{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:35:43Z","timestamp":1740148543359,"version":"3.37.3"},"reference-count":19,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T00:00:00Z","timestamp":1596844800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shanghai Aerospace Science and Engineering Fund","award":["SAST2017-062","17ZR1443500","U1831133","61701296"],"award-info":[{"award-number":["SAST2017-062","17ZR1443500","U1831133","61701296"]}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai","doi-asserted-by":"publisher","award":["SAST2017-062","17ZR1443500","U1831133","61701296"],"award-info":[{"award-number":["SAST2017-062","17ZR1443500","U1831133","61701296"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["SAST2017-062","17ZR1443500","U1831133","61701296"],"award-info":[{"award-number":["SAST2017-062","17ZR1443500","U1831133","61701296"]}],"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":["SAST2017-062","17ZR1443500","U1831133","61701296"],"award-info":[{"award-number":["SAST2017-062","17ZR1443500","U1831133","61701296"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Sensors"],"published-print":{"date-parts":[[2020,8,8]]},"abstract":"<jats:p>In view of the problem of \u201cjumping points\u201d in the phase unwrapping of the multifrequency heterodyne principle, this paper proposes a novel method to improve the multifrequency heterodyne. By solving the root-mean-square error of the original frequency function, it includes the relationship between the error and the adjacent phase in the condition of constrained phase unwrapping, and it compensates phase <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mo>\u00b1<\/mml:mo><mml:mn>2<\/mml:mn><mml:mi>\u03c0<\/mml:mi><\/mml:math> of the skip point. To ensure the accuracy of phase unwrapping, the function with a \u201cjump point\u201d after each phase unwrapping and the absolute phase curve of the principal value function are used to establish the threshold judgment model of the least square method, and the initial phase unwrapping of the principal value function with different frequencies is carried out continuously. The simulation analysis of phase compensation with the four-step phase-shifting method shows that the error is reduced to 36% under the set environment. The experimental result of 3D reconstruction by measuring the flatness of the plate shows that the error decreases by 41% after phase compensation compared with before phase compensation. The three-dimensional reconstruction experiment of pitch measurement with a nut shows that the nut after phase compensation is smooth without noise, and the pitch error is 0.033\u2009mm, which verified the method is workable and effective.<\/jats:p>","DOI":"10.1155\/2020\/8833305","type":"journal-article","created":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T23:32:05Z","timestamp":1596929525000},"page":"1-10","source":"Crossref","is-referenced-by-count":5,"title":["A Multifrequency Heterodyne Phase Error Compensation Method for 3D Reconstruction"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7847-3359","authenticated-orcid":true,"given":"Zihao","family":"Yu","sequence":"first","affiliation":[{"name":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5607-9940","authenticated-orcid":true,"given":"Jin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5286-2989","authenticated-orcid":true,"given":"Haima","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China"}]},{"given":"Bo","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"}]},{"given":"Yumei","family":"Jian","sequence":"additional","affiliation":[{"name":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2016.04.022"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1364\/OL.34.000416"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2016.08.004"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1364\/OE.14.002644"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2017.12.071"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.measurement.2020.107904"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1364\/OPEX.13.001561"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2013.07.026"},{"key":"9","first-page":"332","volume":"2","year":"2018","journal-title":"Current Optics and Photonics"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1364\/OE.26.016277"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1364\/OE.384155"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1088\/0957-0233\/26\/3\/035201"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1364\/OE.23.025171"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.optlaseng.2014.12.001"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2018.03.006"},{"journal-title":"Chaos, Solitons & Fractals","year":"2020","key":"16"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.4028\/www.scientific.net\/AMR.774-776.1582"},{"first-page":"904607","volume-title":"Crosstalk reduction of a color fringe projection system based on multi-frequency heterodyne principle","year":"2013","key":"18"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1364\/AO.46.000036"}],"container-title":["Journal of Sensors"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/js\/2020\/8833305.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/js\/2020\/8833305.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/js\/2020\/8833305.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T23:32:09Z","timestamp":1596929529000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/js\/2020\/8833305\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,8]]},"references-count":19,"alternative-id":["8833305","8833305"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8833305","relation":{},"ISSN":["1687-725X","1687-7268"],"issn-type":[{"type":"print","value":"1687-725X"},{"type":"electronic","value":"1687-7268"}],"subject":[],"published":{"date-parts":[[2020,8,8]]}}}