of the pupil
plane to counter the intrinsic chromaticity within the propagation. To maximise the sensitivity
of the wavefront sensor however and to increase its limiting magnitude, the largest number of
photons, i.e. a broadband source, must be used.
An investigation of these effects was undertaken using Arroyo and the following procedure:
1. Generate a Kolmogorov model turbulent phase screen applying sub-harmonic correction as
proposed by Lane et al. (1992) to simulate the turbulent atmosphere
2. Pass a monochromatic plane wave through the generated phase screen
3. Apply an aperture mask to the wave, representing the aperture of the telescope
4. Propagate to each plane in turn using Fresnel propagation methods.
Monochromatic simulations were performed using light with wavelengths of 500, 700 and 900 nm
with the same turbulent phase screen at the pupil. The wavefront was propagated to multiple
locations either side of the pupil where the amplitude was recorded. Results are shown in Figure
5.3.
The simulations show a divergence in the intensity at different wavelengths as the propagation
distance is increased. Up to around 100km, the effects are limited to a blurring effect. However, as
distances reach that of the non-linear regime, the effects become more pronounced with a
significant difference between wavelengths. This effectively means that it is impossible to
distinguish the amplitude at different wavelengths within this regime and as such, the constraint
provided by the measured intensity, a critical component in the wavefront reconstruction will be
inaccurate.
5.2.1 Strategies to minimise chromatic effects
Due to the significant limitations imposed by the chromatic effects when propagating, it is vital
for these to be controlled if the nlCWFS is to be effective. The best strategy for doing this is to
effectively limit the bandwidth of each image or by providing a correction for the chromatic effects.
65
5.2 Chromatic effects
Figure 5.3: Simulations showing a horizontal cut across images of different wavelengths (500 nm,
700 nm and 900 nm) when propagated from the same pupil wavefront. The figure shows the horizontal
cut across the images at ±10, ±50, ±100 and ±500km for an 8 m telescope with uniform illumination
and a turbulent phase. Close to the telescope pupil, there are only minor chromatic effects however
at larger distances, the higher order structure becomes smeared out. The low-order structure is still
visible at these larger distances.
66
Investigation and simulation of the nlCWFS
Previous work on the nlCWFS by Mateen et al. (2011) developed reimaging optics for use within
their optical system, effectively making the recorded beam at the detector the same as a
monochromatic source. An alternative strategy that has been investigated and developed is the
use of dichroics. This provides a limited bandwidth to each image with only limited chromatic
effects and is discussed fully within Section 6.3.3.
5.3 Beam scaling
In the simulations shown, for example Figure 5.2, it is assumed there are no focusing optics within
the system being modelled. This leads to a beam size of the order of the telescope diameter and
distances where diffraction effects are observed to be hundreds of kilometres. This is clearly
different from observations being undertaken on a telescope where the beam is focused with
optics to a more manageable size and the question is, how to interchange from the simulations to a
practical use.
The solution to this problem comes from considering the kind of diffraction effects within a system.
As discussed in Section 4.3.2, the type of diffraction effects observed at a location within a system
can be described in terms of the Fresnel Number which depends both upon distance from an aperture
i.e. pupil plane, and the size of that aperture. By reimaging a pupil plane at its conjugate plane,
an image of the original aperture can be recovered. By using an appropriate combination of lenses
however, (see Figure 2.2), it is possible to recover a magnified or de-magnified pupil. This can also
be achieved using the optics of the telescope and instrument leading to an effective reduction in
the telescope pupil diameter.
In addition to rescaling the effective aperture size, Fresnel propagation has an intrinsic wavelength
dependence as discussed in Section 5.2. When undertaking the wavefront reconstruction required
to recover the phase at the pupil plane, propagation between planes assumes monochromatic light.
If different wavelengths of light are being used for each image plane, an appropriate scaling can be
done by maintaining the Fresnel Number. A summary of this wavelength and distance scaling is
shown in Table 5.2.
As the Fresnel number is only indicative of the diffraction effects within a system, I undertook
simulations to verify the reliability of the criteria when rescaling beams within the optical system.
These simulations were undertaken in Arroyo with aperture planes being rescaled to the
appropriate beamsize before being propagated to the image plane.
67
5.4 Developing the wavefront reconstruction algorithm
Rescaled output Plane distance relative to original at:
Beam diameter Wavelength 100 km 500 km 750 km
4.2 m 600 nm 116.7 km 583.3 km 875 km
4.2 m 800 nm 87.5 km 437.5 km 656.3 km
1 m 700 nm 5.67 km 28.34 km 42.52 km
1 cm 700 nm 56.67 cm 283.45 cm 425.17 cm
1 mm 700 nm 0.567 cm 2.834 cm 4.242 cm
Table 5.2: Plane positions for rescaled beam diameters at different wavelengths. Positions are relative
to 4.2 m diameter aperture with an incident wavefront at λ = 700 nm.
5.3.1 Plane positioning
As discussed in Section 3.4.2, the Talbot effect describes the order of wavefronts which can be
detected as a beam propagates from the pupil. With this in mind, it is important to choose distances
from the pupil for the imaging planes which provide sufficient signal in the intensity to recover the
orders of interest.
Figure 5.4 shows the simulated wavefront propagation from a 4.2 m telescope aperture. The
wavefront is clearly seen to break into speckles which gradually increase in size at increasing
distances from the pupil. As the adaptive optics system within AOLI is designed to be a low-order
system, sensitivity to the mid- and low-orders is important. By investigating the development of
the speckle structure with distance, the inner plane distance was specified to be within the region
±200-350 km and the outer planes to be at ±550-750 km.
5.4 Developing the wavefront reconstruction algorithm
Previously, the effects and considerations when propagating wavefronts numerically have been
discussed (see Section 4.3.3). With these requirements in mind, I undertook initial wavefront
reconstruction development in Matlab to allow a full investigation of the methodology and
strategies for improvement over the standard Gerchberg-Saxton error reduction algorithm.
Initial work focused on the development of a suitable propagation algorithm for both forwards and
backwards propagation from the pupil aperture based upon the two-step propagation technique
(see Section 4.3.3). The propagation algorithm was verified using standard results e.g. the recovery
of the Airy disk pattern when a uniform amplitude and phase within a circular aperture is used as
the input for reconstruction. The effects of low-order zernike polynomials were also verified.
68
Investigation and simulation of the nlCWFS
Fi
gu
re
5.
4:
Th
e
pr
op
ag
at
io
n
of
lig
ht
(i
nt
en
si
ty
)f
ro
m
th
e
pu
pi
lp
la
ne
of
a
te
le
sc
op
e.
Th
e
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pi
l(
sh
ow
n
in
th
e
ce
nt
re
)h
as
un
if
or
m
ill
um
in
at
io
n
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d
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ph
as
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lu
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to
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h
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ul
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rb
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at
m
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ph
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n
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th
er
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de
of
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e
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l,
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e
in
te
ns
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ea
ks
in
to
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kl
es
.T
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al
le
r
sp
ec
kl
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ow
th
e
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gh
er
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de
r
st
ru
ct
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e
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d
ar
e
lo
ca
te
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ne
ar
er
to
th
e
pu
pi
lw
hi
le
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e
la
rg
er
st
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ct
ur
e,
w
hi
ch
sh
ow
s
th
e
lo
w
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de
rs
,d
ev
el
op
s
as
th
e
pr
op
ag
at
io
n
di
st
an
ce
is
in
cr
ea
se
d.
69
5.4 Developing the wavefront reconstruction algorithm
With the propagation techniques in place, the basic reconstruction process based upon the
Gerchberg-Saxton method was investigated. While this may not be the fastest technique for
convergence as discussed in Section 4.1.1, it does converge to a phase estimate and provides a
simple technique to investigate other effects. The recovery of a selection of sample pupil
wavefronts can be seen in Figure 5.5.
5.4.1 Low photon number reconstruction
In the regime of low photon rates, binning of pixels on CCD detectors is typically used. By doing
this however, the effective pixel spacing of an image is increased and above a certain level this
increases errors in phase retrieval algorithms as small scale structure is lost (see Section 4.3.3). To
understand the effect of this, Peter Aisher, a Part III student at Cambridge, undertook
investigations to focus on using pre-processing techniques with unbinned data prior to the use of
a phase reconstruction algorithm.
The challenge with working in the low-photon number regime is that a pixel which receives no
photons contains no information regarding amplitude and therefore phase. Several processing
methods are available to interpolate image data with small numbers of detected photon events
to attempt to alleviate this issue. With the AOLI wavefront sensor using EMCCDs in photon-
counting mode, it is possible to use a Gaussian convolution for each photon detected. In addition,
as the image plane pairs are at different distances from the pupil, each will have different speckle
scales, so instead of a fixed convolution scale being used, different convolution scales can be used
for each pair i.e. differential Gaussian convolution (DGC). Further methods of interpolation include
area-weighted triangulation filling (AWTF) using Delaunay triangulation and polygon filling using
Veronoi tessellation (Aisher et al., 2012).
The pre-processing methods were investigated using the Input-Output algorithm in the standard
reconstruction process (Fienup, 1982). The DGC and AWTF algorithms were applied to simulated
low photon number data before being used in the reconstruction. These were compared to the
standard method without pre-processing.
Both methods show significant improvements over the standard Input-Output algorithm as shown
in Figure 5.6. DGC can be thought of as a ‘smearing’ effect preserving the location of the photon
count while AWTF distributes the photon intensity over a region. Both methods are particularly
effective for low-order correction as these modes are more spatially spread over the image plane.
AWTF offers a slight benefit compared to DGC although due to the processing involved it requires
significantly more computing time.
70
Investigation and simulation of the nlCWFS
(a) Astigmatism: Z(2,2)
(b) Coma: Z(3,-1)
(c) Astigmatism: Z(6,-2)
(d) Composite input with defocus, coma and trefoil [Z(2,0), Z(3,-1), Z(3,3)]
Figure 5.5: The recovered wavefront after 100 iterations of the Gerchberg-Saxton algorithm for selected
Zernike polynomials. The left hand column shows the recovered phase while the right hand column
shows the input phase at the pupil.
71
5.4 Developing the wavefront reconstruction algorithm
Figure 5.6: Simulated low photon number performance of the Input-Output algorithm with and
without pre-processing. DGC, AWTF and no pre-processing provide little or no correction up until
around 100 photons are detected. Beyond this, the pre-processing methods begin to perform better
until the high photon regime where the conventional method has a lower RMS. The dotted lines show
the upper and lower quartiles. The AWTF method was only used below 2000 photons. Vertical lines
show the I-band magnitude for a nlCWFS running at 10Hz for D=4.2 m (lower label) and D = 10.5 m
(upper label) (Crass et al., 2012).
72
Investigation and simulation of the nlCWFS
5.4.2 Defining a prior for reconstruction
In Section 4.2, it was discussed that initially the best candidate for commencing the reconstruction
process is a plane wavefront which, as a first estimate, is a good approximation. Observing the
wavefront estimate after each iteration of the reconstruction process demonstrates a gradual
convergence towards the actual wavefront value. The low-order effects which contribute the
strongest power to the phase, dominate the reconstruction and it is only when these, in particular
the tip-tilt component, have stabilised that the higher-order components (with significantly
smaller amplitude) are able to be reconstructed. This process is shown in Figure 5.7.
The stepping process observed significantly limits the speed of convergence of the wavefront and
increases the time for reconstruction. With the real-time nature of adaptive optics, it is important
to try and overcome this limitation and reduce the number of iterations required to converge on an
accurate wavefront estimate. The most obvious way to consider this is by obtaining a prior with
the correct tip-tilt value before reconstruction.
One possible method of recovering the tip-tilt component of the phase within the pupil plane is by
looking at the offset from the ‘straight-through’ position of the beam at the imaging planes i.e. the
path when an input wave with uniform phase and amplitude is propagated through the system.
The straight-through position can be calculated either with a calibration source (e.g. a collimated
beam from a point source) or by time-averaging the recorded images with a Kolmogorov based
turbulent phase at the aperture. The effects of this offset can be seen in Figure 5.8.
The principle of recovering the tip-tilt from the imaging planes, as shown in Figure 5.9, can be done
with the use of geometric optics. The amplitude of the tip-tilt component, x, is given by
x =
a sin θ
2
(5.1)
where a is the diameter of the aperture and θ is the offset angle. The offset of the beam from the
straight through position is given by
d = z tan θ (5.2)
where z is the distance from the aperture to the imaging plane. By using the small angle
approximation, tan θ ≈ sin θ ≈ θ, the above equations can be combined to give
x =
ad
2z
. (5.3)
Numerically, the simplest way to calculate the offset between the imaging planes is through the
use of the cross-correlation function (CCF). The cross-correlation of two functions gives a measure
73
5.4 Developing the wavefront reconstruction algorithm
(a) Initial phase estimate for reconstruction (b) Phase estimate after 10 iterations
(c) Phase estimate after 30 iterations (d) Phase estimate after 60 iterations
(e) Phase estimate after 90 iterations (f) Actual phase at the pupil
Figure 5.7: The wavefront reconstruction of a simulated tip-tilt dominated wavefront. The
reconstruction begins from an initial estimate with constant phase. The gradual convergence towards
the actual pupil phase can be seen with the increasing number of iterations.
74
Investigation and simulation of the nlCWFS
50 100 150 200 250 300
50
100
150
200
250
300
(a) Position of ‘straight-through’ beam at ±700 km
50 100 150 200 250 300
50
100
150
200
250
300
(b) Position of beam with tip component at -700 km
50 100 150 200 250 300
50
100
150
200
250
300
(c) Position of beam with tip component at +700 km
Figure 5.8: The simulated effect of a tilt component on a propagated beam at 700 km from a 4.2 m
aperture.
75
5.4 Developing the wavefront reconstruction algorithm
Figure 5.9: The basis of recovery of the tip-tilt component relative to straight through beam.
