{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:08:29Z","timestamp":1760144909864,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T00:00:00Z","timestamp":1716940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds of National Institute of Metrology of China","award":["AKYKF2402","AKYZD2403-2","2021YFF0603802"],"award-info":[{"award-number":["AKYKF2402","AKYZD2403-2","2021YFF0603802"]}]},{"name":"Fundamental Research Funds for the Key Areas of National Institute of Metrology of China","award":["AKYKF2402","AKYZD2403-2","2021YFF0603802"],"award-info":[{"award-number":["AKYKF2402","AKYZD2403-2","2021YFF0603802"]}]},{"name":"National Key R &amp; D Program of China","award":["AKYKF2402","AKYZD2403-2","2021YFF0603802"],"award-info":[{"award-number":["AKYKF2402","AKYZD2403-2","2021YFF0603802"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Absolute distance measurements based on optical frequency combs (OFCs) have greatly promoted advances in both science and technology, owing to the high precision, large non-ambiguity range (NAR), and a high update rate. However, cyclic error, which is extremely difficult to eliminate, reduces the linearity of measurement results. In this study, we quantitatively investigated the impact of cyclic error on absolute distance measurement using OFCs based on two types of interferometry: synthetic wavelength interferometry and single-wavelength interferometry. The numerical calculations indicate that selecting a suitable reference path length can minimize the impact of cyclic error when combining the two types of interferometry. Recommendations for selecting an appropriate synthetic wavelength to address the tradeoff between achieving a large NAR and minimizing the risk of failure when combining the two methods are provided. The results of this study are applicable not only in absolute distance measurements but also in other applications based on OFCs, such as surface profile, vibration analysis, etc.<\/jats:p>","DOI":"10.3390\/s24113497","type":"journal-article","created":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T06:58:07Z","timestamp":1716965887000},"page":"3497","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Impact of Cyclic Error on Absolute Distance Measurement Based on Optical Frequency Combs"],"prefix":"10.3390","volume":"24","author":[{"given":"Runmin","family":"Li","sequence":"first","affiliation":[{"name":"Optoelectronic Technology Center, Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2650-4915","authenticated-orcid":false,"given":"Haochen","family":"Tian","sequence":"additional","affiliation":[{"name":"Division of Time and Frequency Metrology, National Institute of Metrology, Beijing 100029, China"},{"name":"Key Laboratory of State Administration for Market Regulation (Time Frequency and Gravity Primary Standard), Beijing 100029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5454-3375","authenticated-orcid":false,"given":"Junkai","family":"Shi","sequence":"additional","affiliation":[{"name":"Optoelectronic Technology Center, Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China"}]},{"given":"Rongyi","family":"Ji","sequence":"additional","affiliation":[{"name":"Optoelectronic Technology Center, Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China"}]},{"given":"Dengfeng","family":"Dong","sequence":"additional","affiliation":[{"name":"Optoelectronic Technology Center, Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Weihu","family":"Zhou","sequence":"additional","affiliation":[{"name":"Optoelectronic Technology Center, Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1038\/nphoton.2009.86","article-title":"Metrology: Combs rule","volume":"3","author":"Kim","year":"2009","journal-title":"Nat. Photonics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1142\/S0218271809014893","article-title":"A search for new physics with the BEACON mission","volume":"18","author":"Turyshev","year":"2009","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1038\/nphoton.2009.94","article-title":"Rapid and precise absolute distance measurements at long range","volume":"3","author":"Coddington","year":"2009","journal-title":"Nat. Photonics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4284","DOI":"10.1364\/OL.438103","article-title":"Characterization of rubidium thin cell properties with sandwiched structure using a multipath interferometer with an optical frequency comb","volume":"46","author":"Wang","year":"2021","journal-title":"Opt. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1088\/0957-0233\/4\/9\/001","article-title":"Recent advances in displacement measuring interferometry","volume":"4","author":"Bobroff","year":"1993","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"31770","DOI":"10.1038\/srep31770","article-title":"Comb-referenced laser distance interferometer for industrial nanotechnology","volume":"6","author":"Jang","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9121","DOI":"10.1364\/OE.23.009121","article-title":"Absolute positioning by multi-wavelength interferometry referenced to the frequency comb of a femtosecond laser","volume":"23","author":"Wang","year":"2015","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5747","DOI":"10.1364\/OE.26.005747","article-title":"Synthetic-wavelength-based dual-comb interferometry for fast and precise absolute distance measurement","volume":"26","author":"Zhu","year":"2018","journal-title":"Opt. Express"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5954","DOI":"10.1364\/OE.14.005954","article-title":"Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser","volume":"14","author":"Joo","year":"2006","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"183901","DOI":"10.1103\/PhysRevLett.108.183901","article-title":"Many-wavelength interferometry with thousands of lasers for absolute distance measurement","volume":"108","author":"Persijn","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","first-page":"14461","article-title":"Mode resolved frequency comb interferometry for high-accuracy long distance measurement","volume":"5","author":"Bhattacharya","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1364\/AO.413997","article-title":"Correction of the air refractive index using a two-color method for absolute distance measurement without a dead zone","volume":"60","author":"Gao","year":"2021","journal-title":"Appl. Opt."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Liu, T., Matsukuma, H., Suzuki, A., Sato, R., and Gao, W. (2024). Enhanced Data-Processing Algorithms for Dispersive Interferometry Using a Femtosecond Laser. Sensors, 24.","DOI":"10.3390\/s24020370"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1038\/s41566-020-0586-0","article-title":"Ultrafast, sub-nanometre-precision and multifunctional time-of-flight detection","volume":"14","author":"Na","year":"2020","journal-title":"Nat. Photonics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"14057","DOI":"10.1364\/OE.23.014057","article-title":"Effect of timing jitter on time-of-flight distance measurements using dual femtosecond lasers","volume":"23","author":"Shi","year":"2015","journal-title":"Opt. Express"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"37245","DOI":"10.1364\/OE.469415","article-title":"Dynamic and precise long-distance ranging using a free-running dual-comb laser","volume":"30","author":"Camenzind","year":"2022","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5309","DOI":"10.1364\/OL.470211","article-title":"Ultra-rapid dual-comb ranging with an extended non-ambiguity range","volume":"47","author":"Li","year":"2022","journal-title":"Opt. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"33527","DOI":"10.1364\/OE.440728","article-title":"Aliasing-free dual-comb ranging system based on free-running fiber lasers","volume":"29","author":"Jiang","year":"2021","journal-title":"Opt. Express"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2715","DOI":"10.1364\/AO.47.002715","article-title":"High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source","volume":"47","author":"Schuhler","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5512","DOI":"10.1364\/AO.39.005512","article-title":"High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser","volume":"39","author":"Minoshima","year":"2000","journal-title":"Appl. Opt."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"045201","DOI":"10.1088\/0957-0233\/24\/4\/045201","article-title":"Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength","volume":"24","author":"Lee","year":"2013","journal-title":"Meas. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4362","DOI":"10.1038\/s41598-018-22838-0","article-title":"Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement","volume":"8","author":"Wu","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1117\/1.1459053","article-title":"Absolute length measurement using changeable synthetic wavelength chain","volume":"41","author":"Yin","year":"2002","journal-title":"Opt. Eng."},{"key":"ref_24","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":"1996","journal-title":"Meas. Sci. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"S304","DOI":"10.1088\/1464-4258\/4\/6\/373","article-title":"Signal processing and testing of displacement metrology gauges with picometre-scale cyclic nonlinearity","volume":"4","author":"Halverson","year":"2002","journal-title":"J. Opt. A Pure Appl. Opt."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2448","DOI":"10.1364\/OL.37.002448","article-title":"Linearization and minimization of cyclic error with heterodyne laser interferometry","volume":"37","author":"McRae","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0141-6359(92)90054-Z","article-title":"Investigation and compensation of the nonlinearity of heterodyne interferometers","volume":"14","author":"Hou","year":"1992","journal-title":"Precis. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1364\/OL.27.000797","article-title":"Polarization compensation: A passive approach to a reducing heterodyne interferometer nonlinearity","volume":"27","author":"Lay","year":"2002","journal-title":"Opt. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"23299","DOI":"10.1364\/OE.17.023299","article-title":"A passive method to compensate nonlinearity in a homodyne interferometer","volume":"17","author":"Ahn","year":"2009","journal-title":"Opt. Express"},{"key":"ref_30","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_31","doi-asserted-by":"crossref","first-page":"B11","DOI":"10.1364\/JOSAA.396298","article-title":"A compact high-precision periodic-error-free heterodyne interferometer","volume":"37","author":"Joo","year":"2020","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"100308","DOI":"10.1016\/j.rio.2022.100308","article-title":"Reduction of cyclic error induced by electromagnetic contamination in an EO-comb based distance measurement system","volume":"9","author":"Li","year":"2022","journal-title":"Results Opt."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3492","DOI":"10.1364\/AO.44.003492","article-title":"Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system","volume":"44","author":"Keem","year":"2005","journal-title":"Appl. Opt."},{"key":"ref_34","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_35","unstructured":"Minoshima, K., Schibli, T.R., and Matsumoto, H. (2004, January 16\u201321). Study on cyclic errors in a distance measurement using a frequency comb generated by a mode-locked laser. Proceedings of the Conference on Lasers and Electro-Optics, San Francisco, CA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Kim, W., Fu, H., Lee, K., Han, S., Jang, Y.-S., and Kim, S.-W. (2020). Photonic Microwave Distance Interferometry Using a Mode-Locked Laser with Systematic Error Correction. Appl. Sci., 10.","DOI":"10.3390\/app10217649"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4470","DOI":"10.1364\/OE.25.004470","article-title":"Iterative compensation of nonlinear error of heterodyne interferometer","volume":"25","author":"Xie","year":"2017","journal-title":"Opt. Express"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"7000907","DOI":"10.1109\/TIM.2022.3146896","article-title":"Periodic error free all-fiber distance measurement method with photonic microwave modulation toward on-chip-based devices","volume":"71","author":"Jang","year":"2022","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"12229","DOI":"10.1364\/OE.421719","article-title":"Sub-100-nm precision distance measurement by means of all-fiber photonic microwave mixing","volume":"29","author":"Jang","year":"2021","journal-title":"Opt. Express"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3090","DOI":"10.3390\/s150203090","article-title":"Compensation for the variable cyclic error in homodyne laser interferometers","volume":"15","author":"Hu","year":"2015","journal-title":"Sensors"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Kang, H., Lee, J., Kim, Y.J., and Kim, S.W. (2023). Phase-locked synthetic wavelength interferometer using a femtosecond laser for absolute distance measurement without cyclic error. Sensors, 23.","DOI":"10.3390\/s23146253"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1038\/s41566-021-00778-y","article-title":"A six-octave optical frequency comb from a scalable few-cycle erbium fibre laser","volume":"15","author":"Lesko","year":"2021","journal-title":"Nat. Photonics"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"34305","DOI":"10.1364\/OE.26.034305","article-title":"Fast high-precision distance metrology using a pair of modulator-generated dual-color frequency combs","volume":"26","author":"Weimann","year":"2018","journal-title":"Opt. Express"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/11\/3497\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:49:59Z","timestamp":1760107799000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/11\/3497"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,29]]},"references-count":43,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["s24113497"],"URL":"https:\/\/doi.org\/10.3390\/s24113497","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,5,29]]}}}