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Modified Gerchberg–Saxton (G-S) Algorithm and Its Application

The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose...

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Autores principales: Zhao, Tieyu, Chi, Yingying
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7760810/
https://www.ncbi.nlm.nih.gov/pubmed/33266143
http://dx.doi.org/10.3390/e22121354
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author Zhao, Tieyu
Chi, Yingying
author_facet Zhao, Tieyu
Chi, Yingying
author_sort Zhao, Tieyu
collection PubMed
description The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which n plaintexts can be recovered from n ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm.
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spelling pubmed-77608102021-02-24 Modified Gerchberg–Saxton (G-S) Algorithm and Its Application Zhao, Tieyu Chi, Yingying Entropy (Basel) Article The Gerchberg–Saxton (G-S) algorithm is a phase retrieval algorithm that is widely used in beam shaping and optical information processing. However, the G-S algorithm has difficulty obtaining the exact solution after iterating, and an approximate solution is often obtained. In this paper, we propose a series of modified G-S algorithms based on the Fresnel transform domain, including the single-phase retrieval (SPR) algorithm, the double-phase retrieval (DPR) algorithm, and the multiple-phase retrieval (MPR) algorithm. The analysis results show that the convergence of the SPR algorithm is better than that of the G-S algorithm, but the exact solution is not obtained. The DPR and MPR algorithms have good convergence and can obtain exact solutions; that is, the information is recovered losslessly. We discuss the security advantages and verification reliability of the proposed algorithms in image encryption. A multiple-image encryption scheme is proposed, in which n plaintexts can be recovered from n ciphertexts, which greatly improves the efficiency of the system. Finally, the proposed algorithms are compared with the current phase retrieval algorithms, and future applications are discussed. We hope that our research can provide new ideas for the application of the G-S algorithm. MDPI 2020-11-30 /pmc/articles/PMC7760810/ /pubmed/33266143 http://dx.doi.org/10.3390/e22121354 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Zhao, Tieyu
Chi, Yingying
Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
title Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
title_full Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
title_fullStr Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
title_full_unstemmed Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
title_short Modified Gerchberg–Saxton (G-S) Algorithm and Its Application
title_sort modified gerchberg–saxton (g-s) algorithm and its application
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7760810/
https://www.ncbi.nlm.nih.gov/pubmed/33266143
http://dx.doi.org/10.3390/e22121354
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