{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T23:38:14Z","timestamp":1772667494880,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2024,12,20]],"date-time":"2024-12-20T00:00:00Z","timestamp":1734652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Frequency sweeping linearity is essential for Frequency-Modulated Continuous Wave (FMCW) Light Detection and Ranging (LIDAR), as it impacts the ranging resolution and accuracy of the system. Pre-distortion methods can correct for frequency sweeping nonlinearity; however, residual minor nonlinearities can still degrade the system ranging resolution, especially at far distances. Therefore, the precise measurement of minor nonlinearities is particularly essential for long-range FMCW LIDAR. This paper proposes a calibration-free MZI for measuring optical frequency sweeping nonlinearity, which involves alternately inserting two short polarization-maintaining fibers with different delays into one arm of an MZI, and after two rounds of beat collection, the optical frequency sweep curve of the light source is accurately measured for nonlinearity evaluation. Using the proposed method, the nonlinearity of a frequency-swept laser source is measured to be 0.2113%, and the relative nonlinearity is 5.3560 \u00d7 10\u22125. With the measured frequency sweep curve, we simulate the beat signal and compare it with the collected beat signal in time and frequency domain, to verify the accuracy of the proposed method. A test conducted at 24.1 \u00b0C, 30.4 \u00b0C, 39.5 \u00b0C and 44.0 \u00b0C demonstrate the method\u2019s insensitivity to temperature fluctuations. Based on the proposed MZI, a tunable laser is pre-distorted and then used as light source of a FMCW lidar. A wall at 45 m and a building at 1.2 km are ranged by the lidar respectively. Before and after laser pre-distortion, the FWHM of echo beat spectrum are 25.635 kHz and 9.736 kHz for 45 m, 747.880 kHz and 22.012 kHz for 1.2 km.<\/jats:p>","DOI":"10.3390\/rs16244766","type":"journal-article","created":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T09:13:38Z","timestamp":1734945218000},"page":"4766","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optical Frequency Sweeping Nonlinearity Measurement Based on a Calibration-free MZI"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-4892-2936","authenticated-orcid":false,"given":"Pengwei","family":"Sun","sequence":"first","affiliation":[{"name":"National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Science and Technology on Space Optoelectronic Precision Measurement, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2959-3968","authenticated-orcid":false,"given":"Bin","family":"Zhao","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Science and Technology on Space Optoelectronic Precision Measurement, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3084-0126","authenticated-orcid":false,"given":"Bo","family":"Liu","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Key Laboratory of Science and Technology on Space Optoelectronic Precision Measurement, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, R., Wang, B., Xiang, M., Li, C., Wang, S., and Song, C. (2021). Simultaneous time-varying vibration and nonlinearity compensation for one-period triangular-FMCW lidar signal. Remote Sens., 13.","DOI":"10.3390\/rs13091731"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9676","DOI":"10.1364\/AO.56.009676","article-title":"Frequency-modulated multifunction lidar for anemometry, range finding, and velocimetry\u20142. Experimental results","volume":"56","author":"Feneyrou","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Okuya, T., Yoneda, M., and Ogawa, T. (2023, January 24\u201328). Environment Recognition with FMCW-LiDAR-based Dynamic Occupancy Grid Mapping. Proceedings of the 2023 IEEE 26th International Conference on Intelligent Transportation Systems (ITSC), Bilbao, Spain.","DOI":"10.1109\/ITSC57777.2023.10422446"},{"key":"ref_4","first-page":"50","article-title":"Lidar for autonomous driving: The principles, challenges, and trends for automotive lidar and perception systems","volume":"37","author":"Li","year":"2020","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1364\/OPTICA.5.000988","article-title":"Coherent laser ranging for precision imaging through flames","volume":"5","author":"Mitchell","year":"2018","journal-title":"Optica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4640","DOI":"10.1109\/JLT.2018.2840223","article-title":"Photonic integrated circuit-based FMCW coherent LiDAR","volume":"36","author":"Martin","year":"2018","journal-title":"J. Light. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Wu, Z., Song, Y., Liu, J., Chen, Y., Sha, H., Shi, M., Zhang, H., Qin, L., Liang, L., and Jia, P. (2024). Advancements in Key Parameters of Frequency-Modulated Continuous-Wave Light Detection and Ranging: A Research Review. Appl. Sci., 14.","DOI":"10.3390\/app14177810"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3568","DOI":"10.1364\/OL.463007","article-title":"Frequency-modulated continuous-wave 3D imaging with high photon efficiency","volume":"47","author":"Huang","year":"2022","journal-title":"Opt. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1109\/MPOT.2019.2935266","article-title":"Velocity measurement in automotive sensing: How FMCW radar and lidar can work together","volume":"39","author":"Crouch","year":"2019","journal-title":"IEEE Potentials"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Poulton, C.V., Cole, D.B., Yaacobi, A., and Watts, M.R. (2016, January 20\u201324). Frequency-modulated continuous-wave LIDAR module in silicon photonics. Proceedings of the 2016 Optical Fiber Communications Conference and Exhibition (OFC), Anaheim, CA, USA.","DOI":"10.1364\/OFC.2016.W4E.3"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"15991","DOI":"10.1364\/OE.17.015991","article-title":"Precise control of broadband frequency chirps using optoelectronic feedback","volume":"17","author":"Satyan","year":"2009","journal-title":"Opt. Express"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1538","DOI":"10.1364\/AO.515530","article-title":"Interpolation linearization predistortion technology for FMCW LiDAR","volume":"63","author":"Chen","year":"2024","journal-title":"Appl. Opt."