{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T09:50:08Z","timestamp":1782294608408,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T00:00:00Z","timestamp":1575504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["No. 2017YFB1103602"],"award-info":[{"award-number":["No. 2017YFB1103602"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Calibration is a critical step for the phase measuring deflectometry system. Existing calibration methods are mainly optimizing the calibration parameters with respect to the 2D re-projection error criterion. However, such a procedure cannot reduce metric errors in the practical application. Therefore, an accurate and practical calibration method is proposed. In which, conventional calibration means is first applied for the primary calibration. Then, a precise square planar mirror is used for the optimization of system calibration parameters. All the intrinsic and extrinsic parameters are considered as a global multi-objective optimization problem. Three metric error criteria are introduced to evaluate the 3D reconstruction accuracy of the reference mirror. Compared with classical calibration means, which apply the parameter optimization in 2D image space to minimize the re-projection errors, the proposed optimization approach is executed in 3D space directly. An experiment and comparison are conducted to verify that the proposed optimal calibration approach can effectively reduce the system deviation and to improve the system measurement accuracy.<\/jats:p>","DOI":"10.3390\/s19245377","type":"journal-article","created":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T11:16:23Z","timestamp":1575544583000},"page":"5377","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["An Accurate Calibration Means for the Phase Measuring Deflectometry System"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6689-1198","authenticated-orcid":false,"given":"Hao","family":"Han","sequence":"first","affiliation":[{"name":"School of Machinery and Automation, Wuhan University of Science and Technology, Wuhan 430081, China"},{"name":"Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6383-7663","authenticated-orcid":false,"given":"Shiqian","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhan","family":"Song","sequence":"additional","affiliation":[{"name":"Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China"},{"name":"Mechanical and Automation Engineering Department, The Chinese University of Hong Kong, Hong Kong SAR, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"P\u00e9rez, L., Rodr\u00edguez, \u00cd., Rodr\u00edguez, N., Usamentiaga, R., and Garc\u00eda, D.F. (2016). Robot Guidance Using Machine Vision Techniques in Industrial Environments: A Comparative Review. Sensors, 16.","DOI":"10.3390\/s16030335"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Wang, G., Hu, X., Shi, C., Meng, L., and Yang, H. (2019). Guided, Fusion-Based, Large Depth-of-field 3D Imaging Using a Focal Stack. Sensors, 19.","DOI":"10.3390\/s19224845"},{"key":"ref_3","first-page":"3876","article-title":"Pose Guided 310 RGBD Feature Learning for 3D Object Pose Estimation","volume":"311","author":"Balntas","year":"2017","journal-title":"Proc. IEEE Int. Conf. Comput. Vis."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ravankar, A., Ravankar, A.A., Kobayashi, Y., Hoshino, Y., and Peng, C.-C. (2018). Path Smoothing Techniques in Robot Navigation: State-of-the-Art, Current and Future Challenges. Sensors, 18.","DOI":"10.3390\/s18093170"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Song, L., Li, X., Yang, Y.-G., Zhu, X., Guo, Q., and Liu, H. (2018). Structured-Light Based 3D Reconstruction System for Cultural Relic Packaging. Sensors, 18.","DOI":"10.3390\/s18092981"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1109\/TIE.2012.2188875","article-title":"An accurate and robust strip-edge-based structured light means for shiny surface micromeasurement in 3-D","volume":"60","author":"Song","year":"2013","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.optlaseng.2009.03.008","article-title":"Recent progresses on real-time 3D shape measurement using digital fringe projection techniques","volume":"48","author":"Zhang","year":"2010","journal-title":"Opt. Lasers Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2666","DOI":"10.1016\/j.patcog.2010.03.004","article-title":"A state of the art in structured light patterns for surface profilometry","volume":"43","author":"Salvi","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Schmitz, B., Holst, C., Medic, T., Lichti, D.D., and Kuhlmann, H. (2019). How to Efficiently Determine the Range Precision of 3D Terrestrial Laser Scanners. Sensors, 19.","DOI":"10.3390\/s19061466"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1117\/12.545704","article-title":"Phase measuring deflectometry: A new approach to measure specular free-form surfaces","volume":"5457","author":"Knauer","year":"2004","journal-title":"Opt. Metrol. Prod. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.optlaseng.2018.03.026","article-title":"Review of phase measuring deflectometry","volume":"107","author":"Huang","year":"2018","journal-title":"Opt. Lasers Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Wang, Y., Huang, S., Liu, Y., Chang, C., Gao, F., and Jiang, X. (2017). Three-dimensional shape measurements of specular objects using phase-measuring deflectometry. Sensors, 17.","DOI":"10.3390\/s17122835"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.optlaseng.2014.07.002","article-title":"Comparison of two-dimensional integration methods for shape reconstruction from gradient data","volume":"64","author":"Huang","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1364\/AO.56.00F144","article-title":"2017 Improved zonal integration method for high accurate surface reconstruction in quantitative deflectometry","volume":"56","author":"Li","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1364\/AO.47.002091","article-title":"Shape reconstruction from gradient data","volume":"47","author":"Ettl","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7018","DOI":"10.1364\/AO.55.007018","article-title":"Improved system calibration for specular surface measurement by using reflections from a plane mirror","volume":"55","author":"Zhou","year":"2016","journal-title":"Appl. Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"22060","DOI":"10.1364\/OE.23.022060","article-title":"Iterative optimization calibration method for stereo deflectometry","volume":"23","author":"Ren","year":"2015","journal-title":"Opt. Express"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/JRA.1987.1087109","article-title":"A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses","volume":"3","author":"Tsai","year":"1987","journal-title":"IEEE J. Robot. Autom."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1109\/34.888718","article-title":"A flexible new technique for camera calibration","volume":"22","author":"Zhang","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6278","DOI":"10.1364\/AO.52.006278","article-title":"Flexible camera calibration using not-measured imperfect target","volume":"52","author":"Huang","year":"2013","journal-title":"Appl. Opt."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Huang, R., Su, P., and Burge, J.H. (2015, January 27). Deflectometry measurement of Daniel K. Inouye Solar Telescope primary mirror. In Proceedings of the Optical Manufacturing and Testing XI, San Diego, CA, USA.","DOI":"10.1117\/12.2189258"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"12393","DOI":"10.1364\/OE.20.012393","article-title":"Non-null full field X-ray mirror metrology using SCOTS: A reflection deflectometry approach","volume":"20","author":"Su","year":"2012","journal-title":"Opt. Express"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"084103","DOI":"10.1117\/1.OE.54.8.084103","article-title":"High-accuracy aspheric x-ray mirror metrology using Software Configurable Optical Test System\/deflectometry","volume":"54","author":"Huang","year":"2015","journal-title":"Opt. Eng."},{"key":"ref_24","first-page":"100230X","article-title":"Full-field 3D shape measurement of specular surfaces by direct phase to depth relationship","volume":"10023","author":"Zhang","year":"2016","journal-title":"Opt. Metrol. Insp. Ind. Appl. IV"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Petz, M., and Tutsch, R. (2005, January 18). Reflection grating photogrammetry: A technique for absolute shape measurement of specular free-form surfaces. Proceedings of the Optical Manufacturing and Testing VI, San Diego, CA, USA.","DOI":"10.1117\/12.617325"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Sturm, P., and Bonfort, T. (2006, January 4\u20136). How to compute the pose of an object without a direct view?. Proceedings of the Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Oeiras, Portugal.","DOI":"10.1007\/11612704_3"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.optlaseng.2018.01.013","article-title":"Optical fringe-reflection deflectometry with bundle adjustment","volume":"105","author":"Xiao","year":"2018","journal-title":"Opt. Lasers Eng."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Takahashi, K., Nobuhara, S., and Matsuyama, T. (2012, January 16\u201321). A new mirror-based extrinsic camera calibration using an orthogonality constraint. Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition, Providence, RI, USA.","DOI":"10.1109\/CVPR.2012.6247783"},{"key":"ref_29","first-page":"2","article-title":"Deflectometric Self-Calibration for arbitrary specular surfaces","volume":"3","author":"Olesch","year":"2011","journal-title":"DGaO Proc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7523","DOI":"10.1364\/OE.27.007523","article-title":"Self-calibration of in situ monoscopic deflectometric measurement in precision optical manufacturing","volume":"27","author":"Xu","year":"2019","journal-title":"Opt. Express"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"24649","DOI":"10.1364\/OE.24.024649","article-title":"Modal phase measuring deflectometry","volume":"24","author":"Huang","year":"2016","journal-title":"Opt. Express"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.optlaseng.2018.02.018","article-title":"A holistic calibration method with iterative distortion compensation for stereo deflectometry","volume":"106","author":"Xu","year":"2018","journal-title":"Opt. Lasers Eng."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Hesch, J.A., Mourikis, A.I., and Roumeliotis, S.I. (2010). Mirror based extrinsic camera calibration. Algorithmic Foundation of Robotics VIII, Springer.","DOI":"10.1007\/978-3-642-00312-7_18"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1137\/S0895479898338561","article-title":"Householder transformations revisited","volume":"22","author":"Dubrulle","year":"2000","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_35","unstructured":"Gembicki, F.W. (1974). Vector Optimization for Control with Performance and Parameter Sensitivity Indices. [Ph.D. Thesis, Case Western Reserve University]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/24\/5377\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:40:40Z","timestamp":1760190040000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/24\/5377"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,5]]},"references-count":35,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["s19245377"],"URL":"https:\/\/doi.org\/10.3390\/s19245377","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,5]]}}}