76
Investigation and simulation of the nlCWFS
of the similarity of the functions as one is gradually offset relative to the other. The peak in the
CCF occurs at the offset where the two functions are most similar. In Figure 5.8, the two planes
either side of the pupil show a similar structure which is offset from the ‘straight-through’ beam
due to the tip-tilt component. By performing the CCF on a pair of images equidistant from the
pupil, the offset can be calculated, giving a value of twice the image offset i.e. 2d. For the nlCWFS,
it is preferred to use the inner imaging planes for this process as, although the tip-tilt offset will be
less, the cross-correlation is improved due to minimal other low order effects which would adjust
the shape of the beam at the imaging planes.
The two-dimensional CCF can be performed using the ‘brute force’ method where one imaging
plane is moved relative to each other changing the location one pixel at a time. This is
computationally expensive however, requiring O(N2) calculations where N is the number of
pixels in the image. A more efficient way to calculate the CCF is by considering its relationship
with the convolution.
For the simple case of two one-dimensional functions, f(x) and g(x), the CCF is defined as
C(η) = f ⊗ g =
∫ ∞
−∞
f∗(x) g(x+ η) dx (5.4)
where f∗(x) is the complex conjugate of f(x) and η is the offset. By using the Wiener-Kinchin
theorem, we can write that the Fourier transform of the cross-correlation of f(x) and g(x) as
C˜(k) =
√
2pi [f˜(k)]∗ g˜(k) (5.5)
i.e. the Fourier transform is just the product of the individual Fourier transforms multiplied by√
2pi. To obtain the CCF from the output of this multiplication, it is simply a case of then taking the
inverse transform.
Expanding this example to the two-dimensional case allows the offset in both the x and y directions
to be calculated.
As previously discussed, Fourier transforms are particularly well optimised operations particularly
with advancing computing hardware such as GPUs. By undertaking this method rather than the
brute force approach, the computational time is O(N logN) offering a significant speed up, vital
for use in a real-time application.
Tip-tilt and phase unwrapping
The cross-correlation technique of recovering the tip-tilt offers an independent measure of the
strongest phase distortions at the pupil plane. These distortions are the dominant component
77
5.5 Summary
within the overall value of the phase as higher-order distortions have a lesser effect.
The calculated tip-tilt values provide a potential reference surface to use during phase unwrapping.
While other techniques previously discussed can be employed, this method provides additional
information to aid the process. While the tip-tilt component will vary with time, this will be more
slowly varying than the higher-order components and as such, the cross-correlation only needs to
be undertaken every few frames to maintain an accurate reference for this process. Alternatively, it
may be possible to use the previously unwrapped phase as an approximate reference.
Subsequent reconstructions
Once a phase value has been successfully recovered using the reconstruction algorithm, it is likely
this will be a significantly better prior for the reconstruction process compared to either a plane
wavefront or the tip-tilt information. This assumes however that the total computation time to
recover a wavefront is less than that of the coherence time which will ensure some level of
correlation between the recovered wavefront and the one being recorded at the image planes.
Having a better prior will, theoretically, lead to a reduction in the number of iterations required to
obtain the next reconstructed wavefront which in turn will mean an even better prior. The
challenge however is to achieve the minimum quality of reconstructed wavefront to enter this
regime as without it, one will always need to return to the tip-tilt information to begin the
wavefront reconstruction process.
5.5 Summary
The investigation of the non-linear curvature wavefront sensor has been undertaken using two
principal simulation tools. The C++ package Arroyo has been used to verify the characteristics of
beam propagation through a nlCWFS system, simulating both Fresnel propagation and
Kolmogorov type turbulence. The simulations showed that chromatic effects are particularly
strong due to the need for Fresnel propagation and these must be mitigated to allow good
constraints at the imaging planes. In addition, a verification of beam size rescaling and equivalent
plane distances was performed.
Following on from the simulation work, the reconstruction algorithm for the nlCWFS was
implemented. This development was undertaken in Matlab to allow an understanding of the best
strategies and processes to employ. The outcome of this work has demonstrated, with simulated
data, the ability to recover the input phase with only amplitude constraints at the image planes
and the pupil mask. To speed up this process, an improved prior for the initial estimate of the
reconstruction can be found by taking the cross-correlation of the two inner-imaging planes to
78
Investigation and simulation of the nlCWFS
calculate their relative offset. This however should only be needed for the first iteration of the
algorithm as once a good wavefront fit has been recovered, this should be used as the prior for the
subsequent iteration.
79
5.5 Summary
80
“A scientist can discover a new star,
but he cannot make one. He would
have to ask an engineer to do that.”
Gordon L. Glegg
6
The AOLI instrument: Optical design
Following on from the simulation work described in the previous chapter, several test-bed
systems were employed to further develop an understanding of the non-linear curvature
wavefront sensor from its theoretical basis to a practical application. The design of these systems
and the understanding gained from each is discussed in this chapter before presenting the optical
design for the first light use of AOLI on the William Herschel Telescope in September 2013 and
modifications since then. The optical design work for AOLI has principally been undertaken by
David King. The implementation and building of the AOLI optical system has principally being
undertaken by David King and I. I have led the work on the development systems.
6.1 Development systems and verification
6.1.1 Thorlabs AO kit
To investigate the effects of nlCWFS, an Adaptive Optics Kit from Thorlabs was used to provide a
controllable beam and reference sensor. The system comprises a 635 nm laser diode source
providing a 4 mm diameter beam which passes through a one-to-one reimaging optics train onto a
81
6.1 Development systems and verification
140 actuator gold-coated MEMS deformable mirror. The beam is then reimaged once more onto a
Shack-Hartmann wavefront sensor comprising a 39x31 lenslet array and CCD detector run at
15 Hz. The layout of the system can be seen in Figure 6.1.
The deformable mirror actuators are arranged in a 12x12 square grid (the corner elements are
inactive) providing a total aperture size of 4.4 mm square. The maximum displacement of each
actuator is 3.5 microns and the mirror surface has a reflectivity greater than 90% from
600-1100 nm.
Initial tests with the system were undertaken to verify the rescaling of the beam and the validity
of the Fresnel Number conservation as discussed in Section 5.3. This was achieved by reimaging
the beam through a combination of lenses to reduce the beam to 1 mm in diameter. This beam
was then aligned with a conventional CCD detector from Opticstar mounted on a movable stage
to allow different imaging planes to be recorded. This allowed both the recording of the imaging
planes as well as verifying the position and illumination of the pupil plane.
System limitations
While the Thorlabs kit provided an excellent tool to investigate the fundamental phenomena of
the nlCWFS, its design limits its capability for multi-wavelength investigation, principally due to
the reimaging lenses in the system being singlets designed for use with the laser diode source. As
such, although a second laser beam at 532 nm was combined into the system, the capabilities of the
system to investigate chromatic effects were limited.
6.1.2 AOLI development system
Following on from the work with the Thorlabs AO Kit, a first stage design of the AOLI instrument
was developed. To further investigate the nlCWFS technique, this initial design was implemented
using off-the-shelf optics and standard components to minimise cost.
The system was based around the common optics of the AOLI design (see Section 6.3.1) before
being reimaged to reduce the beam diameter. The conventional CCD detector from the Thorlabs
AO Kit setup was again used on a mountable stage to record imaging planes either side of the
pupil. The use of the common optics fed from a focal plane allowed both monochromatic and
narrowband (maximum 100 nm bandwidth) illumination of the system.
While the system only allowed a narrow bandwidth of light, it proved to be a particularly useful
tool for investigating the chromatic effects of the nlCWFS, the outcome of which heavily influenced
the optical design of the wavefront sensor module as discussed in Section 6.3.3. In addition, the
beam diameter passing through the common optics was large enough to allow the testing and
82
The AOLI instrument: Optical design
(a) The optical design for the Thorlabs AO kit and reimaging optics. A neutral
density filter (not shown) was added to the system at the pupil plane after the
pellicle to reduce the intensity at the CCD detector.
(b) The Thorlabs AO kit delivering a controlled phase distorted beam to a
movable CCD detector. The AO kit can be seen centrally with the deformable
mirror and its control cables being located on the raised stage and the Shack-
Hartmann reference sensor being located on the right hand edge of the optical
breadboard. The beam is then reimaged, reduced in intensity and folded before
being recorded on the stage mounted CCD shown at the top centre.
Figure 6.1: Thorlabs AO kit with reimaging optics to investigate the nlCWFS.
83
6.2 Deformable mirror selection
development of a deformable mirror from Alpao which now forms part of the final instrument
design.
6.2 Deformable mirror selection
Initial designs for AOLI were based around using the deformable mirror supplied with the
Thorlabs AO kit for wavefront correction. Early on in the design process however, it was
identified that this mirror would have insufficient stroke to provide correction for the
lowest-order and largest amplitude distortions. While a woofer-tweeter configuration (see Section
3.5.1) was considered, the preferred solution was to use a single mirror which could provide
appropriate levels of correction.
Members of the AOLI team at the Instituto de Astrofı´sica de Canarias identified a suitable mirror
being used as part of another project which offered the required levels of correction. This
deformable mirror, the DM97-15 from ALPAO, is a classical type of deformable mirror however its
actuators are based upon a new solenoid technology. This new type of actuator offers significantly
more stroke than previous technologies and as such allows a single mirror to be used within the
AO correction system. The full characteristics of the DM97-15 can be found in Table 6.1.
DM97-15 DM241-25
Number of actuators 97 241
Pupil diameter ( mm) 13.5 mm 37.5 mm
Actuators across diameter 11 17
Mirror best flat (RMS) 7.0 nm
Wavefront tip/tilt stroke (Peak to Valley [PtV]) 60µm 25µm
Inter-actuator stroke > 3µm(PtV)
Settling time ( ms at ±5%) 1.0 2.0
Coating Protected Silver
Table 6.1: Specifications of ALPAO DM97-15 and DM241-25 deformable mirrors (ALPAO, 2014).
Although discussions and plans were made to make the DM97-15 available for use within AOLI,
due to hardware challenges with another deformable mirror, it was re-tasked to another project.
Having already tested and investigated the technology, it was decided to pursue using another
deformable mirror based on the same technology to allow the one mirror configuration within the
84
The AOLI instrument: Optical design
optical system to be maintained.
When selecting a deformable mirror, the order of correction required governs the numbers of
actuators needed. For the WHT, the DM97-15 offered 11 elements across the diameter allowing
correction of turbulence scales down to around 40 cm in size. As the deformable mirror is the most
costly component of the entire optical system, work was undertaken to establish the level of
correction which would be required for AOLI at both the WHT and also on the larger 10.4 m GTC
which is the long term aim of the project.
After undertaking the calculations, the DM241-25 mirror was selected for purchase. This provides
both sufficient stroke to correct without the need for a tip-tilt mirror and allows scales of turbulence
down to around 60 cm to be corrected. The full specification is listed in Table 6.1.
6.3 Optical layout for the William Herschel Telescope
AOLI is designed for use within the GHRIL (Ground based High Resolution Imaging Laboratory)
enclosure on one of the WHT Nasmyth platforms as shown in Figure 6.2 . The telescope optics
provide a 4.18 m working diameter beam from a concave paraboloid primary mirror, via a
hyperboloid secondary and flat tertiary into the enclosure. This provides an f/11 beam as the
input to the instrument. To prevent rotation of the image with the tracking of the telescope, AOLI
uses the derotator designed for use with the CANARY instrument at the entrance aperture of the
GHRIL enclosure. This is specified to provide a 2.5 arcmin field-of-view with a pupil stability of
better than 1.5%.
AOLI can be used on two different optical benches, one owned by the ING and permanently based
at the WHT and the other, a Thorlabs bench, being specifically purchased for the instrument. Due
to instrument shipping constraints, for the first light run the ING bench was used to mount and
commission the instrument however it is expected during subsequent runs the dedicated AOLI
bench will be used. The beam from the telescope and derotator comes to a focus 100 mm onto the
AOLI bench and 10mm onto the ING bench and this location is used as the reference point for
optical alignment.
The full optical design for AOLI comprises four principal components:
1. Common optics to reimage beam from the telescope optics
2. Lucky imaging science camera
3. Non-linear wavefront sensor system
4. A calibration system
85
6.3 Optical layout for the William Herschel Telescope
(a) The 4.2 m William Herschel Telescope.
(b) AOLI being craned into the GHRIL enclosure on the Nasmyth platform.
Figure 6.2: AOLI at the William Herschel Telescope.
86
The AOLI instrument: Optical design
The positioning of each of these elements on the optical bench can be seen in Figure 6.3.
6.3.1 Common optics
The input beam from the telescope must be reimaged to provide the appropriate beam diameter
to illuminate the deformable mirror. This is done through a set of common optics, as shown in
Figure 6.4, comprising both ‘off-the-shelf’ components and custom lenses designed by David King
and manufactured by Rocky Mountain Instruments. The need for custom optics has principally
been driven by the need to provide diffraction limited imaging across a broad bandpass region
(500-1100 nm), maximising both the science use of the instrument and sensitivity of the nlCWFS.
The layout of the common optics is shown in Figure 6.4. The beam from the WHT focus passes
through a long-pass filter (with a cutoff wavelength of 500 nm) before being collimated and passed
through an atmospheric dispersion corrector (ADC) comprising two counter rotating prisms. The
beam is then reflected off the surface of the deformable mirror before being brought to a focal
plane where a pickoff mirror mechanism is used to reflect the light from a reference object to the
wavefront sensor system. For testing and development purposes, the deformable mirror can be
interchanged with 2” diameter circular plane mirror with a surface quality of λ/10.
6.3.2 Lucky imaging science camera
The lucky imaging based science camera is located directly after the pickoff mirror mechanism in
the optical train of AOLI. The camera uses four back illuminated EMCCDs from E2V Techologies
(CCD 201) each providing up to 25 frames per second when reading the full 1024×1024 imaging
region of the detector. A summary of the specification of the EMCCDs and their characteristics can
be found in Table 6.2 and Figure 6.5. Readout from and control of the CCDs is done using custom
electronics developed in Cambridge.
Characteristic Value
Active imaging area 13.3×13.3 mm
Active pixels 1024×1024
Pixel size 13×13µm
Operating temperature ( ◦C) -120 to +75
Table 6.2: Specification and characteristics of the electron-multiplying CCD201 from E2V Technologies
(E2V Technologies Limited, 2005).
87
6.3 Optical layout for the William Herschel Telescope
Figure 6.3: The layout of the AOLI optical bench showing the main components of the instrument.
