{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T14:24:30Z","timestamp":1768746270141,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T00:00:00Z","timestamp":1661299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11772225"],"award-info":[{"award-number":["11772225"]}]},{"name":"National Natural Science Foundation of China","award":["52075147"],"award-info":[{"award-number":["52075147"]}]},{"name":"National Natural Science Foundation of China","award":["2019M660013"],"award-info":[{"award-number":["2019M660013"]}]},{"name":"National Natural Science Foundation of China","award":["2021T140043"],"award-info":[{"award-number":["2021T140043"]}]},{"name":"China Postdoctoral Science Foundation","award":["11772225"],"award-info":[{"award-number":["11772225"]}]},{"name":"China Postdoctoral Science Foundation","award":["52075147"],"award-info":[{"award-number":["52075147"]}]},{"name":"China Postdoctoral Science Foundation","award":["2019M660013"],"award-info":[{"award-number":["2019M660013"]}]},{"name":"China Postdoctoral Science Foundation","award":["2021T140043"],"award-info":[{"award-number":["2021T140043"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We propose a method for accurately calibrating a telecentric structured light system consisting of a camera attached to a bilateral telecentric lens and a pin-hole projector. The proposed method can be split into two parts: axial calibration and transverse calibration. The first part is used for building the relationship between phase and depth by means of a planar plate with ring markers on its surface at several different positions in the measuring volume. The second part is used for establishing the relationship between transverse coordinates and pixel positions with the depth offered by a translation stage and the extracted ring centers. Compared with existing methods that require projector calibration, the proposed method can avoid a propagation of the correspondence error between the camera imaging plane and projector imaging plane, thus increasing calibration accuracy. The calibrated telecentric structured light system is further used for three-dimensional (3D) reconstructions of a planar, a ruled surface, and complex surfaces. Experimental results demonstrate that the proposed system calibration method can be used for accurate 3D measurement.<\/jats:p>","DOI":"10.3390\/s22176370","type":"journal-article","created":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T23:48:58Z","timestamp":1661384938000},"page":"6370","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A High-Accuracy Calibration Method for a Telecentric Structured Light System"],"prefix":"10.3390","volume":"22","author":[{"given":"Chao","family":"Chen","sequence":"first","affiliation":[{"name":"Tianjin Key Laboratory of Refrigeration Technology, Tianjin University of Commerce, Tianjin 300134, China"},{"name":"School of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, China"}]},{"given":"Ya","family":"Kong","sequence":"additional","affiliation":[{"name":"Tianjin Xunlian Technology Co., Ltd., Tianjin 300308, China"}]},{"given":"Huaiwen","family":"Wang","sequence":"additional","affiliation":[{"name":"Tianjin Key Laboratory of Refrigeration Technology, Tianjin University of Commerce, Tianjin 300134, China"},{"name":"School of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6645-6647","authenticated-orcid":false,"given":"Zonghua","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.optlaseng.2018.09.011","article-title":"A new microscopic telecentric stereo vision system-Calibration, rectification, and three-dimensional reconstruction","volume":"113","author":"Hu","year":"2019","journal-title":"Opt. Lasers Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chen, K., Shi, T., Liu, Q., Tang, Z., and Liao, G. (2018). Microscopic three-dimensional measurement based on telecentric stereo and speckle projection methods. Sensors, 18.","DOI":"10.3390\/s18113882"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4951","DOI":"10.1364\/OL.41.004951","article-title":"Circular fringe projection profilometry","volume":"41","author":"Zhao","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1364\/OE.27.002465","article-title":"Three-dimensional measurement based on optimized circular fringe projection technique","volume":"27","author":"Zhang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"055203","DOI":"10.1088\/1361-6501\/ab63b0","article-title":"Efficient method for detecting a zero-phase point in off-axis circular fringe projection profilometry","volume":"31","author":"Zhang","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106366","DOI":"10.1016\/j.optlaseng.2020.106366","article-title":"A convenient 3D reconstruction model based on parallel-axis structured light system","volume":"138","author":"Zhang","year":"2020","journal-title":"Opt. Lasers Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"085003","DOI":"10.1088\/1361-6501\/ab63b2","article-title":"Uniaxial three-dimensional phase-shifting profilometry using a dual-telecentric structured light system in micro-scale device","volume":"31","author":"Zhong","year":"2020","journal-title":"Meas. Sci. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"31826","DOI":"10.1364\/OE.22.031826","article-title":"Telecentric 3D profilometry based on phase-shifting fringe projection","volume":"22","author":"Li","year":"2014","journal-title":"Opt. Express"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"25795","DOI":"10.1364\/OE.23.025795","article-title":"Flexible calibration method for microscopic structured light system using telecentric lens","volume":"23","author":"Li","year":"2015","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1364\/OE.24.001222","article-title":"Flexible calibration method for telecentric fringe projection profilometry systems","volume":"24","author":"Rao","year":"2016","journal-title":"Opt. Express"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"31492","DOI":"10.1364\/OE.25.031492","article-title":"Calibration method for projector-camera-based telecentric fringe projection profilometry system","volume":"25","author":"Liu","year":"2017","journal-title":"Opt. Express"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6846","DOI":"10.1364\/OE.23.006846","article-title":"Fringe projection 3D microscopy with the general imaging model","volume":"23","author":"Yin","year":"2015","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.optlaseng.2016.06.009","article-title":"Microscopic structured light 3D profilometry: Binary defocusing technique vs. sinusoidal fringe projection","volume":"96","author":"Li","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Pistellato, M., Albarelli, A., and Bergamasco, F. (2022, January 3). Calibration of a telecentric structured-light device for micrometric 3D reconstruction. Proceedings of the ICPRAM, Vienna, Austria.","DOI":"10.5220\/0010841700003122"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.optlaseng.2014.01.021","article-title":"Telecentric stereo micro-vision system: Calibration method and experiments","volume":"57","author":"Chen","year":"2014","journal-title":"Opt. Lasers Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"12218","DOI":"10.1364\/OE.21.012218","article-title":"A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system","volume":"21","author":"Zhang","year":"2013","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1364\/OL.36.001257","article-title":"Simple. Flexible calibration of phase calculation-based three-dimensional imaging system","volume":"36","author":"Zhang","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105202","DOI":"10.1088\/0957-0233\/27\/10\/105202","article-title":"Simplification of high order polynomial calibration model for fringe projection profilometry","volume":"27","author":"Yu","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"125004","DOI":"10.1088\/1361-6501\/ac1bec","article-title":"Telecentric camera calibration with virtual patterns","volume":"32","author":"Chen","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6444","DOI":"10.1364\/OE.14.006444","article-title":"Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency selection","volume":"14","author":"Zhang","year":"2006","journal-title":"Opt. Express"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1971","DOI":"10.1007\/s00607-019-00723-6","article-title":"An accurate and flexible technique for camera calibration","volume":"101","author":"Jiang","year":"2019","journal-title":"Computing"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"27547","DOI":"10.1109\/ACCESS.2019.2894863","article-title":"Weak micro-scratch detection based on deep convolutional neural network","volume":"7","author":"Song","year":"2019","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Ku, Y.-S., Chang, P.-Y., Lee, H.-W., Lo, C.-W., Chen, Y.-C., and Cho, C.-H. (2022). Metrology for measuring bumps in a projection layer based on phase shifting fringe projection. Appl. Sci., 12.","DOI":"10.3390\/app12020898"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/17\/6370\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:14:35Z","timestamp":1760141675000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/17\/6370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,24]]},"references-count":23,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["s22176370"],"URL":"https:\/\/doi.org\/10.3390\/s22176370","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,24]]}}}