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"9965","DOI":"10.1364\/OE.27.009965","article-title":"Laser frequency sweep linearization by iterative learning pre-distortion for FMCW LiDAR","volume":"27","author":"Zhang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_14","first-page":"1","article-title":"Laser ranging method of frequency modulation interference based on equal optical frequency subdivision resampling","volume":"44","author":"Zhang","year":"2020","journal-title":"Laser Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"30420","DOI":"10.1364\/OE.465858","article-title":"Hybrid integrated ultralow-linewidth and fast-chirped laser for FMCW LiDAR","volume":"30","author":"Tang","year":"2022","journal-title":"Opt. Express"},{"key":"ref_16","first-page":"1","article-title":"Dynamic range enhanced optical frequency domain reflectometry using dual-loop composite optical phase-locking","volume":"13","author":"Meng","year":"2021","journal-title":"IEEE Photonics J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107961","DOI":"10.1016\/j.optlaseng.2023.107961","article-title":"Wide range linearization calibration method for DFB Laser in FMCW LiDAR","volume":"174","author":"Zhang","year":"2024","journal-title":"Opt. Lasers Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1109\/LPT.2022.3203063","article-title":"Narrow linewidth external cavity laser capable of high repetition frequency tuning for FMCW LiDAR","volume":"34","author":"Wu","year":"2022","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/JLT.1983.1072134","article-title":"Zero path-length difference in fiber-optic interferometers","volume":"1","author":"Dandridge","year":"1983","journal-title":"J. Light. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"085007","DOI":"10.1088\/1361-6501\/aa73a9","article-title":"Improved path imbalance measurement of a fiber-optic interferometer based on frequency scanning interferometry","volume":"28","author":"Hou","year":"2017","journal-title":"Meas. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, H., Lou, M., Huang, W., and Zhang, W. (2024). Real-Time Measurement and Uncertainty Evaluation of Optical Path Difference in Fiber Optic Interferometer Based on Auxiliary Interferometer. Sensors, 24.","DOI":"10.3390\/s24072038"},{"key":"ref_22","first-page":"93","article-title":"Fiber waveguides: A novel technique for investigating attenuation characteristics","volume":"165","author":"Barnoski","year":"2001","journal-title":"SPIE Milest. Ser."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1364\/AO.16.002375","article-title":"Optical time domain reflectometer","volume":"16","author":"Barnoski","year":"1977","journal-title":"Appl. Opt."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2976","DOI":"10.1364\/AO.25.002976","article-title":"Distance measurement by the wavelength shift of laser diode light","volume":"25","author":"Kikuta","year":"1986","journal-title":"Appl. Opt."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1063\/1.92872","article-title":"Optical frequency domain reflectometry in single-mode fiber","volume":"39","author":"Eickhoff","year":"1981","journal-title":"Appl. Phys. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1364\/AO.49.000213","article-title":"Accuracy of active chirp linearization for broadband frequency modulated continuous wave ladar","volume":"49","author":"Barber","year":"2010","journal-title":"Appl. Opt."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"7630","DOI":"10.1364\/AO.44.007630","article-title":"Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation","volume":"44","author":"Ahn","year":"2005","journal-title":"Appl. Opt."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1109\/50.254098","article-title":"Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides","volume":"11","author":"Glombitza","year":"1993","journal-title":"J. Light. Technol."},{"key":"ref_29","unstructured":"Hall, J.L., Taubman, M.S., and Ye, J. (1999). Laser stabilization. OSA Handbook v14, University of Colorado."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"107523","DOI":"10.1016\/j.optlaseng.2023.107523","article-title":"Optical frequency shifted FMCW Lidar system for unambiguous measurement of distance and velocity","volume":"164","author":"Na","year":"2023","journal-title":"Opt. Lasers Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2394","DOI":"10.1364\/AO.46.002394","article-title":"Analysis of nonlinear frequency sweep in high-speed tunable laser sources using a self-homodyne measurement and Hilbert transformation","volume":"46","author":"Ahn","year":"2007","journal-title":"Appl. Opt."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1076-K04","DOI":"10.1557\/PROC-1076-K04-06","article-title":"Linear FMCW Laser Radar for Precision Range and Vector Velocity Measurements","volume":"1076","author":"Pierrottet","year":"2008","journal-title":"MRS Online Proc. Libr."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1002\/rob.22291","article-title":"FMCW Radar on LiDAR map localization in structural urban environments","volume":"41","author":"Ma","year":"2024","journal-title":"J. Field Robot."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/24\/4766\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:57:07Z","timestamp":1760115427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/24\/4766"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,20]]},"references-count":33,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["rs16244766"],"URL":"https:\/\/doi.org\/10.3390\/rs16244766","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,20]]}}}