The beam from the WHT telescope enters from the left before being collimated to a pupil plane at the
deformable mirror location. The beam is then refocused to a pickoff mirror plane before being split to
feed both the nlCWFS module and the science instrument.
88
The AOLI instrument: Optical design
Figure 6.4: The common optics layout of AOLI. Light enters the system from the telescope optics after
passing through the CANARY derotator. The light is recollimated and propagated to a conjugate pupil
plane where the deformable mirror is located. The beam is then refocused onto a pickoff mirror where
the light from a reference object is reflected into the nlCWFS module and the science light is transmitted
through the mirror mechanism.
89
6.3 Optical layout for the William Herschel Telescope
Figure 6.5: Quantum efficiency curve for the CCD201 at -20 ◦C (E2V Technologies Limited, 2005).
As the camera uses EMCCDs, it must be cooled to temperatures around -120 ◦C to minimise any
dark current. This is achieved by locating the detectors within a vacuum dewer cooled with liquid
nitrogen. In addition, due to the additional electronics required on EMCCDs compared to their
conventional counterparts, these detectors are non-buttable and as such each has a separate
window within the dewar as shown in Figure 6.6.
The incident beam from the pickoff mirror must be reimaged onto these four CCDs simultaneously
to provide a continuous field of view on the four detectors. This 2048×2048 pixel field is achieved
by collimating the beam from the pickoff location and then focusing the beam, using a 160 mm focal
length lens, onto a pyramid mirror which separates the field of view into four equal sections. Each
section is then reimaged separately onto an individual CCD with a separate set of filters as shown
in Figure 6.7. By having independent set of filters for each detector (R, I, Z, 630 nm long pass and
715 nm long pass filters for each detector with narrow band filters 488±10 nm and 500±10 nm in
two of the four detectors and 656±10 nm and 670±10 nm in the remaining two), the CCDs can be
used for a different purpose when imaging, for example a broader band-pass being used on one
camera to provide a high-signal to noise on a reference object and a narrower band being used for
science data collection.
The collimating lens after the pickoff mirror can be changed during an observing run to allow three
different magnifications/plate scales as shown in Figure 6.8. In the I band, the diffraction limit of
the WHT is ∼45 milli-arcsecond and to allow sufficient sampling of the PSF, the science camera
provides a pixel scale of between 18 and 55 milli-arcseconds. This allows the fields of view and
90
The AOLI instrument: Optical design
Figure 6.6: The AOLI science camera dewar - the four individual windows and EMCCDs are shown.
The additional electronics required for these types of detector are also visible surrounding the dark
detector region.
91
6.3 Optical layout for the William Herschel Telescope
Figure 6.7: Optical layout of the AOLI science camera showing the incoming beam being separated
into four separate beams by a pyramid mirror due to the EMCCD detectors being non-buttable. The
incoming beam (not shown) enters between the fold mirrors and is projected onto the pyramid mirror,
comprising four plane surfaces, which redirects the light onto relay mirrors. This is then reimaged
onto the EMCCD detectors.
92
The AOLI instrument: Optical design
Figure 6.8: Common collimating lenses located after the pick-off mirror plane. The focal lengths of the
lenses (from left to right) are 50 mm, 80 mm and 150 mm.
pixel scales to be matched with the science target being observed with a field of view ranging from
37.5×37.5 to 112.5×112.5 arcseconds.
In addition, a controllable iris is included just after the collimating lens to restrict the beam diameter
in the case of bad seeing conditions, increasing the probability of a ‘lucky image’ being recorded.
The entire science camera optical system is mounted on several mechanisms giving adjustment in
three dimensions. This allows the repositioning of the camera to change magnifying lenses, allows
the focusing of the instrument and facilitates an off axis imaging field to be selected, minimising
the requirements on telescope control and feedback.
6.3.3 Wavefront sensor design
As discussed in Section 5.3, the beam from the WHT can be rescaled to a smaller diameter to allow
the distance between a conjugate pupil and imaging planes to be chosen. This process however is
a trade-off between the size of detector, available space within the overall instrument and
maintaining sufficient separation between optical components to allow them to be mounted
accurately. In addition, as with any optical system, the smaller the beam size, the more stringent
the requirements on optical alignment to maintain the beam quality.
93
6.3 Optical layout for the William Herschel Telescope
The primary constraint for the rescaling used in AOLI is the need to maintain a sufficiently high
frame-rate from the EMCCD detectors used within the wavefront system. Two synchronised
detectors, identical in specification to those in the science camera and mounted in individual
dewars, are used within the nlCWFS system, each having two imaging planes recorded on it.
While this setup does place constraints on the optical layout of the wavefront sensor, it does
simplify the readout and control electronics for the cameras and reduce the overall cost.
The AOLI nlCWFS is required to run at∼100 Hz to provide the useful level of wavefront correction
to the science camera. To achieve this, only a limited region of the detectors, 1024×256, is read
out, delivering a frame rate just below four times that of the science detector with full read out.
The physical size of the imaging region is 13.31×3.33 mm and places an upper limit on the beam
size to fit within this region. Practically, the beam at the pupil plane needs to be smaller than this
limit to allow diverging beams which will increase in size as they propagate away from the pupil
(or conversely converging beams which will be largest before arriving at the pupil) to be fully
recorded.
To account for both of the conditions mentioned, a beam size of 2 mm was selected for propagation
from the pupil plane. To achieve this, a set of three lenses are used after the pickoff mirror to
reimage the reference object as shown in Figure 6.9.
Producing the four imaging beams
In Figure 6.9, the reimaging optics shown simply produce one beam. In this simple configuration,
it is only possible to image one plane at a time by simply moving the detector (as was done with
the demonstration systems discussed in Section 6.1.1). This setup, while useful for investigation is
not practical for real-time application within an adaptive optics system.
Previous systems have used an oscillating membrane to vary the effective distance between a pupil
and imaging planes (Guyon, 2007). This system works well for the case of two planes but poses
technical challenges, particularly for higher speed reconstruction. In addition, it fails to provide
any method to minimise chromatic effects within the system. An alternative approach to provide
four beams is to use fixed optical components to divide the incoming beam into four separate
beams. This is the method used within AOLI and allows each beam to be steered and reimaged
onto detectors with the correct plane distances from the pupil plane.
Conventionally, when producing multiple beams from a single source, beamsplitters are used to
divide the beam by intensity with a certain fraction of light being reflected and transmitted. While
this works well in a monochromatic case, as discussed previously the chromatic effects with the
wavefront propagation are particularly strong and splitting in intensity does nothing to minimise
this. Another possible solution is to split into equal wavelength bands by using dichroics. This
94
The AOLI instrument: Optical design
Figure 6.9: Layout of the nlCWFS reimaging optics relative to the common optics of AOLI. A
combination of three lenses, f =40 mm, 400 mm and 250 mm, are used to reimage the beam from
the pickoff mirror to a 2 mm pupil diameter after the last optical component.
95
6.3 Optical layout for the William Herschel Telescope
restricts each output beam to a quarter of the incident bandpass, reducing the chromatic effects in
each propagation and improving the quality of any wavefront reconstruction.
Fixed reimaging optics The initial optical design proposed for the nlCWFS used conventional
beamsplitting techniques to divide the beam from the pickoff mirror mechanism into four beams
of approximately equal intensity. This design used a combination of custom beamsplitters located
after a collimating lens as shown Figure 6.10. While efficient at producing the four beams at the
locations required for recording onto the EMCCD detectors, this system fails to control the
intrinsic chromatic effects previously discussed. While the use of dichroics embedded within the
beamsplitters was investigated, only the s-polarisation of light was sensitive to these surfaces and
the p-polarisation was unaffected making it no better than the beamsplitting approach.
The additional challenge of using this type of beamsplitter approach is that the distance of the
imaging planes from the pupil is fixed. As additional investigation of the imaging plane location
was one of the requirements of the nlCWFS setup, having a fixed distance makes this untenable.
Because of this and the challenge of minimising chromatic effects, an alternative optical design was
sought.
Dichroic splitting Due to the limitations of using fixed beamsplitters and dichroic splitting
between two glass surfaces, the optical design of the wavefront sensor arm was redesigned using
individually mounted components. This gives the advantage of allowing different wavelength
bandpasses to be tested by simply changing the dichroics. In addition, by varying the positioning
of the EMCCD detectors relative to the components, the distance from the pupil to imaging planes
can be adjusted. The optical layout of this design and implementation at the WHT can be seen in
Figures 6.11 and 6.12 respectively. The straight through beam from the first dichroic provides the
inner image planes while the reflected beam produces the outer. Each beam is re-collimated after
the first dichroic and then split in wavelength again with the reflected beam providing the
post-pupil imaging plane and the transmitted being the pre-pupil plane. The beams in each arm
are once again aligned using a D-mirror before being reflected vertically onto a single EMCCD
detector.
To maximise the overall sensitivity of the wavefront sensor, the widest overall wavelength range
should be used, however, this conflicts with need to minimise chromatic effects. The compromise is
to match the overall wavelength range to the regions of highest quantum efficiency on the EMCCD
detectors while staying within the diffraction limited regime of the optics and to divide this incident
light into regions of approximately equal sensitivity. With these constraints, the dichroic splitting
for AOLI provides beams with bandpasses of 500-600 nm, 600-700 nm, 700-800 nm and 800-950 nm.
The longest wavelength beam has a larger bandwidth due to the decrease in quantum efficiency
within this wavelength range.
96
The AOLI instrument: Optical design
(a) Optical layout of the nlCWFS after the common optics and pickoff mirror.
(b) Schematic showing the three beamsplitters within the optical reimaging
system.
(c) The reflected output from the cube beamsplitter is
reimaged and passed through a lateral displacement
beamsplitter to produce the two inner imaging planes.
(d) The transmitted output from the cube beamsplitter
is passed through a pentaprism beamsplitter to produce
the two outer imaging planes.
Figure 6.10: The nlCWFS setup using fixed beamsplitters.
97
6.3 Optical layout for the William Herschel Telescope
Figure 6.11: The optical layout of the nlCWFS beam splitting optics. The beam from the pickoff mirror
mechanism is shown at the top right and is initially split at a wavelength of 700 nm. The two beams are
then re-collimated independently before again being split at 600 nm and 800 nm as shown. The beams
are finally aligned together before being vertically folded onto the imaging detectors.
98
The AOLI instrument: Optical design
Figure 6.12: The nlCWFS optical components for wavelength splitting using dichroics. The beam
from the pickoff mirror enters from the left and is incident on the first dichroic which transmits light
between 500-700 nm and reflects 700-950nm. Both beams are then recollimated before again being split
with a second dichroic in each arm with transition boundaries at 600 nm and 800 nm respectively. The
reflected beam is passed through a ‘trombone’ to provide the increased path length required for the
post pupil imaging planes.
99
6.4 Calibration system
As each beam has a different wavelength, the effective distance of propagation differs from that for
the monochromatic case. There are two possible solutions to this issue:
1. Account for the modified distance during the software reconstruction by allowing image
planes to no longer be equidistant either side of the pupil plane.
2. Adjust the trombone in each arm of the wavefront sensor to account for the distance change.
For AOLI, the optical setup has been designed to account for the wavelength change and maintain
the Fresnel Number relative to the monochromatic case, specified at 700 nm. The image planes
selected are equivalent to those at ±200 km and ±650 km for a 4.2 m and are listed in Table 6.3.
4.2 m diameter beam 2 mm diameter beam
Plane distance λMonochromatic Plane distance λCentral
Effective setup for reconstruction
±200 km 700 nm ±45 mm 700 nm
±650 km 700 nm ±147 mm 700 nm
Physical setup for reconstruction
+200 km 700 nm +58 mm 550 nm
-200 km 700 nm -49 mm 650 nm
+650 km 700 nm +121 mm 850 nm
-650 km 700 nm -138 mm 750 nm
Table 6.3: Plane positions for rescaled beam diameters at different wavelengths. Positions are relative
to 4.2 m diameter aperture with an incident monochromatic wavefront at λ = 700 nm. For the 2 mm
beam, the listed wavelengths are for the bandpasses previously discussed.
It is important to note that the four beams from this system have different numbers of reflections;
neglecting the vertical fold, the beam which is transmitted through both dichroics is unreflected
while the beam reflected at both dichroics undergoes four reflections. While this is not a problem
optically, it is important that this is handled within the software for wavefront reconstruction,
performing the relevant image flips when necessary before undertaking reconstruction. The effect
of this flipping can be seen in Figure 6.13.
6.4 Calibration system
To facilitate laboratory testing, development and commissioning of AOLI, a calibration system has
been designed and constructed to feed an input beam into the common optics of the instrument
100
The AOLI instrument: Optical design
(a) Image showing the recorded inner imaging
planes for the nlCWFS. The left hand beam is the
post-pupil plane while the right is the pre-pupil
plane.
(b) Image showing the recorded outer imaging
planes for the nlCWFS. The left hand beam is the
pre-pupil plane while the right is the post-pupil
plane.
Figure 6.13: Images from the nlCWFS with no phase distortion prior to the pupil aperture. These
images have been recorded using the same 100 nm bandpass and beamsplitting optics. The left hand
image is recorded with the transmitted beam from the first beamsplitter (or dichroic) while the right
hand image shows the reflected beam. The pre- and post-pupil images are switched between the inner
and outer planes due to the trombone in each arm reflecting in the opposite direction.
simulating both the effects of the WHT and atmospheric turbulence. The first iteration of this
process has been led by the team at the Instituto de Astrofı´sica de Canarias with the optical design
for this system being shown in Figure 6.14. The system can be interchanged with the light from the
telescope by adding a fold mirror on the optical axis defined by the beam from the telescope.
The system comprises a single fibre used as a source which is collimated by an achromat lens from
Qioptic (f=600 mm). This collimated beam is passed through a phase plate encoded with phase
values consistent with the Kolmogorov model of turbulence before passing through an aperture
18.3 mm in diameter with a central obscuration and supporting spiders to simulate the WHT pupil
as shown in Figure 6.15. The beam from the aperture is brought to a focus with another achromat
from Edmund’s Scientific (f=200 mm) which provides an f/11 beam with a focal plane location
identical to that from the WHT optics. This allows the system to be used interchangeably with the
telescope during commissioning.
