An optical Fourier transform coprocessor with direct phase determination.

Change log
Macfaden, Alexander J 
Gordon, George SD 
Wilkinson, Timothy D 

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

0802 Computation Theory and Mathematics
Journal Title
Sci Rep
Conference Name
Journal ISSN
Volume Title
Springer Science and Business Media LLC
EPSRC (1361953)
Engineering and Physical Sciences Research Council (EP/G037256/1)
Cancer Research UK (C20/A20976)