{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T18:53:50Z","timestamp":1771700030579,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,22]],"date-time":"2018-08-22T00:00:00Z","timestamp":1534896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51675138"],"award-info":[{"award-number":["51675138"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2017T100234"],"award-info":[{"award-number":["2017T100234"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018537","name":"National Science and Technology Major Project","doi-asserted-by":"publisher","award":["2017ZX02101006-005"],"award-info":[{"award-number":["2017ZX02101006-005"]}],"id":[{"id":"10.13039\/501100018537","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The phase quadrature measurement method is capable of measuring nonlinearity in heterodyne laser interferometers with picometer accuracy whereas it cannot be applied in the new kind of heterodyne interferometers with bidirectional Doppler frequency shift especially in the condition of non-uniform motion of the target. To solve this problem, a novel measurement method of nonlinearity is proposed in this paper. By employing double-channel quadrature demodulation and substituting the external reference signal with internal ones, this method is free from the type of heterodyne laser interferometer and the motion state of the target. For phase demodulation, the phase differential algorithm is utilized to improve the computing efficiency. Experimental verification is carried out and the results indicate that the proposed measurement method achieves accuracy better than 2 pm.<\/jats:p>","DOI":"10.3390\/s18092768","type":"journal-article","created":{"date-parts":[[2018,8,23]],"date-time":"2018-08-23T03:00:46Z","timestamp":1534993246000},"page":"2768","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Measurement Method for Nonlinearity in Heterodyne Laser Interferometers Based on Double-Channel Quadrature Demodulation"],"prefix":"10.3390","volume":"18","author":[{"given":"Haijin","family":"Fu","sequence":"first","affiliation":[{"name":"Institute of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Ruidong","family":"Ji","sequence":"additional","affiliation":[{"name":"Institute of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2471-7036","authenticated-orcid":false,"given":"Pengcheng","family":"Hu","sequence":"additional","affiliation":[{"name":"Institute of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Yue","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Guolong","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150001, China"}]},{"given":"Jiubin","family":"Tan","sequence":"additional","affiliation":[{"name":"Institute of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1364\/AO.24.000808","article-title":"High-accuracy displacement interferometry refin air","volume":"24","author":"Estler","year":"1985","journal-title":"Appl. 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