Differing diameters of fibre can be used as an input to the system. These include a 9µm fibre to
simulate a point source at the diffraction limit of the WHT in I band, a 62.5µm fibre for aligning the
system and a 200µm fibre to illuminate a focal plane mask. This mask can be located at the focal
plane after the final lens in the calibration system to allow the testing and verification of the science
camera. In addition, different brightness of the source feeding the fibre allow different magnitudes
of reference object to be simulated.
To accurately simulate the atmosphere, a custom phase plate was commissioned from Lexitek
simulating average seeing conditions at the WHT (r0=15 cm at 635 nm when illuminated with a
beam of ∼18.3 mm in diameter). This phase plate can be rotated to simulate the motion of the
turbulence layers within the atmosphere, the strongest effects of which are large scale motion i.e.
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6.4 Calibration system
Figure 6.14: The AOLI calibration system. The system comprises a fibre feed which is collimated
to provide an incident beam for a Kolmogorov simulated phase plate. The beam from the plate
is constrained with a pupil mask before being re-collimated to a focal plane. This figure has been
provided by Marta Puga Antolı´n.
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The AOLI instrument: Optical design
Figure 6.15: The pupil mask and phase plate of the AOLI calibration system. The pupil mask has been
manufactured to simulate the obscuration by the WHT secondary mirror and spiders to within 5%.
The phase plate has turbulence encoded within an annulus and as such, the beam can either be passed
through the annulus to simulate turbulent conditions or passed through the central region where no
turbulence is encoded.
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6.5 Mechanisms and software control
the wind. In addition, several other phase plates are available and these can be combined to
provide a multi-layered simulated turbulence. Currently, only one phase plate has been used
simulating a single atmospheric layer at an altitude of ∼5 km.
6.5 Mechanisms and software control
While many of the optical components within AOLI are fixed, in particular the common optics and
wavefront sensor, there are key locations in the instrument where optical components must be able
to be moved during observing:
1. Within the common optics, it is required that the deformable mirror is able to be interchanged
with a plane mirror for testing and development purposes.
2. At the pickoff mirror plane, different reflective spots must be able to be moved into the beam
to select the reference object.
3. The science camera must allow lenses to be interchanged to provide different magnifications.
For the first observing run, the change between the plane and deformable mirror was undertaken
manually as the aim of this run was to record data rather than apply a correction. The other two
mechanisms were designed and tested during commissioning.
6.5.1 Pickoff mirror mechanism
The pickoff mirror mechanism design for AOLI reflects a small section of the science field into the
wavefront sensor reimaging optics while allowing the rest of the light to be transmitted through to
the science instrument. This process is done by using a small reflective elliptical spot deposited on
a thin glass substrate.
Depending on the seeing conditions, different spot sizes may be required. For example, in very
good seeing (0.5 arcsec or better), using a large spot would obscure a larger area than required
however, in poorer seeing (>1.5 arcsec) a larger spot would be needed to ensure all the light from
the reference object is collected. With this in mind, it is useful to have multiple spots which can be
interchanged depending on the seeing conditions.
A range of different spots with a field size of 3/4 arcsec to 10 arcsec were selectable for use with the
instrument. These were individually coated in a circular pattern onto the substrate and each spot
can be rotated into the beam. The spots are sufficiently separated so only one lies in the science
imaging field at one time. The largest spots are principally designed to be used for alignment while
the small and intermediate spots are designed for use on-sky.
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The AOLI instrument: Optical design
In addition to having spots of different sizes, spots with two different reflection percentages were
produced at ∼50% and ∼95%. This allows light to be either fully reflected into the nlCWFS or
equally split between the WFS and science camera. For faint reference objects, as many photons as
possible need to be directed to the wavefront sensor to maintain a good signal-to-noise. However, if
using a bright reference object, splitting the light between the science camera and WFS allows both
a measurement of the wavefront and a measurement of the PSF of the reference object at the same
instant. This allows a comparison to be made between the two and also allows the same reference
object to be used for the lucky imaging processing.
The different reflection percentages were manufactured on two different glass substrates, each with
the range of pickoff spot sizes previously discussed. As such, the pickoff mirror mechanism uses
a lateral shift to interchange the two glass plates as well as having the ability to rotate each plate
individually.
6.5.2 Camera mechanisms
As shown in Figure 6.8, the science camera has three interchangeable lenses to vary the image
size and scale at the EMCCD detectors. To allow these to be positioned correctly, each needs to
be moved into the beam from the pickoff mirror and located at an appropriate distance from the
pickoff mirror mechanism to produce a collimated output. This sets the requirement to be able to
move both the lenses as well as the full science camera relative to the pickoff mirror mechanism.
In addition, to select the relevant section of the imaging field relative to the reference object, the
whole mechanism can be moved laterally and vertically. The overall system with the mechanisms
is shown in Figure 6.16.
6.5.3 Camera control and software
Many of the control systems and software used with AOLI are based around the software
previously written in Cambridge for the LuckyCam instrument. Mechanism control is undertaken
through a centralised control interface which sends the relevant commands to a controller box
while camera control and data collection is undertaken with two pieces of software, Lucky Console
and PixCel, shown in Figure 6.17.
EMCCD camera electronics and control
The EMCCDs used with AOLI have a custom set of electronics attached to each detector. These
electronics control the configuration of the cameras, their temperature through on-board heating
systems as well as starting and stopping data readout. The systems have been designed and built in
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6.5 Mechanisms and software control
Figure 6.16: The science camera mechanism structure. The EMCCD dewer is mounted at the top of a
support structure containing the pyramid mirror and reimaging optics. The entire mechanism can be
raised vertically through the use of two lab jacks while the lateral and perpendicular movement and
lens positioning is done with linear slides. These mechanisms are all driven with stepper motors. The
pickoff mirror mechanism can be seen in the bottom right of the image.
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The AOLI instrument: Optical design
Cambridge and are based around the same technology used in the LuckyCam instrument (Mackay
et al., 2010). Each detector is effectively standalone with its own electronics and control interface.
Although each camera is independent, it is important for both science observations and wavefront
sensing that data taken by the cameras is synchronised.
Lucky Console Lucky Console is a command line program designed to provide the interface to
the camera controllers and works over a serial to USB interface. Each individual camera has its own
configuration parameters which are loaded, through Lucky Console, at the time of initialisation to
govern or monitor physical characteristics of each detector. The program allows the gain of the
detector to be set, provides a monitor of temperature and frame rates and can allow triggering of
the detector to start and stop data collection.
Camera synchronisation When recording observations of a target source, a single reference object
is typically used within the field which will only be imaged on one detector. As such, the images
from this detector will be used for ranking frame quality and to maintain the characteristics of
image processing (e.g. photometry), it is important that all cameras are synchronised together. For
wavefront sensing, it is vital that the data recorded at each imaging plane is for the same wavefront
distortion at the pupil plane. To achieve this, both wavefront sensor cameras must be synchronised.
In addition, there is a requirement for developing post-processing data techniques that both the
wavefront and science camera data be synchronised.
The clock speed within the electronics on all camera boards is run at between 27.5-30.0 MHz giving
a frame rate of between 22-24 fps with full detector readout (1024×1024). This is slower than the
coherence time of the atmosphere and as such is too slow for the wavefront sensor images. To
counter this, a limited region of the detector is read out, as discussed in Section 6.3.3, giving a
frame rate of 88-96 fps.
Synchronisation between cameras when working at these speeds can be challenging to maintain;
if the synchronisation fails there can be significant interference between the imaging detectors.
The cameras are set up to share a common clock and trigger signal from one ‘master’ camera with
all of the others running as ‘slaves’. This is achieved through the use of on-board circuitry within
the science camera dewar or with external cabling between the two wavefront sensor dewars.
Signals from the master camera control the data acquisition on the other detectors although all
other characteristics e.g. the gain are still controlled separately. The complication with the AOLI
configuration is that the wavefront sensor cameras must provide a higher frame rate and as such,
additional electronics are required to manage this multi-frame rate configuration.
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6.5 Mechanisms and software control
(a) Interface for Lucky Console, the control software for the EMCCD
detectors.
(b) PixCel, the data acquisition and storage software used with AOLI.
Figure 6.17: The AOLI EMCCD control software.
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The AOLI instrument: Optical design
Camera data
Data from the EMCCD detectors is transmitted via high speed interface cards into standard
computer systems running Windows. The output from two cameras can be collected with one
Adlink PCIe-7300A card and multiple cards can be used within the same computer system. For
the science camera system, the four cameras are input into one machine via two interface cards
while the wavefront sensor detectors are input into a separate machine.
The input from the interface cards is processed using software developed in Cambridge called
PixCel. This software has been designed for high speed imaging, in particular lucky imaging, and
has many features for doing real-time analysis. The software also handles data storage, a particular
challenge with this kind of technique. Two different versions of the software are used; one for the
four detector configuration in the science camera and the other for the two camera configuration in
the wavefront sensor.
Raw data rates for each EMCCD detectors is around 50 MB/s. For the science camera machine,
the raw data totals over 200 MB/s which must be compressed before being stored due to hard
drive write speed limitations. This process, all handled within PixCel, produces custom-format
compressed data files with several frames included within each file.
6.6 Current optical design
Following the first light run on the WHT in September 2013, the layout of the components of AOLI
were re-evaluated following several challenges (see Sections 7.1.2, 7.2, 7.3.1 and 8.2). The principal
challenge with the system was the accurate selection of the reference object from the pickoff mirror
mechanism. To improve this process, the science camera and wavefront sensor positions have been
switched so that the reference object is transmitted through the pickoff mirror mechanism while
the science beam is reflected. To allow this change to occur with the science mechanism fitting fully
on the optical bench, the deformable mirror has been adjusted to reflect the beam in the opposite
direction from the original design. This has required the calibration system to be relocated and
folded. The new optical layout is shown in Figure 6.18.
6.6.1 Improvements to the AOLI calibration system
During the first on-sky run with AOLI at the WHT, several issues were identified with the current
calibration system particularly relating to the optical quality of beams within the wavefront
sensor. Upon further investigation (see Sections 7.3.1 and 8.2), it became clear that there is a
significant chromatic focal shift due to the optical quality and specification of the lenses within the
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6.6 Current optical design
Figure 6.18: The current optical design of AOLI. The newly designed calibration system is shown
providing a broadband feed to the WHT focal plane. The common optics, comprising the same
components as previously used, have been reconfigured to account for the beam from the deformable
mirror being reflected in the opposite direction. The beam is refocused to the pickoff mirror where the
light to the science camera is reflected and the reference for wavefront sensing is transmitted to the
WFS module.
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The AOLI instrument: Optical design
system. This effect means that instead of a single focal plane being produced after the final lens in
the system, each wavelength comes to a focus at a slightly different distance after the lens. The
focal shift at this location means the beam being input into the common optics does not correctly
collimate at all wavelengths and, due to the optical path length of the system, the effect becomes
exacerbated with increasing propagation through the system. As each beam within the wavefront
sensor arm works at a different wavelength and this wavelength splitting is done as the final stage
in the instrument, this effect is clearly noticeable.
The calibration system is currently being redesigned to remove these chromatic effects. This is
achieved by replacing the lenses with chromatic characteristics with reflecting off-axis paraboloids
as shown in Figure 6.19. In addition, the phase plate is being repositioned as close to the pupil
plane as possible to simulate ground layer turbulence.
6.7 Summary
The optical design of AOLI has two distinct goals; to provide diffraction limited imaging from
the WHT optics to a lucky imaging based science camera and to generate the four imaging planes
required for the non-linear curvature wavefront sensor. To define the full optical requirements of
the instrument, several demonstration systems have been developed allowing simulation work, in
particular of chromatic effects, to be verified and practical challenges to be addressed. This work
has culminated in an optical design which was used on-sky at the William Herschel Telescope in
September 2013 as discussed in Chapter 7.
The science camera for AOLI uses reimaging optics to provide an image with a field-of-view
ranging from 37.5×37.5 to 112.5×112.5 arcsec recorded onto four EMCCD detectors. The data
from these detectors is collected and they are controlled using custom software developed in
Cambridge. The same type of EMCCD detectors are used within the nlCWFS module where four
beams, generated using dichroic splitting and each having a different wavelength range, are
imaged onto a sub-section of the detector area. This allows readout at the required frame-rates for
wavefront sensing.
To allow development away from the telescope, a calibration system has been designed to
simulate light from the WHT beam. This includes a simulated point source, pupil mask and
ground-layer turbulence simulation. The system is currently being modified to remove chromatic
effects allowing simulation across the full wavelength range of the instrument.
Work is currently continuing to refine the AOLI optical design and mechanisms to remove any
residual systematic effects within the system. This work is discussed in Chapter 8.
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6.7 Summary
Figure 6.19: The AOLI calibration system using off-axis paraboloids. The system is designed to provide
diffraction limited imaging to the WHT focal plane of AOLI with a common focus location from 500-
950 nm.
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“What is a scientist after all? It is a
curious man looking through a
keyhole, the keyhole of nature, trying
to know what‘s going on.”
Jacques Cousteau
7
Observing at the William Herschel Telescope
The first on-sky observing run for AOLI took place on the nights of the 24th and 25th September
2013 at the William Herschel Telescope. The goal of this run was to test and verify AOLI and
its components and record data for post-processing analysis. This can be broken down into four
principal aims:
1. To collect data from the nlCWFS for post-processing analysis and reconstruction.
2. To collect data using the science camera to verify its optical quality and sensitivity.
3. To collect synchronised data between the nlCWFS and science camera to allow comparison
between reconstructed wavefronts and the science image.
4. To collect data with the calibration system to verify its characteristics against on-sky data.
7.1 Instrument commissioning
The majority of components for AOLI were transported to the WHT from Cambridge having been
tested, constructed or used within the AOLI development system. To minimise shipping
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7.1 Instrument commissioning
requirements, many components were disassembled for shipping although where possible,
mechanisms and other optical support structures were transported intact. The calibration system
was shipped from the IAC in Tenerife.
