{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T19:09:41Z","timestamp":1773428981694,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,9]],"date-time":"2018-04-09T00:00:00Z","timestamp":1523232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we demonstrate a method using a frequency comb, which can precisely measure the refractive index of water. We have developed a simple system, in which a Michelson interferometer is placed into a quartz-glass container with a low expansion coefficient, and for which compensation of the thermal expansion of the water container is not required. By scanning a mirror on a moving stage, a pair of cross-correlation patterns can be generated. We can obtain the length information via these cross-correlation patterns, with or without water in the container. The refractive index of water can be measured by the resulting lengths. Long-term experimental results show that our method can measure the refractive index of water with a high degree of accuracy\u2014measurement uncertainty at 10\u22125 level has been achieved, compared with the values calculated by the empirical formula.<\/jats:p>","DOI":"10.3390\/s18041143","type":"journal-article","created":{"date-parts":[[2018,4,10]],"date-time":"2018-04-10T13:06:08Z","timestamp":1523365568000},"page":"1143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Absolute Measurement of the Refractive Index of Water by a Mode-Locked Laser at 518 nm"],"prefix":"10.3390","volume":"18","author":[{"given":"Zhaopeng","family":"Meng","sequence":"first","affiliation":[{"name":"School of Computer Software, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoyu","family":"Zhai","sequence":"additional","affiliation":[{"name":"School of Computer Software, Tianjin University, Tianjin 300072, China"},{"name":"National Ocean Technology Center, Tianjin 300112, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianguo","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Computer Software, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiyang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanzhong","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1664","DOI":"10.1364\/OL.42.001664","article-title":"Directly modulated green-light diode-pumped solid-state laser for underwater wireless optical communication","volume":"42","author":"Xu","year":"2017","journal-title":"Opt. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1109\/JOE.2011.2122630","article-title":"Principal component analysis of single-beam echo-sounder signal features for seafloor classification","volume":"36","author":"Snellen","year":"2011","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/48.922790","article-title":"Underwater vehicle obstacle avoidance and path planning using a multi-beam forward looking sonar","volume":"26","author":"Petillot","year":"2001","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3427","DOI":"10.3390\/rs4113427","article-title":"Evaluation of four supervised learning methods for benthic habitat mapping using backscatter from multi-beam sonar","volume":"4","author":"Hasan","year":"2012","journal-title":"Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1109\/JOE.2015.2433851","article-title":"Development of underwater short-range sensor using electromagnetic wave attenuation","volume":"41","author":"Park","year":"2016","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2843","DOI":"10.1109\/TAP.2004.834449","article-title":"Propagation of electromagnetic waves at MHz frequencies through seawater","volume":"52","author":"Shaw","year":"2004","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9826","DOI":"10.1364\/OE.24.009826","article-title":"Underwater image recovery considering polarization effects of objects","volume":"24","author":"Huang","year":"2016","journal-title":"Opt. Express"},{"key":"ref_8","first-page":"626","article-title":"Polarimetric imaging and retrieval of target polarization characteristics in underwater environment","volume":"55","author":"Gu","year":"2016","journal-title":"Opt. Express"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"13101","DOI":"10.1364\/OE.24.013101","article-title":"Model-based restoration of underwater spectral images captured with narrowband filters","volume":"24","author":"Guo","year":"2016","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7130","DOI":"10.1364\/AO.44.007130","article-title":"Underwater three-dimensional imaging with an amplitude-modulated laser radar at a 405 nm wavelength","volume":"44","author":"Bartolini","year":"2005","journal-title":"Appl. Opt."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1238\/Physica.Regular.065a00167","article-title":"Refractive index measurement and its applications","volume":"65","author":"Singh","year":"2002","journal-title":"Phys. Scr."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1063\/1.555859","article-title":"Refractive index of water and steam as function of wavelength, temperature and density","volume":"19","author":"Schiebener","year":"1990","journal-title":"J. Phys. Chem. Ref. Data"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1063\/1.556029","article-title":"Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density","volume":"27","author":"Harvey","year":"1998","journal-title":"J. Phys. Chem. Ref. Data"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1364\/AO.30.001711","article-title":"Measurement of the index of refraction of the plastic Phenoxy PKFE","volume":"30","author":"Kuhler","year":"1991","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3010","DOI":"10.1364\/AO.23.003010","article-title":"Laser light refractometer","volume":"23","author":"Moreels","year":"1984","journal-title":"Appl. Opt."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4430","DOI":"10.1364\/AO.48.004430","article-title":"Measurement method for the refractive index of thick solid and liquid layers","volume":"48","author":"Santic","year":"2009","journal-title":"Appl. Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6690","DOI":"10.1364\/AO.31.006690","article-title":"Measurement of the refractive index of liquid using laser beam displacement","volume":"31","author":"Nemoto","year":"1992","journal-title":"Appl. Opt."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3992","DOI":"10.1364\/AO.32.003992","article-title":"Two-wavelength interferometric technique for measuring the refractive index of salt-water solutions","volume":"32","author":"Lu","year":"1993","journal-title":"Appl. Opt."