{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T17:02:32Z","timestamp":1793120552317,"version":"4.5.0"},"reference-count":18,"publisher":"Optica Publishing Group","issue":"15","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"National Science and Technology\n\t\t\t\t\t\tCouncil","award":["113\u20132221\u2013E\u2013035\u2013037"],"award-info":[{"award-number":["113\u20132221\u2013E\u2013035\u2013037"]}],"id":[{"id":"https:\/\/ror.org\/02kv4zf79","id-type":"ROR","asserted-by":"publisher"}]},{"name":"National Science and Technology\n\t\t\t\t\t\tCouncil","award":["114\u20132221\u2013E\u2013035\u2013013\u2013MY2"],"award-info":[{"award-number":["114\u20132221\u2013E\u2013035\u2013013\u2013MY2"]}],"id":[{"id":"https:\/\/ror.org\/02kv4zf79","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2026,5,20]]},"abstract":"<jats:p>This paper presents a heterodyne moir\u00e9 fringe technique with real-time\n\t\t\t\t\ttunable fringe pitch for high-precision surface profilometry. The\n\t\t\t\t\tproposed method combines tunable fringe projection, heterodyne\n\t\t\t\t\tfrequency-shifting, and a least-squares sinusoidal fitting algorithm\n\t\t\t\t\tto achieve stable and high-resolution phase extraction and surface\n\t\t\t\t\treconstruction. A computer-generated dynamic grating pattern is\n\t\t\t\t\tprojected onto a spatial light modulator, and the reflected fringe\n\t\t\t\t\tpattern, deformed by the object\u2019s surface profile, is captured by a\n\t\t\t\t\tcamera. This deformed fringe is then digitally superimposed with a\n\t\t\t\t\tvirtual reference grating to generate a time-varying heterodyne moir\u00e9\n\t\t\t\t\tsignal. Phase information is retrieved through phase analysis and\n\t\t\t\t\tunwrapped when necessary to reconstruct the continuous 3D surface\n\t\t\t\t\tprofile. Experimental validation using a coin and a plaster statue\n\t\t\t\t\tdemonstrated a height measurement error of approximately 1.4\u00a0\u00b5m.\n\t\t\t\t\tCompared with conventional physical grating systems, the proposed\n\t\t\t\t\tapproach offers real-time pitch tunability, non-contact operation, a\n\t\t\t\t\tsimplified setup, and ease of use, demonstrating strong potential for\n\t\t\t\t\tapplications in precision optical metrology.<\/jats:p>","DOI":"10.1364\/ao.583392","type":"journal-article","created":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T14:00:09Z","timestamp":1766152809000},"page":"G10","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Surface profile measurement using heterodyne moir\u00e9 signals with an adjustable grating period"],"prefix":"10.1364","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4448-1999","authenticated-orcid":true,"given":"Kun-Huang","family":"Chen","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05vhczg54","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chia-Hung","family":"Tsai","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05vhczg54","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sheng-Chun","family":"Hung","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05vhczg54","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0804-4564","authenticated-orcid":true,"given":"Jing-Heng","family":"Chen","sequence":"additional","affiliation":[{"name":"Feng Chia University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"ao-65-15-G10-R1","doi-asserted-by":"publisher","first-page":"053603","DOI":"10.1117\/1.3574399","type":"journal-article","volume":"50","author":"Nakazawa","year":"2011","journal-title":"Opt. 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All rights, including\n\t\t\t\t\tfor text and data mining (TDM), Artificial Intelligence (AI) training,\n\t\t\t\t\tand similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}