To further help with transport, the decision was taken for the first light run to use the common use
optical bench owned by the Isaac Newton Group to build the instrument rather than the
dedicated AOLI bench. With this in mind, ten days were scheduled for construction, alignment
and commissioning of the instrument prior to the on-sky time.
7.1.1 The commissioning process
The commissioning of AOLI was initially carried out in the aluminising area on the ground floor
of the telescope building prior to the instrument being installed in the GHRIL. This was due to the
CANARY instrument, which also uses the Nasmyth platform, being on-sky five days before the
AOLI run. In addition, the aluminising area offers additional space for construction compared to
the limited space within the GHRIL.
The rebuilding of AOLI was divided into three main areas, the common and nlCWFS optics, the
science camera system and the calibration system. The work on the common and nlCWFS optics
was undertaken by myself and David King.
It is critical when not constructing an instrument in situ that the alignment of the bench and
optical axis matches well with that of the beam from the telescope optics. To achieve this, an
alignment laser is installed between the two Nasymth plaforms at the WHT which is aligned with
the optical axis of the telescope. Measurements were taken by members of the IAC staff in
advance of commissioning to measure this beam height relative to the surface of the ING optical
bench. These measurements were used to set the optical axis for rebuilding AOLI.
7.1.2 Commissioning challenges
During commissioning, several issues were identified with mechanism and support structures
within the system. These included:
1. The pickoff mirror mechanism not reliably returning to the same position when commanded.
This made the selection of a reference target particularly challenging.
2. Problems with supporting the reimaging lens in the nlCWFS system directly after the pickoff
mirror mechanism.
3. A misalignment within the calibration system due to mounts for the optical components
centering the optics off the optical axis.
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Observing at the William Herschel Telescope
4. An electronics problem on the science camera developed during the shipping which meant
that only one EMCCD was fully operational. This limited the field of view of the camera but
still permitted testing of the instrument and its capabilities during the commissioning run.
Pickoff mirror mechanism
As described in Section 6.5.1, the pickoff mirror mechanism in AOLI uses two glass substrates, each
of which can be placed in the beam through lateral movement and individually rotated to select
a pickoff spot. Upon alignment of the full instrument, it became apparent that the mechanism,
although stable, failed to provide a repeatable position for the pickoff spot. This was principally
due to the pickoff mirror spots not being centred around the axis of rotation which only became
apparent when undertaking the full alignment process. For each spot, both the lateral movement
and rotation needed to be corrected and the resolution of the control on the rotational control failed
to allow this.
An alignment process using the illumination of the pickoff plane was attempted and although
successful, this was particularly time consuming and was not suitable for use on-sky. With this in
mind, it was decided to use a fixed 2 arcsec pickoff mirror spot for observations which was aligned
in advance.
nlCWFS lens support
The short focal length (40 mm) of the lens directly after the pickoff mirror caused significant issues
for beam alignment in the nlCWFS. Due to the distance between this component and the imaging
detectors being around 2 m, any slight angular offset of this lens from the optical axis leads to a
significant shift by the time the beam is recorded. As such, the alignment of this component is
critical.
On the optical bench, the region below the lens was obstructed by the support structure of the
pickoff mirror mechanism. As such, the lens had to be attached to the bench further away from
the mechanism and supported to allow its correct positioning. To achieve this, a standard optical
support was used with the lens located in a 6 inch lens extension tube.
During the commissioning process, it became clear that this supporting technique would not
provide the required level of stability for this lens. While the lens could be aligned correctly
within the system, due to general background motions and vibrations, the positioning could
deviate. To alleviate this, an additional support structure was constructed over the pickoff mirror
mechanism to provide the additional stability required for the lens positioning.
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7.2 Challenges during observing
7.1.3 Installation in the GHRIL
With AOLI being built and commissioned on the ground floor of the WHT building, it was
necessary for the instrument to be craned into the GHRIL enclosure. This was undertaken on the
23rd September by the ING staff to ensure sufficient time for final commissioning on the Nasmyth
platform.
Upon installation in the GHRIL, the optical alignment was checked using the alignment laser
between the two Nasymth platforms and the optical axis of AOLI. Initial indications showed a
significant misalignment of the beam between the telescope and the instrument.
On further inspection, it became clear the beam was not horizontal relative to the bench and
varied with the rotation of the CANARY derotator implying the stability of the derotator was well
outside of its specified range. A report documents the full details, however, at the largest ranges of
deviation, by the time the beam had propagated through the optical train it failed to enter the WFS
module correctly (King, 2013b).
Due to the limited time before on-sky observing, a decision was made to use the derotator in a fixed
position. While it would have been preferable to remove it fully from the optical path this would
change the location of the WHT focus on the optical bench. The derotator was fixed in position at
a setting of approximately 180◦. The required correction for the beam deviation was applied with
the two fold mirrors in the common optics.
The testing and identification of the derotator issue took a significant portion of the final testing
time allocated for AOLI in the GHRIL. In addition, due to the constraints on beam rotation and
alignment, this limited AOLI to a reduced functionality.
Following the adjustments to the common optics to account for the issues with the derotator, the
calibration system was realigned with the system. This was to allow final testing of both the
science camera and wavefront sensor alignment after the installation in the GHRIL. This process
was completed just prior to dusk on the 24th September, the first night of observing.
7.2 Challenges during observing
After the commissioning process, it was hoped that the observing nights would be much less
eventful! There were significant challenges with the weather conditions on the observing nights
which significantly limited the overall instrument verification. In addition, there were a few other
technical challenges, although these did not prevent instrument verification being undertaken.
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Observing at the William Herschel Telescope
7.2.1 Weather conditions
Both observing nights were significantly impacted by bad weather conditions with 4 hours and 20
minutes being lost on the night of the 24th September (with an additional 5 minutes technical time)
and 5 hours and 52 minutes being lost on the 25th. These weather conditions limited the number of
targets able to be observed with the seeing rapidly fluctuating between at best, around 1 arcsec and
at worst, greater than 5 arcsec. This caused significant issues in the wavefront sensor imaging data
where the 2 mm beam was imaged onto a 3.3 mm imaging region. With the significant turbulent
effects, the strongest of which were tip-tilt and defocus, the beams on the first night of observing
frequently went outside of the imaging region on the EMCCD detector. The effects of the poor
seeing conditions can be seen in Figure 7.1.
For the second night of observing, I proposed a change to the alignment of the nlCWFS to allow
a larger imaging region on the EMCCD to be used. The region was changed from 256 pixels in
height to 512 pixels. This increased the imaging region for each beam to 6.66 mm for a 2 mm pupil
diameter which provided sufficient coverage to record the displaced beams as shown in Figure
7.1. The trade-off for having this increased readout region is a slower frame rate of approximately
45 Hz. This would be insufficient for undertaking high accuracy wavefront correction but was
sufficient to record useful data for verification purposes.
With the poor weather conditions, it was decided to use the close time of the telescope to obtain
data with the calibration system and verify the characteristics of the AOLI instrument. The results
of these tests are presented in Section 7.3.
7.2.2 Wavefront sensor camera dewar
As part of running the EMCCD detectors, it is important to monitor their temperature to ensure
they remain cooled. Running at high gain settings without this cooling can significantly limit their
performance due to increases in dark current and can permanently damage the detector.
On the night of the 24th, it was noticed around 4 hours into the observing run that the EMCCD
camera recording the inner imaging planes for the nlCWFS was increasing in temperature. The
camera dewar had been filled with liquid nitrogen just prior to the observing run and as such, this
implied a leak in the vacuum seal of the dewar. Upon inspection, it was noticed that condensation
was beginning to form on the dewar window, confirming the lack of vacuum. To prevent any
damage to the detector, this entire dewar was removed from the GHRIL for the remainder of this
evening to prevent any further condensation. This meant that due to the weather and this issue,
no on-sky data was taken with the nlCWFS on the first night of observing and the full time was
dedicated to science camera data.
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7.2 Challenges during observing
(a) Images from the AOLI science camera.
(b) Images from the inner imaging planes of the nlCWFS.
(c) Images from the outer imaging planes of the nlCWFS.
Figure 7.1: Seeing conditions at the WHT on the night of the 25th September 2013. These observations
are of the star HIP 14002, a F-type star with a magnitude of 7.42 in the V band. The columns of
images were taken synchronously approximately 20 s apart. The PSF FWHM in the science image is
∼1.5 arcsec in the left hand image and ∼6 arcsec in the right.
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Observing at the William Herschel Telescope
The following day, the camera was tested and it was confirmed no damage had been sustained.
The dewar was re-pumped to provide a vacuum and performed as expected for the rest of the
observing run. On full inspection in the return to Cambridge, it was noticed that one of the O-ring
seals, instead of being rubber, was constructed of a soft metal material. This was replaced with a
rubber O-ring and since then no further problems have occurred with the vacuum on this dewar.
7.2.3 Wavefront sensor gains
During data collection from both on-sky targets and the calibration system, it was noticed that the
gain setting (which can be thought of as a factor governing the number of electrons generated per
incident photon) of the two EMCCD detectors within the wavefront sensors was different for the
same reference object. This was particularly surprising as the optical design of the system should
produce similar counts on the detectors (within a factor of two accounting for the bandwidth
splitting and quantum efficiency as discussed in Section 8.2) and both detectors had been
previously calibrated to provide approximately the same signal-to-noise for the same brightness
source.
The outer imaging planes in the system appeared to require a gain setting significantly higher than
those on the inner imaging planes. Unfortunately due to time constraints it was not possible to
identify the cause of the issue while at the WHT. Upon returning to Cambridge, both cameras
were re-calibrated with a number of changes being made to the configuration file for the detector
imaging the outer planes. These changes now mean both detectors require a similar gain setting
for the same brightness of input source.
7.3 Calibration system data
Due to the poor weather during the observing nights, testing was undertaken of both the science
camera and nlCWFS systems with the calibration system. This included testing the quality of the
optics with the science camera, in particular verifying diffraction characteristics, as well as
recording a full set of calibration data with multiple phase plates for analysis away from the
telescope.
For these tests, the 9µm fibre was used in the calibration system to simulate a diffraction limited
point source passing through the WHT optics. Several different phase plates simulating different
values of r0 were used and recorded with the system. It is important to note that all data taken with
the calibration system also suffered from the EMCCD gain problems discussed in Section 7.2.3.
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7.3 Calibration system data
(a) Inner imaging planes
(b) Outer imaging planes
Figure 7.2: Images from the nlCWFS with the AOLI calibration system. As clearly seen, while the inner
imaging planes show the structure as expected, the outer imaging planes fail to be imaged correctly.
7.3.1 Beam sizes of the nlCWFS
To initially test the calibration system, the phase plate was set to a location where no turbulence
was introduced into the system. With a good optical alignment, the beams on each detector should
be approximately equal in size due to them being equidistant from the pupil. The results from this
test can be seen in Figure 7.2.
As is clearly seen in the figure, although all beams do show the spider structure, it is clear that
the outer imaging planes are not equal in size or sharpness. The right hand beam in Figure 7.2(b),
which is for the post-pupil plane, is clearly larger and shows more structure compared to the pre-
pupil plane.
Focal adjustments were made to the lenses within the nlCWFS system. It was deduced that the
effect must only be in the longer wavelength arm generating the outer planes as the beams at
shorter wavelengths behaved as expected. By adjusting the position of the final lens in the system
i.e. after the first dichroic, it was expected that these two outer plane beams would balance in
size. Unfortunately adjusting the focus simply changed both beams in the same manner which
was unexpected.
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Observing at the William Herschel Telescope
As the data being taken with the calibration system was secondary to on-sky data, the lenses within
the nlCWFS system were returned to their original positioning as best as possible. When observing
an on-sky target, as shown in Figure 7.1, the difference between the beam sizes, while still apparent,
was much reduced. With this in mind, the cause of this effect needed to be fully examined in a
laboratory environment and this work is discussed in Section 8.2.
7.3.2 Phase plate data
Although challenges with the beam sizes in the nlCWFS remained, it was decided to still record
data to verify the characteristics of the wavefront sensor as much as possible. This was done
initially using the 200µm fibre source to illuminate the pupil plane with a range of input
intensities using neutral density (ND) filters. Two phase plate scales with simulated values of r0 =
15 cm and r0 = 23 cm were also used. Data collected for different brightness of reference source
can be seen in Figure 7.3.
As expected, with decreasing brightness, the speckle structure within the beam loses contrast. To
undertake further testing, the 200µm fibre was replaced with a 9µm fibre which simulated a point
source. This allowed the effect of different source brightness to be investigated in the science
camera and wavefront sensor. An example of the data recorded can be seen in Figure 7.4.
Due to the issues with gain settings for the outer imaging plane EMCCD and the beam size
discrepancies, it has been particularly challenging to use this data for anything more than a visual
check of beam characteristics. The recording of calibration data did highlight several effects
within both the nlCWFS components and calibration, the investigation of which is discussed in
Section 8.2.
7.4 On-sky data
With the poor weather on both observing nights, only a limited set of targets were observed and
all of these in poor seeing conditions. A number of science targets were imaged, in particular
binaries, to characterise the plate scale of the instrument and determine its observing capabilities.
In addition, a number of single target stars were observed as reference objects for the nlCWFS and
recorded simultaneously with the science camera.
7.4.1 On-sky wavefront sensor data
The quality of the data from the nlCWFS is particularly limited principally due to the weather
conditions. The data are also affected by the EMCCD gain problems as discussed in Section 7.3.1
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7.4 On-sky data
(a) No neutral density filter (Camera gain=1 & 1)
(b) ND1 (Camera gain=1 & 30)
(c) ND2 (Camera gain=10 & 100)
(d) ND3 (Camera gain=30 & 1148)
(e) ND4 (Camera gain=100 & 3337)
Figure 7.3: Images recorded with the nlCWFS for different brightness of reference source from the
AOLI calibration system for a simulated value of r0=23 cm. The left hand column shows imaging of the
inner planes while the right shows the outer. Intensity changes were made by adding neutral density
(ND) filters at the entry of the fibre feed. Note the gain difference between detectors as discussed in
Section 7.2.3.
