{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T09:13:28Z","timestamp":1771665208251,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,11,24]],"date-time":"2017-11-24T00:00:00Z","timestamp":1511481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Scientific Instrument and Equipment Development Project of China","award":["2014YQ350461"],"award-info":[{"award-number":["2014YQ350461"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A method for measuring the nonlinearity of laser interferometer using optical frequency tuning technique is presented in this paper. The basic principle of this method is to make the fractional part of an interference fringe change by tuning the laser frequency and determining the nonlinearity of interferometer by comparing the fractional fringe change measured by the interferometer to that calculated from the laser frequency change. An experimental interferometric system with a wavelength tunable laser source is set up and the nonlinearity of the interferometer is measured. Since it does not require the precise displacement mechanism to produce the optical path difference change, this method is more convenient to use and may achieve a higher accuracy than the conventional measurement methods. The nonlinearity of the arbitrary interferometric phase can be measured by changing the laser frequency with this method. Experiments results have shown that the repeatability of nonlinearity measurement is less than 0.2 nm. This method can be applied to interferometry-based high precision dimensional measurements, such as coordinate measurement and displacement sensor calibration.<\/jats:p>","DOI":"10.3390\/s17122721","type":"journal-article","created":{"date-parts":[[2017,11,24]],"date-time":"2017-11-24T06:39:25Z","timestamp":1511505565000},"page":"2721","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Method for Measurement of Nonlinearity of Laser Interferometer Based on Optical Frequency Tuning"],"prefix":"10.3390","volume":"17","author":[{"given":"Zhenyu","family":"Zhu","sequence":"first","affiliation":[{"name":"College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China"},{"name":"Changcheng Institute of Metrology &amp; Measurement, Beijing, 100095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Fu","sequence":"additional","affiliation":[{"name":"College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongmei","family":"Ren","sequence":"additional","affiliation":[{"name":"Changcheng Institute of Metrology &amp; Measurement, Beijing, 100095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Wan","sequence":"additional","affiliation":[{"name":"Changcheng Institute of Metrology &amp; Measurement, Beijing, 100095, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ji","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1088\/0957-0233\/16\/11\/001","article-title":"Nanometre resolution metrology with the Molecular Measuring Machine","volume":"16","author":"Kramar","year":"2005","journal-title":"Meas. Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1088\/0957-0233\/17\/3\/S02","article-title":"Recent advances in traceable nanoscale dimension and force metrology in the UK","volume":"17","author":"Leach","year":"2006","journal-title":"Meas. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"84008","DOI":"10.1088\/0957-0233\/20\/8\/084008","article-title":"A homodyne Michelson interferometer with sub-picometer resolution","volume":"20","author":"Pisani","year":"2009","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"105301","DOI":"10.1088\/0957-0233\/21\/10\/105301","article-title":"Long-term dimensional stability and longitudinal uniformity of line scales made of glass ceramics","volume":"21","author":"Takahashi","year":"2010","journal-title":"Meas. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"74001","DOI":"10.1088\/0957-0233\/23\/7\/074001","article-title":"Recent developments and challenges of nanopositioning and nanomeasuring technology","volume":"23","author":"Manske","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.measurement.2015.08.037","article-title":"Improvement and validity of shock measurements using heterodyne laser interferometer","volume":"77","author":"Nozato","year":"2016","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1016\/S0890-6955(03)00083-X","article-title":"Dynamic calibration of the positioning accuracy of machine tools and coordinate measuring machines using a laser interferometer","volume":"43","author":"Castro","year":"2003","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3945","DOI":"10.1016\/j.apsusc.2006.08.027","article-title":"A calibrated atomic force microscope using an orthogonal scanner and a calibrated laser interferometer","volume":"253","author":"Lee","year":"2007","journal-title":"Appl. Surf. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"94029","DOI":"10.1088\/0957-0233\/22\/9\/094029","article-title":"Toward interferometry for dimensional drift measurements with nanometer uncertainty","volume":"22","author":"Voigt","year":"2011","journal-title":"Meas. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1088\/0957-0233\/7\/4\/009","article-title":"Correction of nonlinearity in one-frequency optical interferometry","volume":"7","author":"Wu","year":"1996","journal-title":"Meas. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1088\/0957-0233\/7\/1\/009","article-title":"Nonlinearity in measurements of length by optical interferometry","volume":"7","author":"Wu","year":"1998","journal-title":"Meas. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4089","DOI":"10.1364\/AO.38.004089","article-title":"Heterodyne interferometer with subatomic periodic nonlinearity","volume":"38","author":"Wu","year":"1999","journal-title":"Appl. Opt."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.precisioneng.2011.10.008","article-title":"Theoretical analysis of errors in correction algorithms for periodic nonlinearity in displacement measuring interferometers","volume":"36","author":"Ellis","year":"2012","journal-title":"Precis. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2910","DOI":"10.1088\/0957-0233\/23\/9\/094005","article-title":"A heterodyne interferometer with periodic nonlinearities smaller than \u00b1 10\u2009pm","volume":"23","author":"Weichert","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3382","DOI":"10.1364\/AO.20.003382","article-title":"Determination and correction of quadrature fringe measurement errors in interferometers","volume":"20","author":"Heydemann","year":"1981","journal-title":"Appl. Opt."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1364\/OL.27.000619","article-title":"Elimination of heterodyne interferometer nonlinearity by carrier phase modulation","volume":"27","author":"Dubovitsky","year":"2002","journal-title":"Opt. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"105303","DOI":"10.1088\/0957-0233\/20\/10\/105303","article-title":"A simple technique for eliminating the nonlinearity of a heterodyne interferometer","volume":"20","author":"Hou","year":"2009","journal-title":"Meas. Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"35305","DOI":"10.1088\/0957-0233\/22\/3\/035305","article-title":"Sensitivity analysis of periodic errors in heterodyne interferometry","volume":"22","author":"Ganguly","year":"2011","journal-title":"Meas. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.precisioneng.2011.12.004","article-title":"Efficient performance of neural networks for nonlinearity error modeling of three-longitudinal-mode interferometer in nano-metrology system","volume":"36","author":"Olyaee","year":"2012","journal-title":"Precis. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0141-6359(99)00026-4","article-title":"A frequency domain method for the measurement of nonlinearity in heterodyne interferometry","volume":"24","author":"Badami","year":"2000","journal-title":"Precis. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3327","DOI":"10.1364\/OE.23.003327","article-title":"Self-calibrating common-path interferometry","volume":"23","author":"Porrasaguilar","year":"2015","journal-title":"Opt. Express"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0141-6359(90)90003-H","article-title":"Optical sources of non-linearity in heterodyne interferometers","volume":"12","author":"Rosenbluth","year":"1990","journal-title":"Precis. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1364\/AO.43.002443","article-title":"Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems","volume":"43","author":"Keem","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"74004","DOI":"10.1088\/0957-0233\/23\/7\/074004","article-title":"Interference signal demodulation for nanopositioning and nanomeasuring machines","volume":"23","author":"Hausotte","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_25","unstructured":"General Administration of Quality Supervision, Inspection and Quarantine of the PRC (2017, November 24). Verification Regulation of 633 nm Frequency Stabilized Lasers, Available online: http:\/\/www.gbstandards.org\/GB_standards\/JJ-%20353-2006.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/12\/2721\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:51:07Z","timestamp":1760208667000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/12\/2721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,24]]},"references-count":25,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["s17122721"],"URL":"https:\/\/doi.org\/10.3390\/s17122721","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,24]]}}}