{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:39:35Z","timestamp":1760233175876,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2022YFB3403603","2022YFB3403602","2021YFB3400300","52035013","52175439","LD22E050010"],"award-info":[{"award-number":["2022YFB3403603","2022YFB3403602","2021YFB3400300","52035013","52175439","LD22E050010"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022YFB3403603","2022YFB3403602","2021YFB3400300","52035013","52175439","LD22E050010"],"award-info":[{"award-number":["2022YFB3403603","2022YFB3403602","2021YFB3400300","52035013","52175439","LD22E050010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of Zhejiang Province","award":["2022YFB3403603","2022YFB3403602","2021YFB3400300","52035013","52175439","LD22E050010"],"award-info":[{"award-number":["2022YFB3403603","2022YFB3403602","2021YFB3400300","52035013","52175439","LD22E050010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a fiber-based chromatic dispersion probe for simultaneous measurement of X-axis and Z-axis displacements with nanometric resolutions by using the full width at half maxima (FWHM) of the detected spectral signal has been proposed and demonstrated. For X-axis, FWHM is employed for indicating the X-axis displacement based on the fact that the FWHM remains almost constant with the varying Z-axis displacement of the fiber detector and shows a linear relationship with the X-axis displacement within a specific Z-axis displacement range. For the Z-axis, the linear relationship between the centroid wavelength \u03bb of the detected spectral signal and the Z-axis displacement is employed for indicating the Z-axis displacement based on the fact that the sensitivity (slope of the \u03bb-Z curve) is also linear with X-axis displacement within a certain X-axis displacement range. Theoretical and experimental investigations have verified the feasibility of the proposed chromatic dispersion probe, which yields X- and Z-axis measurement ranges of 2.3 \u03bcm and 15 \u03bcm and X- and Z-axis measurement resolutions of better than 25 nm and 50 nm, respectively. Experiments were further performed to evaluate the basic performance of the prototype probe and the maximum measurement errors were less than 10 nm and 60 nm for X- and Z-axis displacements, respectively.<\/jats:p>","DOI":"10.3390\/s23010051","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T06:11:24Z","timestamp":1671603084000},"page":"51","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Fiber-Based Chromatic Dispersion Probe for Simultaneous Measurement of X-Axis and Z-Axis Displacements with Nanometric Resolutions"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2449-3255","authenticated-orcid":false,"given":"Ran","family":"Zhao","sequence":"first","affiliation":[{"name":"The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chong","family":"Chen","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Xiong","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan-Liu","family":"Chen","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058, China"},{"name":"Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing-Feng","family":"Ju","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310058, China"},{"name":"Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Baier, V., Schardt, M., Fink, M., Jakobi, M., and Koch, A.W. (2022). MEMS-Scanner Testbench for High Field of View LiDAR Applications. Sensors, 22.","DOI":"10.3390\/s22010039"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1364\/OPTICA.4.000692","article-title":"Chip-scale demonstration of hybrid III\u2013V\/silicon photonic integration for an FBG interrogator","volume":"4","author":"Li","year":"2017","journal-title":"Optica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.tsf.2015.02.006","article-title":"Development of a broadband Mueller matrix ellipsometer as a powerful tool for nanostructure metrology","volume":"584","author":"Liu","year":"2015","journal-title":"Thin Solid Films"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"102688","DOI":"10.1016\/j.rinp.2019.102688","article-title":"Optical design of the freeform reflective imaging system with wide rectangular FOV and low F-number","volume":"15","author":"Wu","year":"2019","journal-title":"Results Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15759","DOI":"10.1364\/OE.26.015759","article-title":"Three-dimensional super-resolution correlation-differential confocal microscopy with nanometer axial focusing accuracy","volume":"26","author":"Zhao","year":"2018","journal-title":"Opt. Express"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"13069","DOI":"10.1364\/OE.23.013069","article-title":"Pulse-to-pulse alignment based on interference fringes and the second-order temporal coherence function of optical frequency combs for distance measurement","volume":"23","author":"Zhu","year":"2015","journal-title":"Opt. Express"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1109\/JMEMS.2011.2177071","article-title":"Interchangeable Stage and Probe Mechanisms for Microscale Universal Mechanical Tester","volume":"21","author":"Brown","year":"2012","journal-title":"J. Microelectromech. