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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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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. |
format | Online Article Text |
id | pubmed-7760810 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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