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Opt. Soc. Am. A"],"published-print":{"date-parts":[[2026,5,1]]},"abstract":"<jats:p>In order to solve the problem of the traditional head-up display system being able to present information only on a single plane, which leads to visual confusion and other poor results, this paper proposes an augmented reality head-up display (AR-HUD) system using a single spatial light modulator (SLM) to realize multi-depth information presentation. The adaptive compensated Gerchberg\u2013Saxton (ACGS) algorithm was used to construct multi-focal plane computer-generated holograms (CGHs), and the weight factor of the constraint function was adaptively compensated in each iteration to optimize the final phase distribution. A nonlinear weighting mechanism is introduced to comprehensively consider the image error and local contrast, so as to improve the imaging quality and detail contrast of the AR-HUD and realize the multi-focal plane AR-HUD. Simulation and experimental results show that the root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM) of the multi-focal plane images are improved by more than 37% compared to the conventional multi-focal plane algorithm. This paper provides an ideal scheme for a high-definition multi-focal plane AR-HUD.<\/jats:p>","DOI":"10.1364\/josaa.587718","type":"journal-article","created":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T14:00:09Z","timestamp":1774360809000},"page":"847","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-depth augmented reality head-up display based on LCoS using the adaptive compensation GS\u00a0algorithm"],"prefix":"10.1364","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3211-9458","authenticated-orcid":true,"given":"Gaoyu","family":"Dai","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/006teas31","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5392-3605","authenticated-orcid":true,"given":"Fei","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/006teas31","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luqiao","family":"Yin","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/006teas31","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanan","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/006teas31","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianhua","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/006teas31","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,5,1]]},"reference":[{"key":"josaa-43-5-847-R1","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1016\/j.ijhcs.2004.06.002","type":"journal-article","volume":"61","author":"Liu","year":"2004","journal-title":"Int. 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