{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T18:07:39Z","timestamp":1774030059180,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,6]],"date-time":"2018-01-06T00:00:00Z","timestamp":1515196800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key R&amp;D Program of China","award":["2017YFF0106404"],"award-info":[{"award-number":["2017YFF0106404"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51675160"],"award-info":[{"award-number":["51675160"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Basic Research Project of Applied Basic Research Programs Supported by Hebei Province","award":["15961701D"],"award-info":[{"award-number":["15961701D"]}]},{"name":"Research Project for High-level Talents in Hebei University","award":["GCC2014049"],"award-info":[{"award-number":["GCC2014049"]}]},{"name":"Talents Project Training Funds in Hebei Province","award":["A201500503"],"award-info":[{"award-number":["A201500503"]}]},{"name":"\u201cInnovative and Entrepreneurial Talent\u201d Project Supported by Jiangsu Province","award":["2016A377"],"award-info":[{"award-number":["2016A377"]}]},{"name":"European Horizon 2020 through the Marie Sklodowska-Curie Fellowship Scheme","award":["707466-3DRM"],"award-info":[{"award-number":["707466-3DRM"]}]},{"name":"the UK\u2019s Engineering and Physical Sciences Research Council (EPSRC) funding of Future Advanced Metrology Hub","award":["EP\/P006930\/1"],"award-info":[{"award-number":["EP\/P006930\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The recently developed direct phase measuring deflectometry (DPMD) method can directly measure the three-dimensional (3D) shape of specular objects with discontinuous surfaces, but requires a calibrated distance between a reference plane and liquid crystal display screen. Because the plane and screen are different distances from the imaging device, they cannot be clearly captured given the limited depth of field (DOF) of the lens. Therefore, existing machine vision-based methods cannot be used to effectively calibrate a DPMD system. In this paper, a new distance calibration method that uses a mirror with a hollow ring matrix pattern and a mobile stage is presented. The direction of the mobile stage in the camera coordinate system is determined by the mirror\u2019s pattern at several positions in the camera\u2019s DOF so that the reference position outside of the DOF can be calculated. The screen\u2019s position can also be calibrated by displaying patterns at a known scale. Therefore, the required distance is accurately obtained in the camera coordinate system. Evaluation results show that the maximum value of the absolute error is less than 0.031 mm. The experimental results on an artificial stepped mirror and a reflected diamond distribution surface demonstrate the accuracy and practicality of the proposed method.<\/jats:p>","DOI":"10.3390\/s18010144","type":"journal-article","created":{"date-parts":[[2018,1,8]],"date-time":"2018-01-08T12:26:02Z","timestamp":1515414362000},"page":"144","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Distance Calibration between Reference Plane and Screen in Direct Phase Measuring Deflectometry"],"prefix":"10.3390","volume":"18","author":[{"given":"Shujun","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"},{"name":"Centre for Precision Technologies, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nan","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"},{"name":"Centre for Precision Technologies, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3835-6929","authenticated-orcid":false,"given":"Feng","family":"Gao","sequence":"additional","affiliation":[{"name":"Centre for Precision Technologies, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangqian","family":"Jiang","sequence":"additional","affiliation":[{"name":"Centre for Precision Technologies, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1016\/j.optlaseng.2012.03.009","article-title":"An absolute phase technique for 3D profile measurement using four-step structured light pattern","volume":"50","author":"Xu","year":"2012","journal-title":"Opt. 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