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Observing at the William Herschel Telescope
(a) No neutral density filter (Camera gain = 30, 10 & 30)
(b) ND1 (Camera gain = 100, 30 & 2160)
(c) ND2 (Camera gain = 476, 100 & 3337)
Figure 7.4: Data from the AOLI calibration system simulating turbulence with r0=15 cm. The left hand
column shows data from the science camera for a single point simulated by a 9µm fibre. The centre
column shows the inner imaging planes and the right hand column shows the outer imaging planes.
The different source brightnesses were achieved using ND filters as listed.
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7.4 On-sky data
which meant only bright reference objects could be used.
All observations with the nlCWFS were undertaken on the night of the 25th September. The targets
recorded were selected from the Hipparcos catalogue and are listed in Table 7.1 with some of the
‘better quality’ data from the wavefront sensor shown in Figure 7.5.
Target Name V Magnitude Spectral Type
HIP 10670 4.00 A1
HIP 11548 5.91 G0
HIP 14002 7.42 F5
Table 7.1: Target list for the nlCWFS observations with their characteristics. These were observed on
the night of the 25th September 2013.
Recovery of the wavefront at the pupil plane has been attempted using the data with limited
success. The principal cause is the poor seeing conditions leading to a significant change in the
wavefront between frames. In addition, the complexities due to the gain on one EMCCD detector
and the differing beam sizes has proved to be problematic for providing reliable intensity
information at the imaging planes. As such, the use of this data set for reconstruction has not been
pursued further.
7.4.2 On-sky science camera data
When observing with AOLI, it is useful to be able to perform real-time lucky imaging on sources
to ensure the correct functioning of the instrument. In addition, all data can be recorded allowing
post processing to be carried out. The preliminary results from both methods are discussed in this
section.
Real-time lucky imaging
With PixCel, the AOLI data collection software, it is possible to perform real-time lucky imaging
of target objects. A number of observations were taken principally of binary targets with a known
separation. I have undertaken the analysis of this data to verify the capabilities of the AOLI science
instrument.
LkHα 263 The LkHα 263 system is comprised of three major components, a close binary LkHα
263 AB with a separation of∼0.41 arcsec and a third object LkHα 263 C which is located∼4.1 arcsec
from LkHα 263 A. A fourth star, LkHα 262 at a distance of ∼15.25 arcsec from the binary has also
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Observing at the William Herschel Telescope
(a) HIP 10670 (Camera gain = 100, 30 & 3337).
(b) HIP 11548 (Camera gain = 100, 30 & 3337).
(c) HIP 14002 (Camera gain = 267, 100 & 3337).
Figure 7.5: On-sky data from the AOLI science camera and nlCWFS for the targets HIP 10670 (mv=4.0),
HIP 11548 (mv=5.91) and HIP 14002 (mv=7.42). The left hand column shows the data recorded in the
science camera, the central column shows the inner imaging planes for the nlCWFS and the right hand
column shows the outer imaging plane. The gain settings for the EMCCD detectors are listed.
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7.4 On-sky data
Figure 7.6: A real-time lucky image of the LkHα 263 system. The two brightest components in the
system are the binary LkHα 263 AB on the left and LkHα 262 on the right. The inset shows the
separated binary components. LkHα 263 C is visible to the lower left of LkHα 263 AB.
been associated with the system (Chauvin et al., 2002). The output of the real-time lucky imaging
process can be seen in Figure 7.6.
STF 2576 FG The double star STF 2576 FG in the constellation of Cygnus. The two stars have a
separation of 3.0 arcsec and magnitudes of 8.47 and 8.58. The pixel scale calculated from this image
is 55 milli-arcsec/pixel as shown in Figure 7.7.
Post-processed data
Analysis of the AOLI science camera data has been undertaken by researchers at the IAC and
Universita¨t zu Ko¨ln, led by Sergio Velasco.
Observations of M15 The globular cluster M15 was observed, allowing a measurement of both
the sensitivity of the instrument and its plate scale. The plate scale of the AOLI science camera
was measured to be 55 milli-arcsec/pixel which was calculated using simple star triangulation. An
example image of M15 can be seen in Figure 7.8.
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Observing at the William Herschel Telescope
Figure 7.7: The double star STF 2576 FG as imaged with AOLI. The pixel spacing between the stars is
54.4 pixels which gives a pixel scale of 55 milli-arcsec/pixel.
Figure 7.8: Left: the image of M15 taken with AOLI at WHT. The field of view is 50x50 arcsec; Right: A
zoom on the same field as previously observed with FastCam at the NOT (Velasco, 2014).
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7.4 On-sky data
Figure 7.9: Images of the system LkHα 263 AB. On the left is the image by Jayawardhana team,
obtained by by private communication. LkHα 263 AB is the largest object with LkHα 263 C being
visible as a double disc. The image on the right is taken with AOLI. This shows LkHα 263 C in the top
left with LkHα 263 AB and 262 being the two brighter objects (Velasco, 2014).
Observations of the close binary LkHα 263AB Observations were undertaken of the close binary
LkHα 263 AB with a separation of ∼0.41 arcsec. The system has been previously observed to have
significant mid-IR excess due to the presence of circumstellar disks (Jayawardhana et al., 2001) and
has also been observed to be part of a potential quadruple system (Chauvin et al., 2002). The AOLI
image of the system can be seen in Figure 7.9.
7.4.3 Magnitude values of the calibration system
To be able to fully utilise the AOLI calibration system, different input brightnesses from the source
fibres need to be related to their apparent magnitude on the sky. To do this, data must be taken
with the same camera gain (due to EMCCDs having a non-linear avalanche effect that is highly
dependent on the gain) of both the calibration system source and an on-sky target where the
magnitude is known. Theoretically, it should then be possible to use standard aperture
photometry methods to calculate the effective magnitude of the calibration system source by
either using the science camera or one of the beams in the wavefront sensor.
This analysis was undertaken using the 9µm fibre source with an ND1 filter. For this setup, the
science camera gain was set to 100 while the detector imaging the inner planes had a gain of 30.
The same settings were used for the on-sky observing of HIP 10670 and HIP 11548 allowing these
to be used as reference sources.
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Observing at the William Herschel Telescope
Using the science camera data, the value for the magnitude of the calibration system source was
calculated to be mv = 8.7± 0.4 using HIP 11548 as the reference and mv = 8.8± 0.4 for HIP 10670.
Combining these results gives an overall value of mv = 8.7± 0.3.
The same analysis has been undertaken using the wavefront sensor beams. While this should
provide consistent values as the detectors are effectively counting photons, the results are not
consistent when using the two reference sources. The cause of this is likely to be the need for large
apertures to be used as the data is recorded around a pupil plane rather than the conventional
focal plane. This will lead to more background noise being detected on top of the signal which,
combined with potential issues with gain stability due to temperature (this detector is within the
dewar with the failed vacuum seal as discussed in Section 7.2.2) is the probable cause for this
discrepancy.
While it was hoped to be able to calculate the effective magnitude for other fibre sources, the gain
of the science camera was not consistent for any other on-sky and calibration system brightness.
7.5 Summary
While there were many challenges during the observing run at the William Herschel Telescope,
the underlying capabilities of AOLI were demonstrated. The poor weather conditions
significantly restricted the target sources observed, however, verification of the system and its
characteristics was still possible. The measured pixel scale of 55 milli-arcsec/pixel has been
calculated with two independent sources and matches well with expected value of
54.96 milli-arcsec/pixel from the optical design. In addition, it has been possible to target sources
with different magnitude components to test the instrument sensitivity.
Problems with both the instrument layout, electronics and calibration system were identified and
solutions are discussed in Chapter 8. In addition, the problems with the CANARY derotator are
now being addressed by the ING staff and the CANARY team and will be implemented in time for
the next visit to the telescope.
Data from the nlCWFS have been used to verify the characteristics expected at the imaging planes
based upon previous simulation work. While it was not possible to use this data for wavefront
reconstruction due to systematic effects, these images can be used as a reference for future
development work both in the laboratory and simulations.
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7.5 Summary
130
“The most exciting phrase to hear in
science, the one that heralds new
discoveries, is not ’Eureka!’ but ’That’s
funny...”
Isaac Asimov
8
nlCWFS laboratory data
Following the observing run at the William Herschel Telescope, the full AOLI instrument was
shipped to Cambridge for re-assembly and further testing. The system and its use is discussed in
this chapter including results from reconstruction with limited wavelength data. This has been the
focus of my work since the observing run at the WHT.
8.1 Reconstructing AOLI in Cambridge
Prior to the arrival of AOLI back in Cambridge after the observing run at the WHT, the layout of
the instrument was examined to identify any possible changes to increase space for critical
mechanisms, support structures and to determine possible solutions to the issues with the pickoff
mirror reliability.
8.1.1 Pickoff mirror stability
Analysis, undertaken by David King, identified the stability requirements of the pickoff mirror
mechanism within the AOLI optical train. To ensure alignment with the EMCCD detectors within
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8.1 Reconstructing AOLI in Cambridge
the nlCWFS, the x-y positioning of each pickoff spot must be reproducible to within 50µm which
is a challenging requirement for this kind of component positioning (King, 2013a).
To reduce the demands on the pickoff spot location, the decision was taken to relocate both the
science camera and wavefront sensor relative to the common optics of AOLI with the two systems
effectively being interchanged on the optical bench. The majority of the optical beam is now
reflected from the pickoff mirror plane into the science camera by a mirrored surface containing a
small hole. This hole allows the light from a reference object to pass to the WFS module. To allow
for the repositioning of the science camera, the common optics have been modified to fold in the
opposite direction, allowing the science camera mechanism to be located fully on the optical
bench. This change also requires the relocation of the calibration system for both the laboratory
setup, shown in Figure 8.1, and the on-sky instrument design, shown in Figure 6.18.
8.1.2 Alignment and commissioning of the laboratory setup
Upon the arrival of AOLI back in Cambridge, the instrument was constructed with the relocated
modules, as shown in Figure 8.1. To allow the issue with the science camera electronics to be
investigated (as discussed in Section 7.1.2), the entire science camera assembly was replaced with a
single EMCCD dewar, similar in design to the WFS camera dewars, combined with two reimaging
lenses located after the pickoff mirror plane. This provided sufficient area to allow a single point
source from the calibration system, i.e. a single fibre, to be recorded. In addition, to allow the
redesign of the pickoff mirror mechanism, a pellicle (R=45%:T=55%) was installed at the pickoff
mirror location to provide both the transmitted and reflected beams.
During the reconstruction of AOLI, several changes were made to the supporting structure of
optical components to aid in the alignment relative to the optical axis. The wavefront sensor
system was constructed within a cage assembly allowing significantly easier positioning of
components and solving the nlCWFS lens support problem discussed in Section 7.1.2. The new
support structure can be seen in Figure 8.2.
In addition to modifying the support structure within the nlCWFS, the optical supports for many
of the optical components within the common optics and calibration system were changed to a
linear stage system. This allowed, as a minimum, horizontal motion in two dimensions for each
component with micron level accuracy and, for some components, full three-dimensional
adjustment is possible. While not essential, this change significantly aids in the alignment process
of the instrument which will be of principal benefit when shipping and rebuilding at the telescope.
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nlCWFS laboratory data
Figure 8.1: Optical layout of the nlCWFS for use in the laboratory setup. The wavefront sensor module
and science camera have been changed to reduce the requirements on the pickoff mirror mechanism.
In addition, the calibration system has been relocated and folded to fit within the available bench area.
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8.1 Reconstructing AOLI in Cambridge
(a) The cage support system for the first components in the nlCWFS after the pickoff
mirror. The pickoff mirror location is shown on the left and the beam from the plane
passes to the first reimaging lens.
(b) The cage support system for the dichroic beam splitting optics. The beam enters from the
reimaging lens and the upper left before being folded towards the wavefront sensor detectors.
Figure 8.2: The redesigned cage support system for the nlCWFS.
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nlCWFS laboratory data
Fibre sizes and illumination
The fibres and light source used as the input to the calibration system at the WHT were not shipped
to Cambridge due to their required use at the IAC on another project. Similar fibres were purchased
with diameters of 10, 50 and 100µm. As done at the WHT, the 10µm fibre was used to simulate a
point source, the 50µm was used for alignment purposes and the 100µm was used to illuminate a
focal plane mask.
From the data collected with the calibration system while at the WHT, it was noticed that using
neutral density filters with only integer values limited the brightnesses of reference objects which
could be simulated. To accommodate a wider range of brightnesses, a small illumination system
was constructed comprising a halogen lamp source (temperature ∼3000 K) kept at a constant
voltage to maintain the brightness temperature, a lens to focus the beam onto the end of the fibre
and a filter wheel containing NDs with values 0.3, 0.5 and 0.7. These could be combined with NDs
with integer values to simulate a range of brightness from ND of 0 to 4.7.
Phase plate location and rotation
When using the calibration system at the WHT, the phase plate to simulate atmospheric
turbulence was positioned ∼10 cm away from the aperture mask defining the pupil plane location.
This simulated a turbulent layer at an altitude of around 5 km above the WHT entrance. As
discussed in Section 2.3.1, the strongest atmospheric effects are located in the ground layer, i.e. at
zero altitude. To account for this, the phase plate was moved as close to the pupil as possible
accounting for the support required for the mask. This reduced the distance of the plate from the
pupil plane to around 7 mm giving a turbulent layer altitude of around 350 m.
In addition to the phase plate repositioning, the speed of the plate rotation was considered. The
plate itself has an annulus of simulated phase distortions between 34 and 83 mm from the centre
of rotation. The rotation of the phase plate is controlled with a stepper motor with 19000 steps per
full rotation. The default speed for rotation (and the speed used with the calibration system at the
WHT), is 2000 steps per second giving a crossing time for the 18.3 mm beam of around 0.75 s. This
is equivalent to a wind speed of around 5.5 m s−1 or 20 km hr−1 at the WHT which is the average
value.
For the laboratory testing, the EMCCDs were run with full readout i.e. 1024×1024 pixels rather than
the limited region readout used at the WHT. This reduces the frame rate from around 100 Hz on-sky
to around 25 Hz and as such, the rotation speed of the phase plate must be modified accordingly.
The speed of rotation was reduced to 600 steps per second, maintaining the number of frames
recorded in the crossing time of the telescope aperture.
