{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T12:50:59Z","timestamp":1768481459766,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T00:00:00Z","timestamp":1684713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NSFC)","award":["61905241"],"award-info":[{"award-number":["61905241"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["62005279"],"award-info":[{"award-number":["62005279"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["61805235"],"award-info":[{"award-number":["61805235"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The presence of manufacture error in large mirrors introduces high-order aberrations, which can severely influence the intensity distribution of point spread function. Therefore, high-resolution phase diversity wavefront sensing is usually needed. However, high-resolution phase diversity wavefront sensing is restricted with the problem of low efficiency and stagnation. This paper proposes a fast high-resolution phase diversity method with limited memory Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno (L-BFGS) algorithm, which can accurately detect aberrations in the presence of high-order aberrations. An analytical gradient of the objective function for phase-diversity is integrated into the framework of the L-BFGS nonlinear optimization algorithm. L-BFGS algorithm is specifically suitable for high-resolution wavefront sensing where a large phase matrix is optimized. The performance of phase diversity with L-BFGS is compared to other iterative method through simulations and a real experiment. This work contributes to fast high-resolution image-based wavefront sensing with a high robustness.<\/jats:p>","DOI":"10.3390\/s23104966","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T05:49:32Z","timestamp":1684734572000},"page":"4966","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Fast High-Resolution Phase Diversity Wavefront Sensing with L-BFGS Algorithm"],"prefix":"10.3390","volume":"23","author":[{"given":"Haoyuan","family":"Zhang","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"},{"name":"Chinese Academy of Sciences Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guohao","family":"Ju","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"Chinese Academy of Sciences Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Guo","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"},{"name":"Chinese Academy of Sciences Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boqian","family":"Xu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"Chinese Academy of Sciences Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoquan","family":"Bai","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"Chinese Academy of Sciences Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengyi","family":"Jiang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"Chinese Academy of Sciences Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuyan","family":"Xu","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"Chinese Academy of Sciences Key Laboratory of On-Orbit Manufacturing and Integration for Space Optics System, Changchun 130033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"key":"ref_1","first-page":"3","article-title":"Active optics in modern large optical telescopes","volume":"43","author":"Noethe","year":"2002","journal-title":"Prog. 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