{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:38:24Z","timestamp":1760143104448,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T00:00:00Z","timestamp":1705881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The phase recovery module is dedicated to acquiring phase distribution information within imaging systems, enabling the monitoring and adjustment of a system\u2019s performance. Traditional phase inversion techniques exhibit limitations, such as the speed of the sensor and complexity of the system. Therefore, we propose an indirect phase retrieval approach based on a diffraction neural network. By utilizing non-source diffraction through multiple layers of diffraction units, this approach reconstructs coefficients based on Zernike polynomials from incident beams with distorted phases, thereby indirectly synthesizing interference phases. Through network training and simulation testing, we validate the effectiveness of this approach, showcasing the trained network\u2019s capacity for single-order phase recognition and multi-order composite phase inversion. We conduct an analysis of the network\u2019s generalization and evaluate the impact of the network depth on the restoration accuracy. The test results reveal an average root mean square error of 0.086\u03bb for phase inversion. This research provides new insights and methodologies for the development of the phase recovery component in adaptive optics systems.<\/jats:p>","DOI":"10.3390\/s24020698","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T12:01:13Z","timestamp":1705924873000},"page":"698","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Using Diffraction Deep Neural Networks for Indirect Phase Recovery Based on Zernike Polynomials"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9486-6431","authenticated-orcid":false,"given":"Fang","family":"Yuan","sequence":"first","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Sun","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuting","family":"Han","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hairong","family":"Chu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianxiang","family":"Ma","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8085-9805","authenticated-orcid":false,"given":"Honghai","family":"Shen","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"31859","DOI":"10.1364\/OE.438379","article-title":"COACH-based Shack\u2013Hartmann wavefront sensor with an array of phase coded masks","volume":"29","author":"Dubey","year":"2021","journal-title":"Opt. 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