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8.2 Calibration system chromaticity
8.2 Calibration system chromaticity
In Sections 7.2.3 and 7.3.1, issues regarding recording the four light beams within the wavefront
sensor system were discussed; the gain settings on the EMCCD detectors and differing beam sizes.
The significant difference in gains required for the two detectors was observed when using both
the calibration system and on-sky targets. This implied the issue was not in the calibration system
and pointed to an issue with the detectors. The discrepancy with beam size was significantly more
prominent when using the calibration system compared to the on-sky data. This indicated an issue
within the calibration system and further tests were undertaken with the reconstructed laboratory
setup to identify the cause.
8.2.1 Throughput and reference star spectral types
An initial hypothesis for the gain discrepancies between the two wavefront sensor EMCCDs was
due to the quantum efficiency (QE) falloff at longer wavelengths as shown in Figure 6.5. The QE of
the wavelengths where the inner imaging planes are recorded, 500-700 nm, is over 90%. The outer
imaging planes, where a higher gain was needed, have a QE of around 75% at 750 nm and 45% at
875 nm. While a larger bandwidth was used in the longest wavelength arm to counter this effect
(150 nm compared to 100 nm), this was still a concern and I undertook simulations to estimate the
signal in each waveband.
Calculations were undertaken for the different wavelength bands used in the nlCWFS to
determine the relative sensitivity of the system in each band. This was done by assuming a
wavelength-independent throughput from all optical components (as specified in their design)
and simply considering the QE and the black-body curve for the source object.
While the brightness temperature of the lamp used as the light source in calibration system can
be varied, even at the maximum power output, the highest temperature which can be achieved is
around 3000 K. This gives a peak in the black-body spectrum at∼950 nm. For stars, the temperature
value is higher ranging from around 3800 K for M-type to 7240 K for F-type. These shorten the peak
wavelength range to 760 nm and 400 nm respectively.
By combining the average emission across each wavelength range with the quantum efficiency, the
relative intensity in each band recorded by the detector was calculated. For cooler M-type stars,
the difference in measured intensity between the wavebands was less than 30%. This is due to the
peak wavelength coinciding with the drop in quantum efficiency. For hotter stars, where the peak
moves to shorter wavelengths, the difference in measured intensity increases up to around 60%.
While this may appear significant, this is still within an order of magnitude and cannot account for
the large gain differences (factors of 15 or more) required to record the imaging planes.
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nlCWFS laboratory data
Following on from this analysis, both wavefront sensor cameras were recalibrated and the
configuration for the outer imaging plane detector was significantly modified. Since this process
both cameras have behaved as expected with approximately the same gain setting being used in
both detectors for the same source.
8.2.2 Beam sizes with the nlCWFS
One of the first investigations undertaken with the laboratory setup of AOLI was to attempt to
reproduce the different beam sizes seen at the WHT when using the calibration system as shown in
Figure 7.2. After ensuring the correct positioning of the nlCWFS optics, the same effect was clearly
visible.
As attempted previously, the final lenses in both wavefront sensor arms were adjusted to attempt
to rectify the issue with no effect. The beam sizes changed with the lens adjustment, however, the
relative size of the beams on each detector remained the same. Having exhausted this avenue as
the source of error, the remaining lenses between the pickoff mirror and the detector were also
adjusted to observe the effect. While the adjustment of the 40 mm focal length lens nearest the
pickoff mirror had a noticeable effect, this again simply adjusted the size of all beams, maintaining
the same relative size between them.
Having exhausted all options of the source being within the wavefront sensor optics, the next most
likely source was the calibration system, particularly as the effect was more noticeable when using
the simulated source rather than an on-sky target. By adjusting the positioning of the final 200 mm
focal length lens in the system relative to the pupil mask, it was possible to adjust the relative size
of the beams within the wavefront sensor detector. Finally, a likely cause of the issue had been
identified!
Upon this discovery, a full analysis of the optical design of the calibration system was undertaken
by David King. The conclusion of this, as shown in Figure 8.3, was that due to the specification
of the lenses within the system, there was a significant shift of the focal plane at the exit of the
system which was dependent upon wavelength. The two lenses used are specified to work within
the range 500-700 nm however outside this, their performance drops significantly.
As the nlCWFS works across the wavelength range from 500-950 nm, any chromatic effects at the
simulated WHT focal plane will be significant by the time they have propagated through the full
optical train. With this in mind, a solution using off-axis paraboloids has been proposed to provide
a common focal plane for all wavelengths as discussed in Section 6.6.1.
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8.2 Calibration system chromaticity
Figure 8.3: The on-axis shift in focal position with wavelength. Across the wavelength range of the
nlCWFS, there is a total shift in excess of 1µm at the simulated WHT focus leading to differing beam
diameters when using dichroic splitting.
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nlCWFS laboratory data
8.3 Limited bandwidth data
Due to the limitations imposed by the lenses within the calibration system, the decision was taken
to use the wavelength range in which the components are specified to provide diffraction limited
imaging, i.e. 500-700 nm. While not a permanent solution, this method allows the investigation of
broadband data and reconstruction while alternative components for the calibration system were
sourced.
To simulate the full calibration system as closely as possible, it was specified that a bandpass of
100 nm should be provided to each beam within the WFS system. Maintaining this wavelength
range would best simulate the broadband effects seen in each arm. The wavelength range 600-
700 nm was initially selected to be used for each beam. To implement this, short-pass and long-pass
filters were installed in the WFS optics after the 40 mm focal length lens. The dichroics within the
final WFS assembly were replaced with pellicle beamsplitters (R=45%:T=55%) to provide the four
imaging planes, each with approximately equal intensity. The positioning of the EMCCD detectors
and fold mirrors were adjusted within this assembly to account for the wavelength change and the
requirement to provide equivalent planes at ±250 km and ±600 km for a 4.2 m aperture. The setup
for the science camera remained unchanged from that described in Section 8.1.2, aside from the
installation of the long-pass filter as used in the common optics of AOLI.
With this limited wavelength range, the beam size in all of the wavefront sensor arms was
approximately consistent as shown in Figure 8.4. Slight intensity differences remain between the
beams, however, this is due to the beamsplitters used having slightly different reflection and
transmission percentages.
Data with simulated turbulence
With the wavefront sensor beam size issue mitigated, data was recorded using a single phase plate
available in Cambridge (r0=15 cm) rotated to simulate the average wind speed at the WHT. This
was done for a range of different source brightnesses with synchronised wavefront and science
cameras. To allow finer control over the camera gains, manual control of the gain voltage was
undertaken to provide count levels of around 2000 above the background. A sample of the images
recorded at different source brightnesses can be seen in Figure 8.5.
8.3.1 Recovering the pupil mask
As shown in Figure 8.4, the effect of the spider support structure at the pupil plane can have a
significant effect on the intensity at the imaging planes. As such, to allow an accurate wavefront
reconstruction, it is important to be able to account for these structures when applying the pupil
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8.3 Limited bandwidth data
(a) Inner imaging planes of the nlCWFS
(b) Outer imaging planes of the nlCWFS
(c) Science camera image
Figure 8.4: Images from the laboratory setup of AOLI. The first two figures show the imaging planes
of the nlCWFS with the same wavelength range of 600-700 nm being used to generate all beams. The
pairs of images for each plane distance are consistent in size as expected. The science camera image
has been recorded with a narrowband filter of 600±10 nm.
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nlCWFS laboratory data
(a) ND0.3
(b) ND1
(c) ND2
(d) ND3
(e) ND4
Figure 8.5: Data from the laboratory setup of AOLI with the calibration system simulating turbulence
with r0=15 cm. The left hand column shows data from the science camera for a single point simulated
by a 10µm fibre. The centre column and right columns show the inner and outer imaging planes of
the nlCWFS respectively. The different source brightness was achieved using ND filters as listed.
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8.3 Limited bandwidth data
mask during this process (see Section 4.4). To do this, the angular position of the spiders needs to be
known. This could be recovered by using a uniform illumination of the pupil plane, i.e. effectively
a flat field image, although as the telescope will track during an observation, the spiders will rotate
making this solution impractical. It would of course be possible to use telemetry information from
the telescope to calculate the angular positions of the spiders however it was investigated to see if
these could be recovered directly from the recorded WFS data.
Due to the random nature of atmospheric turbulence, on average, the light entering the pupil plane
of the telescope should have a mean phase value of zero (remembering the phase ranges from −pi
to pi). While specific short exposure images will show significant structure as they propagate, a
long exposure image, which is just the sum of short exposure images, should generate an image
with an effective phase of zero. With this in mind, any obscuration within the pupil plane, while
not necessary visible on short exposure images, should result in a decreased intensity in a pattern
relating to the obscuration shape.
To investigate if it was possible to recover the pupil mask, a minimum of 500 images for each
wavefront beam were combined together in Matlab and averaged as shown in Figure 8.6. This
was done for a range of brightness sources to simulate the effect of using different magnitudes of
reference star.
Figure 8.6 shows the sensitivity of the imaging planes to different scales of obscuration within the
pupil varies with distance. Small scale structures, which produce high-spatial frequency diffraction
effects, are only visible in the inner imaging planes where the stronger, low-order effects have not
yet developed. As shown in Figure 8.6(b), the outer imaging planes only show the largest structure
i.e. the central obscuration, making it challenging to recover the pupil mask.
Having identified that the pupil mask can be recovered from the inner imaging planes, further
work was done to extract the angular rotation of the mask from a reference position with the spiders
being vertical and horizontal. As the pupil mask is assumed to be rotationally symmetric, the range
of rotation will be from 0-90◦.
Recovering the angle of rotation
To recover the angle of rotation of the pupil mask relative to a vertical reference position, it is first
important to identify the axis of rotation i.e. the centre of the pupil image. As the intensity of the
averaged beams is fairly compact, the simplest approach, and the one adopted for analysis, is to
find the edges of the beam by scanning from the edges of the image one row and column at a time
until the maximum value in a row reaches a certain level. In this case, half of the maximum value
above the background level was chosen which returned two row and two column values for the
boundary of the pupil. By taking the mean of these values, the pixel defining the axis of rotation
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nlCWFS laboratory data
(a) Inner imaging planes with no turbulence (for reference).
(b) ND0.5 - From left to right: The two inner imaging planes (post- and pre- pupil) and the outer
post-pupil imaging plane.
(c) ND3 - The two inner imaging planes.
(d) ND4 - The two inner imaging planes.
Figure 8.6: Recovered pupil masks using combined short exposure images of the nlCWFS beams.
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8.3 Limited bandwidth data
(a) The average intensity in the central column of pixels after rotation of the recovered pupil mask. The minima
show the angular location of the spiders.
(b) The average intensity in the central column of pixels after rotation. This plot is wrapped on a 90◦ period.
Figure 8.7: The angular dependence with intensity of the recovered pupil mask. The figures on the left
are for the post-pupil plane and while the figures on the right are for the pre-pupil plane.
was identified.
There are several techniques possible to attempt to determine the offset of the spiders relative to
vertical. The technique adopted rotates the recovered pupil mask around the axis of rotation and
averages the central column of pixels within the image (this column contains the pixel at the centre
of rotation). As seen in Figure 8.6, the location of the spiders causes a decrease in intensity and
by averaging along this column, when the spider shape best aligns with this column, i.e. when
they are positioned vertically, the average intensity will decrease. When rotating a full 360◦, four
minima in intensity should be visible due to the four spiders at the pupil.
Figure 8.7 shows the outcome of this process using data taken with the laboratory setup of AOLI.
In both the pre- and post-pupil imaging planes, four minima are clearly visible. Using inbuilt
functionality within Matlab, the minima were found to occur at rotation angles separated by 90±2◦.
By wrapping these data sets with a periodicity of 90◦ (as expected due to the spacing of the spiders),
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nlCWFS laboratory data
the consistency of the minima can be seen in Figure 8.7(b).
The successful recovery of the pupil mask and spider rotation angle significantly helps wavefront
reconstruction when on sky. Having an accurate representation of the pupil mask and its
orientation is important when constraining the wavefront estimate as it passes through the pupil
and including the diffraction effects of the spiders when propagating the wavefront between
imaging planes. By being able to recover this information from on-sky data, this removes the need
for telescope pointing data, simplifying the wavefront reconstruction process.
8.4 Wavefront reconstruction
Data from the laboratory setup of AOLI has been used to investigate the nlCWFS wavefront
reconstruction algorithm and its effectiveness at converging on a wavefront estimate. This work
has been undertaken in Matlab and is based upon the code developed as part of the simulations of
the nlCWFS.
Unlike the simulation work discussed in Chapters 4 and 5, the reconstruction work with the
laboratory data uses the scales of the beams and component spacing with AOLI rather than the
full WHT scales. While this should have no overall effect on the reconstruction process, it does
require the initialisation program to be modified to create the relevant beam diameters and pixel
scaling at the imaging planes.
8.4.1 Initialising the algorithm
The initialisation process of the reconstruction algorithm calculates all of the relevant plane
positions and constraining information within the system. In simulation work, an input wavefront
was propagated to the imaging planes to generate the intensity information required to constrain
the beam. To undertake a reconstruction with lab data, this process was replaced with the
following procedure:
1. Identification of beam locations:
(a) Load files for each of the EMCCD detectors with no phase distortion input on the
calibration system.
(b) Identify the centre of the two beams on each detector using this plane input beam.
2. Locate and input intensity data:
(a) Load synchronised frames from the two EMCCD detectors.
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8.4 Wavefront reconstruction
(b) Using the beam locations identified when no phase distortion was applied, select the
region (256×256 pixels) around these locations which will form the basis of the intensity
information at the imaging planes.
(c) Identify if these images are in the correct orientation or are flipped due to an odd number
of reflections. If flipped, correct the orientation.
(d) Perform a background subtraction and standard image correction procedures.
3. Normalisation and edge effects:
(a) For each image plane, the data must be normalised to remove any beam specific gain
sensitivity characteristics.
(b) To prevent the occurrence of spurious high-frequency components during the Fourier
transforming process used within the wavefront propagation, the values in the edge
pixels of the image are gradually decreased to zero. This has been done in a 10 pixel
wide region around each image.
(c) If additional padding is required due to the numerical setup at the pupil and imaging
planes, the recorded data is centred within this region.