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"10095","DOI":"10.3390\/s101110095","article-title":"Polypyrrole Porous Micro Humidity Sensor Integrated with a Ring Oscillator Circuit on Chip","volume":"10","author":"Yang","year":"2010","journal-title":"Sensors"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1109\/TCST.2006.880189","article-title":"A High Precision Motion Control System With Application to Microscale Robotic Deposition","volume":"14","author":"Bristow","year":"2006","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.2193\/0091-7648(2006)34[1345:ACSFMM]2.0.CO;2","article-title":"A Cost-Effective System for Measuring Microscale Habitat Use of Small Mammals with High Precision","volume":"34","author":"McDaniel","year":"2006","journal-title":"Wildl. Soc. Bull."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"110172","DOI":"10.1016\/j.measurement.2021.110172","article-title":"A miniature laser diode interferometer with self-compensation of retroreflector\u2019s motion errors for displacement feedback of small-sized micro\/nano motion stages","volume":"186","author":"Cai","year":"2021","journal-title":"Measurement"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"073701","DOI":"10.1063\/5.0009965","article-title":"Long stroke displacement measurement with reduced coupling error supporting high precision control of a beam flexure-based micro-stage","volume":"91","author":"Lu","year":"2020","journal-title":"Rev. Sci. Instrum."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.mee.2017.11.010","article-title":"Optical fiber Fabry-P\u00e9rot micro-displacement sensor for MEMS in-plane motion stage","volume":"187\u2013188","author":"Kim","year":"2018","journal-title":"Microelectron. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.ymssp.2019.01.046","article-title":"Realtime in-plane displacements tracking of the precision positioning stage based on computer micro-vision","volume":"124","author":"Li","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2010.05.014","article-title":"Nanoscale displacement measurement of electrostatically actuated micro-devices using optical microscopy and digital image correlation","volume":"162","author":"Krylov","year":"2010","journal-title":"Sens. Actuators A Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.sna.2014.02.032","article-title":"A Cr-N thin film displacement sensor for precision positioning of a micro-stage","volume":"211","author":"Peng","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s41871-019-00040-8","article-title":"Integration of a Cr\u2013N Thin-Film Displacement Sensor into an XY Micro-stage for Closed-Loop Nano-positioning","volume":"2","author":"Adachi","year":"2019","journal-title":"Nanomanuf. Metrol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2747","DOI":"10.1088\/0960-1317\/16\/12\/031","article-title":"Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors","volume":"16","author":"Xu","year":"2006","journal-title":"J. Micromechanics Microeng."},{"key":"ref_19","unstructured":"Ji, L., Zhu, Y., Moheimani, S.O.R., and Yuce, M.R. (2010, January 1\u20134). A micromachined 2DOF nanopositioner with integrated capacitive displacement sensor. Proceedings of the SENSORS, 2010 IEEE, Waikoloa, HI, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1109\/JSEN.2009.2029042","article-title":"A Hall Sensor-Based Three-Dimensional Displacement Measurement System for Miniature Magnetically Levitated Rotor","volume":"9","author":"Yang","year":"2009","journal-title":"IEEE Sens. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.cirp.2011.03.052","article-title":"A three-axis autocollimator for detection of angular error motions of a precision stage","volume":"60","author":"Gao","year":"2011","journal-title":"CIRP Ann."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/j.cirp.2007.05.126","article-title":"A Three-axis Displacement Sensor with Nanometric Resolution","volume":"56","author":"Gao","year":"2007","journal-title":"CIRP Ann."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"054101","DOI":"10.1117\/1.OE.54.5.054101","article-title":"Error motion compensating tracking interferometer for the position measurement of objects with rotational degree of freedom","volume":"54","author":"Mirko","year":"2015","journal-title":"Opt. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"075102","DOI":"10.1063\/1.4926645","article-title":"Accurate three-dimensional shape and deformation measurement at microscale using digital image correlation","volume":"86","author":"Ren","year":"2015","journal-title":"Rev. Sci. Instrum."