Unitary Algorithm for Nonseparable Linear Canonical Transforms Applied to Iterative Phase Retrieval
|Title:||Unitary Algorithm for Nonseparable Linear Canonical Transforms Applied to Iterative Phase Retrieval||Authors:||Zhao, Liang; Sheridan, John T.; Healy, John J.||Permanent link:||http://hdl.handle.net/10197/8713||Date:||20-Mar-2017||Online since:||2017-08-14T12:04:48Z||Abstract:||Abstract:Phase retrieval is an important tool with broad applications in optics. The GerchbergSaxton algorithm has been a workhorse in this area for many years. The algorithm extracts phase information from intensities captured in two planes related by a Fourier transform. The ability to capture the two intensities in domains other than the image and Fourier plains adds flexibility; various authors have extended the algorithm to extract phase from intensities captured in two planes related by other optical transforms, e.g., by free space propagation or a fractional Fourier transform. These generalizations are relatively simple once a unitary discrete transform is available to propagate back and forth between the two measurement planes. In the absence of such a unitary transform, errors accumulate quickly as the algorithm propagates back and forth between the two planes. Unitary transforms are available for many separable systems, but there has been limited work reported on nonseparable systems other than the gyrator transform. In this letter, we simulate a nonseparable system in a unitary way by choosing an advantageous sampling rate related to the system parameters. We demonstrate a simulation of phase retrieval from intensities in the image domain and a second domain related to the image domain by a nonseparable linear canonical transform. This work may permit the use of nonseparable systems in many design problems.||Funding Details:||Science Foundation Ireland||Funding Details:||Insight Research Centre||Type of material:||Journal Article||Publisher:||IEEE||Journal:||IEEE Signal Processing Letters||Volume:||24||Issue:||6||Start page:||814||End page:||817||Copyright (published version):||2017 IEEE||Keywords:||Personal sensing; Linear canonical transforms; Phase retrieval; Fourier optics and signal processing; Image reconstruction techniques||DOI:||10.1109/LSP.2017.2684829||Language:||en||Status of Item:||Peer reviewed||This item is made available under a Creative Commons License:||https://creativecommons.org/licenses/by-nc-nd/3.0/ie/|
|Appears in Collections:||Electrical and Electronic Engineering Research Collection|
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