{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:59:59Z","timestamp":1778605199096,"version":"3.51.4"},"reference-count":17,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T00:00:00Z","timestamp":1552953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2017YFB1103200"],"award-info":[{"award-number":["2017YFB1103200"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFB1105800"],"award-info":[{"award-number":["2018YFB1105800"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFB1106503"],"award-info":[{"award-number":["2018YFB1106503"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51505169"],"award-info":[{"award-number":["51505169"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51675165"],"award-info":[{"award-number":["51675165"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Phase-shifting profilometry, especially employing the multi-frequency phase-shifting method, is increasingly used for in situ 3D metrology and for the inspection of industrial parts. However, environmental vibrations cause fatal measurement errors and are inevitable in such applications. To this end, an effective and fast vibration detection and motion compensation method for multi-frequency phase-shifting-based 3D sensors is presented. The proposed method quantitatively indicates the strength of the vibration and compensates for the motion error by revising the wrapped phase without accessing neighboring pixels. Different vibration intensities were simulated using an industrial robot moving to test the feasibility of the method. According to experiments, this method is valid and capable for 3D inspection systems affected by inevitable vibrations.<\/jats:p>","DOI":"10.3390\/s19061368","type":"journal-article","created":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T12:12:25Z","timestamp":1552997545000},"page":"1368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Vibration Detection and Motion Compensation for Multi-Frequency Phase-Shifting-Based 3D Sensors"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0342-0732","authenticated-orcid":false,"given":"Liya","family":"Han","sequence":"first","affiliation":[{"name":"State Key Laboratory of Material Processing and Die &amp; Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongwei","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Material Processing and Die &amp; Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Zhong","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Material Processing and Die &amp; Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xu","family":"Cheng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Material Processing and Die &amp; Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hua","family":"Luo","sequence":"additional","affiliation":[{"name":"Xi\u2019an Aerospace Precision Electromechanical Institute, Xi\u2019an 710100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Liu","sequence":"additional","affiliation":[{"name":"Xi\u2019an Aerospace Precision Electromechanical Institute, Xi\u2019an 710100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junyun","family":"Shang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Aerospace Precision Electromechanical Institute, Xi\u2019an 710100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Congjun","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Material Processing and Die &amp; Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Wuhan Vision 3D Technology Ltd., Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yusheng","family":"Shi","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Material Processing and Die &amp; Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Han, L., Cheng, X., Li, Z., Zhong, K., Shi, Y., and Jiang, H. (2018). A Robot-Driven 3D Shape Measurement System for Automatic Quality Inspection of Thermal Objects on a Forging Production Line. Sensors, 18.","DOI":"10.3390\/s18124368"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"094102","DOI":"10.1117\/1.OE.53.9.094102","article-title":"Phase error elimination considering gamma nonlinearity, system vibration, and noise for fringe projection profilometry","volume":"53","author":"Yao","year":"2014","journal-title":"Opt. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4581","DOI":"10.3390\/s130404581","article-title":"Molecular electric transducers as motion sensors: A review","volume":"13","author":"Huang","year":"2013","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1061\/(ASCE)1090-0241(2002)128:7(602)","article-title":"Predicting soil and structure vibrations from impact machines","volume":"128","author":"Svinkin","year":"2002","journal-title":"J. Geotech. Geoenviron. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.ins.2014.12.055","article-title":"Non-distortion-specific no-reference image quality assessment: A survey","volume":"301","author":"Manap","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"494","DOI":"10.3807\/JOSK.2015.19.5.494","article-title":"Vibration Measurement Using a Fringe Pattern in Reflective Monochromatic Interferometry","volume":"19","author":"Kim","year":"2015","journal-title":"J. Opt. Soc. Korea"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.optlaseng.2016.04.022","article-title":"Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review","volume":"85","author":"Zuo","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1364\/OL.38.001389","article-title":"Multiview phase shifting: A full-resolution and high-speed 3D measurement framework for arbitrary shape dynamic objects","volume":"38","author":"Li","year":"2013","journal-title":"Opt. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Reich, C., Ritter, R., and Thesing, J. (1997). White light heterodyne principle for 3D-measurement. Sensors, Sensor Systems, and Sensor Data Processing, International Society for Optics and Photonics.","DOI":"10.1117\/12.287750"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, S. (2009). Digital multiple wavelength phase shifting algorithm. Optical Inspection and Metrology for Non-Optics Industries, International Society for Optics and Photonics.","DOI":"10.1117\/12.823903"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Weise, T., Leibe, B., and Van Gool, L. (2007, January 17\u201322). Fast 3d scanning with automatic motion compensation. Proceedings of the 2007 IEEE Conference on Computer Vision and Pattern Recognition, Minneapolis, MN, USA.","DOI":"10.1109\/CVPR.2007.383291"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1109\/JSTSP.2014.2378217","article-title":"Accurate dynamic 3d sensing with fourier-assisted phase shifting","volume":"9","author":"Cong","year":"2015","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6715","DOI":"10.1364\/OL.39.006715","article-title":"Improving the accuracy performance of phase-shifting profilometry for the measurement of objects in motion","volume":"39","author":"Lu","year":"2014","journal-title":"Opt. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.optlaseng.2017.12.001","article-title":"Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry","volume":"103","author":"Feng","year":"2018","journal-title":"Opt. Lasers Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"053604","DOI":"10.1117\/1.2931517","article-title":"Accurate calibration method for a structured light system","volume":"47","author":"Li","year":"2008","journal-title":"Opt. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1016\/j.optlaseng.2013.02.012","article-title":"High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection","volume":"51","author":"Zuo","year":"2013","journal-title":"Opt. Lasers Eng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hartley, R., and Zisserman, A. (2003). Multiple View Geometry in Computer Vision, Cambridge University Press.","DOI":"10.1017\/CBO9780511811685"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1368\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:38:55Z","timestamp":1760186335000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/6\/1368"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,19]]},"references-count":17,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19061368"],"URL":"https:\/\/doi.org\/10.3390\/s19061368","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,19]]}}}