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"5066","DOI":"10.1364\/AO.51.005066","article-title":"Nanometer displacement measurement using Fresnel diffraction","volume":"51","author":"Khorshad","year":"2012","journal-title":"Appl. Opt."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"126283","DOI":"10.1016\/j.optcom.2020.126283","article-title":"All-fiber differential interferometer for nanometric displacement measurement","volume":"475","author":"Wang","year":"2020","journal-title":"Opt. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1109\/LEOS.2004.1363211","article-title":"Micro-displacement measurement using a long period fiber grating in a self-referenced fiber optic intensity sensor","volume":"Volume 261","author":"Cazacu","year":"2004","journal-title":"Proceedings of the 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2004, LEOS 2004"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1109\/JSTQE.2011.2159705","article-title":"Fiber-Optic Salinity Sensor Using Fiber-Optic Displacement Measurement With Flat and Concave Mirror","volume":"18","author":"Rahman","year":"2012","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1109\/TIM.2009.2023147","article-title":"Mathematical Modeling of Intensity-Modulated Bent-Tip Optical Fiber Displacement Sensors","volume":"59","author":"Puangmali","year":"2010","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5729","DOI":"10.1364\/OPEX.12.005729","article-title":"High stability multiplexed fibre interferometer and its application on absolute displacement measurement and on-line surface metrology","volume":"12","author":"Lin","year":"2004","journal-title":"Opt. Express"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1364\/AO.38.001103","article-title":"Development of a differential optical-fiber displacement sensor","volume":"38","author":"Suganuma","year":"1999","journal-title":"Appl. Opt."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"105688","DOI":"10.1016\/j.optlastec.2019.105688","article-title":"Two-dimensional displacement optical fiber sensor based on macro-bending effect","volume":"120","author":"Ghaffar","year":"2019","journal-title":"Opt. Laser Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3193","DOI":"10.1364\/OE.21.003193","article-title":"Compact micro-displacement sensor with high sensitivity based on a long-period fiber grating with an air-cavity","volume":"21","author":"Qi","year":"2013","journal-title":"Opt. Express"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1364\/OL.37.000202","article-title":"High precision micro-displacement fiber sensor through a suspended-core Sagnac interferometer","volume":"37","author":"Bravo","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chen, C., Shimizu, Y., Sato, R., Matsukuma, H., and Gao, W. (2020). An off-axis differential method for improvement of a femtosecond laser differential chromatic confocal probe. Appl. Sci., 10.","DOI":"10.3390\/app10207235"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1007\/s11340-011-9467-2","article-title":"Multi-Functional Measurement Using a Single FBG Sensor","volume":"51","author":"Mizutani","year":"2011","journal-title":"Exp. Mech."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1039\/a800153g","article-title":"Optimization of confocal epifluorescence microscopy for microchip-based miniaturized total analysis systems","volume":"123","author":"Ocvirk","year":"1998","journal-title":"Analyst"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2143","DOI":"10.1364\/AO.30.002143","article-title":"Confocal scanning optical microscope using single-mode fiber for signal detection","volume":"30","author":"Kimura","year":"1991","journal-title":"Appl. Opt."},{"key":"ref_39","unstructured":"Goodman, J.W. (1968). Introduction to Fourier Optics, McGraw-Hill."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1080\/713819873","article-title":"Optical Fibre Excitation by Lenses","volume":"26","author":"Barrell","year":"1979","journal-title":"Opt. Acta: Int. J. Opt."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1130","DOI":"10.1109\/TMTT.1969.1127112","article-title":"Asymptotic Expressions for Eigenfunctions and Eigenvalues of a Dielectric or Optical Waveguide","volume":"17","author":"Snyder","year":"1969","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_42","unstructured":"Snyder, A., and Love, J. (1983). Optical Waveguide Theory, Springer Science & Business Media."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:45:23Z","timestamp":1760147123000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,21]]},"references-count":42,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["s23010051"],"URL":"https:\/\/doi.org\/10.3390\/s23010051","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,12,21]]}}}