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Express"],"published-print":{"date-parts":[[2026,10,5]]},"abstract":"<jats:p>Temporal phase unwrapping commonly projects phase-shifted fringes and auxiliary codewords separately, which increases the acquisition burden in dynamic fringe projection profilometry. We propose phase-gradient Gray code (PGGC), which represents four Gray-code bits through controlled reversals of phase-gradient polarity. Successive exchanges of orthogonal sine and cosine fringe pairs form a 12-pattern cyclic sequence, from which five overlapping demodulation groups recover one reference phase and four Gray-code-bearing wrapped phases. Distance-adaptive gradient voting, half-period connectivity, and stable-region voting are then used to decode and refine the fringe orders before phase-polarity restoration and reference-consistency correction. The phase-shifting patterns thereby support both wrapped-phase retrieval and fringe-order decoding without a separate intensity-codeword sequence. In the low-reflectivity experiment, PGGC achieved a fringe-order disagreement rate of 0.118% relative to complementary Gray code (CGC), the lowest among the non-reference methods tested. Static and high-spatial-frequency experiments further demonstrated the reconstruction procedure, and continuous acquisition was evaluated with a model rotating at approximately 4 rpm. At 120 projected patterns\/s, each 12-pattern cycle yields five temporally shared phase outputs, corresponding to an average of 50 phase maps\/s. Reference-consistency correction supports this reconstruction under limited intra-cycle physical phase variation.<\/jats:p>","DOI":"10.1364\/oe.614434","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T15:12:12Z","timestamp":1790781132000},"page":"38284","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["PGGC: phase-gradient Gray code with temporal pattern sharing for 3D measurement"],"prefix":"10.1364","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4111-9211","authenticated-orcid":true,"given":"Haitao","family":"Wu","sequence":"first","affiliation":[{"name":"Southwest Jiaotong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0388-609X","authenticated-orcid":true,"given":"Yiping","family":"Cao","sequence":"additional","affiliation":[{"name":"Sichuan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Southwest Jiaotong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinlong","family":"Li","sequence":"additional","affiliation":[{"name":"Southwest Jiaotong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhijie","family":"Wang","sequence":"additional","affiliation":[{"name":"Southwest Jiaotong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0525-2337","authenticated-orcid":true,"given":"Yingying","family":"Wan","sequence":"additional","affiliation":[{"name":"Southwest Jiaotong University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"oe-34-20-38284-R1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TIM.2024.3427804","type":"journal-article","volume":"73","author":"Zhu","year":"2024","journal-title":"IEEE Trans. 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