CUED Publications database

An optical Fourier transform coprocessor with direct phase determination

MacFaden, AJ and Gordon, GSD and Wilkinson, TD (2017) An optical Fourier transform coprocessor with direct phase determination. Scientific Reports, 7. 13667-.

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Abstract

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.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div B > Photonics
Depositing User: Cron Job
Date Deposited: 29 Sep 2017 20:11
Last Modified: 10 Apr 2021 01:26
DOI: 10.1038/s41598-017-13733-1