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Express"],"published-print":{"date-parts":[[2025,11,17]]},"abstract":"<jats:p>Single-shot fringe projection profilometry (FPP) offers significant advantages for dynamic three-dimensional (3D) measurement. However, existing deep learning-based single-shot methods still struggle to simultaneously and accurately extract the wrapped phase and fringe order. Because the former is a continuous physical quantity while the latter is a discrete integer label, their joint estimation from a single periodic pattern is inherently ambiguous, especially for isolated objects lacking spatial continuity. To address this problem, a deep learning-enabled single-shot FPP method is proposed by integrating inner shifting-phase encoding with a physically constrained dual-network architecture. The fringe order is embedded into the phase-shifting component of a single high-frequency fringe pattern, and two lightweight convolutional neural networks are then employed: one regresses the numerator and denominator of the wrapped phase, while the other classifies the inner shifting-phase value to recover the fringe order. This physically consistent decoupled design avoids the optimization conflicts of end-to-end regression and enables unambiguous absolute phase recovery. Experiments show that the proposed method could achieve high-accuracy absolute phase recovery comparable to traditional multi-frame techniques for measurements of complex and isolated objects, while maintaining low computational complexity. The dynamic experimental results demonstrate its application potential for dynamic 3D measurement.<\/jats:p>","DOI":"10.1364\/oe.576136","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T04:00:07Z","timestamp":1762488007000},"page":"49530","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Deep-learning-enabled single-shot fringe projection profilometry based on inner shifting-phase encoding"],"prefix":"10.1364","volume":"33","author":[{"given":"Jinlong","family":"Li","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hn7w693","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kuo","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hn7w693","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Luo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hn7w693","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gaokun","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hn7w693","id-type":"ROR","asserted-by":"publisher"}]},{"name":"China Railway SIYUAN Survey and Design Group Co., Ltd."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Tang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hn7w693","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhijie","family":"Wang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hn7w693","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0525-2337","authenticated-orcid":true,"given":"Yingying","family":"Wan","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00hn7w693","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2025,11,13]]},"reference":[{"key":"oe-33-23-49530-R1","doi-asserted-by":"publisher","first-page":"113816","DOI":"10.1016\/j.measurement.2023.113816","type":"journal-article","volume":"224","author":"Ojal","year":"2024","journal-title":"Measurement"},{"key":"oe-33-23-49530-R2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41377-021-00680-w","type":"journal-article","volume":"11","author":"Zuo","year":"2022","journal-title":"Light:Sci. 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