Cimmino simultaneously iterative holographic projection
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Authors
El Guendy, Miguel De V
Mouthaan, Ralf
Niculescu, Oana
Soliman, AMR
Milne, Darran
Kaczorowski, Andrzej
Wilkinson, Timothy D
Publication Date
2022Journal Title
OPTICS CONTINUUM
ISSN
2770-0208
Publisher
Optica Publishing Group
Type
Article
This Version
VoR
Metadata
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El Guendy, M. D. V., Mouthaan, R., Kadis, A., Wang, Y., Niculescu, O., Soliman, A., Milne, D., et al. (2022). Cimmino simultaneously iterative holographic projection. OPTICS CONTINUUM https://doi.org/10.1364/OPTCON.451113
Abstract
<jats:p>The Cimmino algorithm is an iterative algorithm used for solving linear equations (<jats:italic>Ax</jats:italic> = <jats:italic>b</jats:italic>) and is part of a wider family of algebraic reconstruction algorithms. Despite being used in computed tomography and digital signal processing, we present an approach for using it in holographic projections in the Fraunhofer region. Following the work carried out by our group on Kaczmarz holography, an earlier algebraic linear equation solver, we compare the performance and speed of Cimmino against this algorithm. Three versions of the Cimmino algorithm, Cimmino full, Cimmino eye, and Cimmino FFT, are evaluated and compared to both Kaczmarz and Gerchberg-Saxton. Interestingly, the derivation and simplification of Kaczmarz and Cimmino leads to the input-output algorithm originally derived by Fienup and while the solution is well-known, the link between these algorithms is not and despite being around since the 1930s, it was originally used to solve linear equations and not phase retrieval. While the Cimmino full and Cimmino eye reflect fairly poorly against Cimmino FFT and Kaczmarz in terms of image quality and speed, the Cimmino FFT delivers better results in terms of image quality than all algorithms considered. It is significantly faster than Kaczmarz, being only a few milliseconds slower than Gerchberg-Saxton.</jats:p>
Relationships
Is supplemented by: https://doi.org/10.17863/CAM.83457
Sponsorship
EPSRC (EP/T008369/1)
EPSRC (2108797)
Engineering and Physical Sciences Research Council (EP/L015455/1)
Identifiers
External DOI: https://doi.org/10.1364/OPTCON.451113
This record's URL: https://www.repository.cam.ac.uk/handle/1810/336240
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