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1364\/JOSA.63.000318","article-title":"Change of refractive index of water as a function of temperature","volume":"63","author":"Dobbins","year":"1973","journal-title":"J. Opt. Soc. Am."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1364\/AO.41.001330","article-title":"Autocompensating interferometer for measuring the changes in refractive index of supercooled water as a function of temperature at 632.8 nm","volume":"41","author":"Carroll","year":"2002","journal-title":"Appl. Opt."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1063\/1.1142459","article-title":"An accurate method for refractive index measurements of liquids using two Michelson laser interferometers","volume":"62","author":"Ge","year":"1991","journal-title":"Rev. Sci. Instrum."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1364\/AO.35.001650","article-title":"Interferometer for measuring the absolute refractive index of liquid water as a function of temperature at 1.064 \u03bcm","volume":"35","author":"Richerzhagen","year":"1996","journal-title":"Appl. Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3649","DOI":"10.1063\/1.1149154","article-title":"Determination of the optical constants of thin films in the visible by static dispersive Fourier transform spectroscopy","volume":"69","author":"Harvey","year":"1998","journal-title":"Rev. Sci. Instrum."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.1088\/0957-0233\/15\/9\/002","article-title":"Measurement of the refractive index of liquids at 1.3 and 1.5 micron using a fiber optic Fresnel ratio meter","volume":"15","author":"Kim","year":"2004","journal-title":"Meas. Sci. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1038\/nphoton.2011.38","article-title":"Searching for applications with a fine-tooth comb","volume":"5","author":"Newbury","year":"2011","journal-title":"Nat. Photonics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"31730","DOI":"10.1364\/OE.25.031730","article-title":"Sensitivity improvement of dual-comb spectroscopy using mode-filtering technique","volume":"25","author":"Nishiyama","year":"2017","journal-title":"Opt. Express"},{"key":"ref_27","first-page":"021016","article-title":"Synchronization of distant optical clocks at the femtosecond level","volume":"6","author":"Deschenes","year":"2016","journal-title":"Phys. Rev. X"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"9300","DOI":"10.1364\/OE.17.009300","article-title":"Femtosecond frequency comb based distance measurement in air","volume":"17","author":"Balling","year":"2009","journal-title":"Opt. Express"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"18339","DOI":"10.1364\/OE.18.018339","article-title":"Thickness and refractive index measurement of a silicon wafer based on an optical comb","volume":"18","author":"Jin","year":"2010","journal-title":"Opt. Express"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"101107","DOI":"10.1063\/1.3563707","article-title":"High-speed nanometer-resolved imaging vibrometer and velocimeter","volume":"98","author":"Mahjoubfar","year":"2011","journal-title":"Appl. Phys. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1976","DOI":"10.1364\/OL.31.001976","article-title":"Frequency-comb-based interferometer for profilometry and tomography","volume":"31","author":"Choi","year":"2006","journal-title":"Opt. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3314","DOI":"10.1364\/OL.30.003314","article-title":"Precision measurement of the refractive index of air with frequency combs","volume":"30","author":"Zhang","year":"2005","journal-title":"Opt. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"26095","DOI":"10.1364\/OE.19.026095","article-title":"High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs","volume":"19","author":"Minoshima","year":"2011","journal-title":"Opt. Express"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"12184","DOI":"10.1364\/OE.20.012184","article-title":"Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser","volume":"20","author":"Maeng","year":"2012","journal-title":"Opt. Express"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6486","DOI":"10.1364\/OE.22.006486","article-title":"Vibration-insensitive measurement of thickness variation of glass panels using double-slit interferometry","volume":"22","author":"Kim","year":"2014","journal-title":"Opt. Express"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"32941","DOI":"10.1364\/OE.23.032941","article-title":"Vibration-insensitive measurements of the thickness profile of large glass panels","volume":"23","author":"Park","year":"2015","journal-title":"Opt. Express"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1364\/AO.35.001566","article-title":"Refractive index of air: New equations for the visible and near infrared","volume":"35","author":"Ciddor","year":"1996","journal-title":"Appl. Opt."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"14661","DOI":"10.1038\/srep14661","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_39","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_40","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1109\/78.134430","article-title":"The theory of bandpass sampling","volume":"39","author":"Vaughan","year":"1991","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1462","DOI":"10.1364\/OL.18.001462","article-title":"Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms","volume":"18","author":"Groot","year":"1993","journal-title":"Opt. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"106602","DOI":"10.7567\/APEX.7.106602","article-title":"Experimental optimization of the repetition rate difference in dual-comb ranging system","volume":"7","author":"Wu","year":"2014","journal-title":"Appl. Phys. Express"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"16671","DOI":"10.1364\/OE.20.016671","article-title":"Portable frequency combs for optical frequency metrology","volume":"20","author":"Lee","year":"2012","journal-title":"Opt. Express"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"251901","DOI":"10.1063\/1.4999537","article-title":"Long distance measurement up to 1.2 km by electro-optic dual-comb interferometry","volume":"111","author":"Wu","year":"2017","journal-title":"Appl. Phys. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1143\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:00:01Z","timestamp":1760194801000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,9]]},"references-count":44,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["s18041143"],"URL":"https:\/\/doi.org\/10.3390\/s18041143","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,9]]}}}