4. Input each processed image to its correct intensity constraint within the reconstruction
algorithm.
Having loaded and processed the images to work correctly within the algorithm, the reconstruction
process was then initiated to attempt to recover the phase at the pupil plane.
8.4.2 Results of the reconstruction
The principal goal of any wavefront reconstruction process is to converge to an answer as quickly
as possible while still maintaining the accuracy of the reconstruction. For the nlCWFS, this
convergence has been examined by comparing the difference in phase value between one iteration
of the reconstruction algorithm and the next. While not giving a complete picture of the
reconstruction process, as there was no ‘truth sensor’ installed within the system, it is difficult to
verify the true accuracy of any reconstruction. In addition, on-going challenges with phase
unwrapping after reconstruction would also limit this verification process.
Figure 8.8 shows the phase recovered at the pupil plane by the reconstruction algorithm for
different source brightnesses. The reconstruction algorithm has been run on data collected with no
turbulent effects (Figure 8.8(a)) and with those simulating r0=15 cm. The difference between the
two can be clearly seen in the recovered phase.
146
nlCWFS laboratory data
(a) ND0.5 with no turbulent phase. (b) ND0.5 with simulated turbulence.
(c) ND1.0 with simulated turbulence. (d) ND2.0 with simulated turbulence.
Figure 8.8: Recovery of the wavefront phase using the nlCWFS reconstruction algorithm. Images show
the wrapped phase after 10 iterations of the algorithm with the pupil mask imposed.
147
8.4 Wavefront reconstruction
(a) ND0.5 with no turbulent phase. (b) ND0.5 with simulated turbulence.
(c) ND1.0 with simulated turbulence. (d) ND2.0 with simulated turbulence.
Figure 8.9: The average change in phase value between iterations of the nlCWFS algorithm. As a good
wavefront estimate is achieved, the change should tend to a value of zero.
To examine the effect of source brightness on the reconstruction algorithm, the average change
in phase value was recorded after each iteration. As the reconstruction algorithm converges to a
stable solution, this value should tend to zero. The algorithm was run for 250 iterations with three
different source brightnesses. The results are shown in Figure 8.9.
The results from the convergence tests clearly showed the reconstruction algorithm taking up to 10
iterations to reach a reasonably stable solution for the phase within the pupil plane. For the case of
no turbulence, this was a gradual convergence towards the solution however for the cases where
turbulence was present, it is a much more erratic procedure with the change between iterations
often increasing before converging to a solution. As perhaps expected, for the fainter reference
source more iterations were required to reach a stable solution. This is not entirely surprising as
the Gerchberg-Saxton method which has been used to date is known to have more limited success
with increasing noise (Fienup, 1982).
148
nlCWFS laboratory data
8.5 Comparison with the SHWFS
One of the limitations with both the laboratory and on-sky configurations of AOLI is its lack of a
‘truth sensor’ to verifying to reconstructed wavefronts generated with the nlCWFS. To attempt to
overcome this problem, a Shack-Hartmann wavefront sensor was installed in the science camera
arm after the pickoff mirror location. This is the same detector which was used in the Thorlabs AO
kit discussed in Section 6.1.1.
The SHWFS comes with a software package which calculates the phase distortions at the pupil
plane for a circular aperture. It was attempted to run this reconstruction software with the
simulated WHT pupil mask within the calibration system however this failed due to the central
obscuration blocking the central spots on the detector. To still allow useful data to be recorded, the
pupil mask was replaced with a simple circular aperture with diameter 18.3 mm.
To ensure the same wavefront distortion was being recorded by both detectors, instead of rotating
the phase plate within the calibration system continuously, it was rotated to a position and then
stopped. Data was then taken with both the SHWFS and nlCWFS systems ensuring the same pupil
phase was maintained.
A comparison between the SHWFS wavefront and that recovered by the nlCWFS is still preliminary
due to the outstanding issues with phase unwrapping. While the SHWFS generates slopes between
each subaperture in the lenslet array, allowing a continuous surface to be generated, all the nlCWFS
data is limited to the 2pi range as previously discussed. While the nlCWFS reconstruction algorithm
does converge on a result, it is not yet possible to make a direct comparison to the SHWFS data.
8.6 Summary
The laboratory setup of AOLI has been an incredibly useful tool to investigate and troubleshoot
a number of effects within the instrument. Many of the issues experienced during the observing
run at the William Herschel Telescope have now had their root cause identified. The need to use
a significantly higher gain in one of the wavefront sensor detectors has now been resolved by re-
calibrating both detectors while the cause of the different beam sizes within the nlCWFS has now
been identified. While a permanent solution to this is currently being implemented, an interim
solution using a limited wavelength range was implemented.
Using this modified setup, the convergence of the AOLI nlCWFS reconstruction algorithm with
broadband camera data has been demonstrated for the first time. This process required a strategy
to recover the pupil mask and it has been shown this is possible by stacking multiple short
exposure images of the inner imaging planes. While it has not yet been possible to make a direct
149
8.6 Summary
comparison to another wavefront sensor, work on this is continuing, in particular the challenges
of phase unwrapping.
In addition to the wavefront sensor verification, it is important to consider the strategy for pushing
the nlCWFS to fainter reference sources. To achieve this, modified algorithms may be required
to overcome the increasing noise level which is known to be a limitation of the Gerchberg-Saxton
method. The use of input-output or similar methods should be considered as discussed in Section
5.4.1.
150
“The scientific theory I like best is that
the rings of Saturn are composed
entirely of lost airline luggage.”
Mark Russell
9
Conclusions
The Adaptive Optics Lucky Imager is the first dedicated instrument to combine the techniques of
adaptive optics and lucky imaging together. This approach overcomes the shortcomings of each
technique to allow diffraction-limited imaging in the visible on large ground-based telescopes.
Developing this kind of capability on the ground is vital as, with the impending retirement of the
Hubble Space Telescope, only this kind of instrument will be able to provide such high-resolution
images.
9.1 Current status
At the beginning of my Ph.D., the AOLI instrument had not advanced significantly beyond a
conceptual idea with a significant quantity of design work and investigation to still be
undertaken. While the science camera component of the instrument has always been based upon
the previous LuckyCam, the adaptive optics system was a relative unknown entity, in particular
the non-linear curvature wavefront sensor which was chosen to mitigate the need for laser guide
stars. Since joining the project, my work has focused on developing an understanding of the
instrument, in particular the wavefront sensor, through simulation, development systems and
151
9.2 Future work
algorithm development. This work culminated in the first observing run of AOLI at the William
Herschel Telescope in September 2013.
While the observing run at the WHT was not as successful as hoped (principally due to poor
weather), a significant amount was learnt from the experience and the capabilities of the science
camera were clearly demonstrated. Several on-sky targets were observed showing that, even in
very poor seeing conditions, the instrument offers significant improvements over conventional
imaging methods. The entire observing run was undertaken without the benefits provided of
wavefront correction and as such, the capabilities of AOLI are only going to improve in
subsequent runs as more functionality is made available.
To continue the development work on AOLI, the instrument has now been reconstructed in
Cambridge with the calibration system being used to simulate the input from the William
Herschel Telescope. Many systematic effects within both the AOLI cameras and calibration system
were identified and these have either been solved entirely or mitigated. This setup has proved to
be an incredibly useful tool for developing the instrument, not only for testing its full capabilities
but also to develop techniques for the nlCWFS in its own right. Many different data sets recorded
with the laboratory instrument have been used with the nlCWFS reconstruction algorithm to
converge on a recovered pupil phase estimate. Work is currently ongoing to also use this setup
with a ‘truth-sensor’ to allow a direct comparison to be made between the nlCWFS recovered
wavefront and a reference measurement.
AOLI is still an ongoing project and as such, there is always more to do and improve. The main
design work of the instrument is now complete and as such, the process is now more focused
towards tuning the instrument and the further development of the nlCWFS and AO system.
9.2 Future work
While the development of AOLI has progressed well to date, there are still many areas of work
to be completed on the instrument. In addition, several technical challenges remain, principally
relating to the nlCWFS and its reconstruction algorithm.
Laboratory setup
While the current laboratory setup has proved to be an invaluable tool in developing the wavefront
sensor algorithm, due to the chromatic effects within the calibration system, this has only been
possible over a 100 nm wavelength range. Data has now been recorded for all configurations of
the 600-700 nm bandpass being used and it is planned to expand this to 500-700 nm. This will still
work within the specified region for the lenses within the calibration system while allowing the
152
Conclusions
inner and outer planes to be imaged at different wavelengths.
The longer term plan for the laboratory setup is to replace the lenses in the calibration system with
off-axis paraboloids. This will allow simulation of the WHT input beam on the full 500-950 nm
specified for the system.
Wavefront reconstruction
The major challenge facing AOLI is the development of the wavefront reconstruction algorithm to
be reliable and fast enough for on-sky performance running at 100 Hz. Due to the iterative process
required in the reconstruction process, significant optimisation of the algorithm will be required
to achieve this real-time performance. Currently, with the unoptimised Matlab implementation
of the reconstruction, each iteration takes around 150 ms and several iterations are required for
convergence.
The current implement of the reconstruction algorithm propagates to each imaging plane in turn,
passing through the pupil as necessary. To complete one full iteration of the algorithm requires
eight propagations, four to and four from the pupil plane. A more efficient way to handle the
problem would be to propagate the wavefront estimate from the pupil plane to each image plane
in parallel. The amplitude constraint could be applied to the estimate at each plane before each
wavefront is propagated back to the pupil. This would leave four independently propagated
wavefronts at the pupil which would need to be combined to provide the next estimate of the
wavefront. The challenge with this process is to combine the wavefronts together. While the
amplitude components would simply add, combining the phase values would need some careful
consideration to ensure wavefront convergence.
As the most time consuming part of the reconstruction process is the Fourier transforms required
to simulate propagation, employing strategies to increase their speed will be important for
optimisation. Currently it is proposed to use the current generation of Nvidia graphics cards to
undertake the Fourier transforms as these devices are well suited to this task. In addition, the
smallest size Fourier transforms should be computed i.e. the smallest image array possible should
be used for propagation. Currently, there are ∼200 pixels across the pupil diameter on the
EMCCD detectors while there are only 17 correction elements across the diameter of the
deformable mirror. As such, it might be possible to bin the recorded imaging planes prior to
reconstruction without a detrimental effect on wavefront reconstruction. This binning process
could be handled either in software or could be implemented partially on the EMCCD detectors.
The current EMCCD detectors used within the nlCWFS are designed to run in a windowed mode
of 1024×256 pixels. As seen at the WHT, in poor seeing conditions this region is not large enough to
record the full beam at the imaging planes when there is a significant tip-tilt term. To overcome this,
153
9.2 Future work
the EMCDDs can be configured to bin data in one direction effectively making rectangular pixels.
This would mean a 1024×512 region could be read out at the same speed as the current 1024×256,
giving a larger imaging area without any impact on reconstruction speed. The data would then
need to be reprocessed in software to account for the rectangular pixels and this process would
provide images with dimensions of 128×128 pixels.
One alternative solution to increase the physical imaging area would be to replace the current
1024×1024 detectors with their equivalent 512×512 model. The pixel size on these detectors is
16µm compared to 13µm for the 1024 version. This would give an imaging area of 4.1 mm for
512×256 readout compared to the current 3.3 mm.
The final area of outstanding work with the reconstruction algorithm is to identify strategies to be
used within the low photon number regime i.e. when using faint reference objects. Simulations
have previously been undertaken by Peter Aisher to investigate the best methods for performing
wavefront reconstruction in this regime, however, this has yet to be tested using camera data.
Wavefront correction
Once a reliable method of wavefront reconstruction has been established, the next stage in
development will be to attempt to correct the phase distortions in the pupil plane. The
conventional strategy for this would be to use the ALPAO deformable mirror, which indeed will
be the strategy on-sky and one that should be tested, however as the science camera and
wavefront sensor camera are synchronised, an alternative solution may be possible.
Currently, only basic testing has been completed with the ALPAO DM241-25 mirror. Several tests
should be undertaken to verify its characteristics (e.g. flatness, temperature dependence, hysteresis
etc.) prior to use within the correction system. This process could be done by using the Zygo
interferometer at the IAC in Tenerife. After characterisation, a control strategy will need to be
considered to allow integration of the mirror control with the wavefront reconstruction algorithm.
The principal challenge with this is identifying the best technique to handle the unwrapping of the
wavefront estimate to allow a continuous surface to be commanded to the mirror surface.
Moving away from conventional correction methods, when a wavefront propagates through the
atmosphere, it experiences effects and undergoes changes which can often be described by an
optical transfer function (OTF). This can be thought of as the response of an optical system to an
input point source i.e. a star entering the top of the atmosphere. By measuring the wavefront
distortion at the pupil plane, it should be possible to reconstruct the atmospheric OTF at that
instantaneous point in time. With this information, by using deconvolution techniques it should
be possible to apply a correction to the science to remove the turbulent effects.
154
Conclusions
Subsequent trips to the WHT
One of the key outstanding questions for the nlCWFS is how faint a reference object can be used for
reconstruction. While the reconstruction algorithm can be developed using the laboratory setup, it
is challenging to calibrate the brightness of the reference source on the bench to on-sky magnitudes.
For any subsequent observing run, it is important that specific on-sky targets are recorded with the
same camera settings as previously recorded calibration system sources brightnesses.
For the next visit to the WHT (currently being planned for 2015), I would expect that wavefront
reconstruction and correction to be implemented within AOLI. This may not be at the full frame
rate and may only be for bright sources however, this would provide sufficient correction to
demonstrate an improvement in lucky imaging selection percentages. As it is a requirement all
wavefront data is recorded as well as being used in real-time, this will also provide a rich data set
for post-processing investigation.
Beyond the WHT
The long-term goal for AOLI is to undertake science observations on the 10.4 m Gran Telescopio
Canarias. While several years away from becoming a reality, the lessons learned while developing
the instrument for the WHT will be invaluable in progressing to the larger telescope. The diffraction
limit for the GTC in the I band is ∼21 milli-arcsec and the combination of AO and lucky imaging
on a telescope of this size has the potential to significantly advance our understanding across the
breadth of astronomy.
155
9.2 Future work
156
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