Unitary Algorithm for Nonseparable Linear Canonical Transforms Applied to Iterative Phase Retrieval

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Title: Unitary Algorithm for Nonseparable Linear Canonical Transforms Applied to Iterative Phase Retrieval
Authors: Zhao, LiangSheridan, 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 sensingLinear canonical transformsPhase retrievalFourier optics and signal processingImage 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
Insight Research Collection

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