{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T10:43:45Z","timestamp":1768992225246,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51905030"],"award-info":[{"award-number":["51905030"]}]},{"name":"National Natural Science Foundation of China","award":["2022XAGG0200"],"award-info":[{"award-number":["2022XAGG0200"]}]},{"name":"Ministry of Science and Technology","award":["51905030"],"award-info":[{"award-number":["51905030"]}]},{"name":"Ministry of Science and Technology","award":["2022XAGG0200"],"award-info":[{"award-number":["2022XAGG0200"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Using polarization-maintaining fiber (PMF) in dual-frequency heterodyne interferometry has the advantages of reducing the laser\u2019s own drift, obtaining high-quality light spots, and improving thermal stability. Using only one single-mode PMF to achieve the transmission of dual-frequency orthogonal, linearly polarized beam requires angular alignment only once to realize the transmission of dual-frequency orthogonal, linearly polarized light, avoiding coupling inconsistency errors, so that it has the advantages of high efficiency and low cost. However, there are still many nonlinear influencing factors in this method, such as the ellipticity and non-orthogonality of the dual-frequency laser, the angular misalignment error of the PMF, and the influence of temperature on the output beam of the PMF. This paper uses the Jones matrix to innovatively construct an error analysis model for the heterodyne interferometry using one single-mode PMF, to realize the quantitative analysis of various nonlinear error influencing factors, and clarify that the main error source is the angular misalignment error of the PMF. For the first time, the simulation provides a goal for the optimization of the alignment scheme of the PMF and the improvement of the accuracy to the sub-nanometer level. In actual measurement, the angular misalignment error of the PMF needs to be smaller than 2.87\u00b0 to achieve sub-nanometer interference accuracy, and smaller than 0.25\u00b0 to make the influence smaller than ten picometers. It provides theoretical guidance and an effective means for improving the design of heterodyne interferometry instruments based on PMF and further reducing measurement errors.<\/jats:p>","DOI":"10.3390\/s23084108","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T02:01:11Z","timestamp":1681956071000},"page":"4108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Error Analysis of Heterodyne Interferometry Based on One Single-Mode Polarization-Maintaining Fiber"],"prefix":"10.3390","volume":"23","author":[{"given":"Yibin","family":"Qian","sequence":"first","affiliation":[{"name":"Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3895-290X","authenticated-orcid":false,"given":"Jiakun","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2854-044X","authenticated-orcid":false,"given":"Qibo","family":"Feng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qixin","family":"He","sequence":"additional","affiliation":[{"name":"Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Long","sequence":"additional","affiliation":[{"name":"Key Laboratory of Luminescence and Optical Information, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1117\/12.545924","article-title":"Ultra-precise distance measurement for nanometrology","volume":"Volume 5457","author":"Cip","year":"2004","journal-title":"Optical Metrology in Production Engineering"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1364\/OPN.15.10.000040","article-title":"Interferometry for accurate displacement metrology","volume":"15","author":"Lawall","year":"2004","journal-title":"Opt. 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