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Proceedings Article

Phase retrieval using theoretically unitary discrete fractional Fourier transform

[+] Author Affiliations
B. M. Hennelly, D. Kelly, A. Corballis, J. T. Sheridan

Univ. College Dublin (Ireland)

Proc. SPIE 5908, Optical Information Systems III, 59080D (September 15, 2005); doi:10.1117/12.617842
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From Conference Volume 5908

  • Optical Information Systems III
  • Bahram Javidi; Demetri Psaltis
  • San Diego, California, United States | July 31, 2005

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.

© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
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 (September 15, 2005); doi:10.1117/12.617842; http://dx.doi.org/10.1117/12.617842


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