Phase retrieval using theoretically unitary discrete fractional Fourier transform

B. M. Hennelly; D. Kelly; A. Corballis; J. T. Sheridan

doi:10.1117/12.617842

15 September 2005 Phase retrieval using theoretically unitary discrete fractional Fourier transform

B. M. Hennelly, D. Kelly, A. Corballis, J. T. Sheridan

Proceedings Volume 5908, Optical Information Systems III; 59080D (2005) https://doi.org/10.1117/12.617842
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

Phase retrieval is the recovery of missing phase information in an optical field using measurable quantities. Usually the directly measurable quantity in an optical system is the intensity of the image and a diffraction pattern. The Gerchberg-Saxton (GS) algorithm utilizes the spatial and the spatial frequency intensities and the Fourier Transform (FT) is used to numerically transform between the two. Recently the fractional Fourier transform (FRT) has been proposed in the same context. Studies have shown that the efficiency of this FRT based Gerchberg-Saxton algorithm is dependent upon the discrete FRT used in the procedure. If this discrete FRT is unitary optimum results are obtained. In this paper we investigate the use of a recently proposed set of theoretically unitary discrete FRT algorithms. These algorithms are based on tracking the shape of the signal's Wigner Distribution Function (WDF) and the relationship between this shape and the Space-Bandwidth Product (SBP). We provide numerical simulations and compare these with those obtained using the traditional FT-GS algorithm.

Citation Download Citation

B. M. Hennelly, D. Kelly, A. Corballis, and J. T. Sheridan "Phase retrieval using theoretically unitary discrete fractional Fourier transform", Proc. SPIE 5908, Optical Information Systems III, 59080D (15 September 2005); https://doi.org/10.1117/12.617842

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