{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T18:48:23Z","timestamp":1777488503905,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,26]],"date-time":"2020-01-26T00:00:00Z","timestamp":1579996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51676105, 51906120, 11972213"],"award-info":[{"award-number":["51676105, 51906120, 11972213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2018M640125, 2019T120088"],"award-info":[{"award-number":["2018M640125, 2019T120088"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Research and Development Plan of China","award":["2016YFC0201104"],"award-info":[{"award-number":["2016YFC0201104"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The absorbance is of great importance in the tunable diode laser absorption spectroscopy (TDLAS) as it contains information of both gas properties and spectroscopic parameters. A novel, calibration-free wavelength modulation-direct absorption spectroscopy (WM-DAS) is proposed and experimentally verified in this two-part paper. This method combines the capability of absorbance measurement from DAS and the advantages of enhanced noise rejection and high sensitivity from WMS. In this Part I, we focus on the full theoretical basis and procedures of this method from the following three aspects: the high-accuracy characterizations of laser frequency and intensity, noise rejection ability by extracting the characteristic spectra through the fast Fourier transform (FFT) of the light intensity, and the simultaneous fitting strategy for both baseline and absorbance. The preliminary validation experiment of CO transition at 4300.6999 cm\u22121 in a static gas cell shows the high accuracy of the proposed method.<\/jats:p>","DOI":"10.3390\/s20030681","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T07:41:11Z","timestamp":1580110871000},"page":"681","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Highly Sensitive, Calibration-Free WM-DAS Method for Recovering Absorbance\u2014Part I: Theoretical Analysis"],"prefix":"10.3390","volume":"20","author":[{"given":"Zhimin","family":"Peng","sequence":"first","affiliation":[{"name":"State Key Laboratory of Power Systems, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanjun","family":"Du","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Systems, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanjun","family":"Ding","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Power Systems, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.pecs.2014.05.001","article-title":"Recent advances in laser absorption and shock tube methods for studies of combustion chemistry","volume":"44","author":"Hanson","year":"2014","journal-title":"Prog. Energ. Combust."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.pecs.2016.12.002","article-title":"Infrared laser-absorption sensing for combustion gases","volume":"60","author":"Goldenstein","year":"2017","journal-title":"Prog. Energ. Combust."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1088\/0957-0233\/9\/4\/001","article-title":"Diode laser absorption sensors for gas-dynamic and combustion flows","volume":"9","author":"Allen","year":"1998","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jms.2015.05.004","article-title":"Near infrared diode laser absorption spectroscopy of acetylene between 6523 and 6587 cm\u22121","volume":"314","author":"Deng","year":"2015","journal-title":"J. Mol. Spectrosc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.optlaseng.2013.12.005","article-title":"Sensor for headspace pressure and H2O concentration measurements in closed vials by tunable diode laser absorption spectroscopy","volume":"58","author":"Cai","year":"2014","journal-title":"Opt. Laser Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"117061","DOI":"10.1016\/j.fuel.2020.117061","article-title":"Effect of radiation reabsorption of C1-C6 hydrocarbon flames at normal and elevated pressures","volume":"266","author":"Zheng","year":"2020","journal-title":"Fuel"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/S0925-4005(99)00177-X","article-title":"Highly sensitive hydrogen sensors using palladium coated fiber optics with exposed cores and evanescent field interactions","volume":"56","author":"Sutapun","year":"1999","journal-title":"Sensor Actuat. B-Chem."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"054001","DOI":"10.1088\/0963-0252\/24\/5\/054001","article-title":"Review on VUV to MIR absorption spectroscopy of atmospheric pressure plasma jets","volume":"24","author":"Reuter","year":"2015","journal-title":"Plasma Sources Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.proci.2010.09.007","article-title":"Applications of quantitative laser sensors to kinetics, propulsion and practical energy systems","volume":"33","author":"Hanson","year":"2011","journal-title":"Proc. Combust. Inst."},{"key":"ref_10","first-page":"811","article-title":"Recovery of absolute gas absorption line shapes using tunable diode laser spectroscopy with wavelength modulation\u2014Part I, theoretical analysis","volume":"29","author":"Stewart","year":"2011","journal-title":"J. Lightwave Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1109\/JLT.2011.2107729","article-title":"Recovery of absolute gas absorption line shapes using tunable diode laser spectroscopy with wavelength modulation\u2014Part II: Experimental investigation","volume":"29","author":"Bain","year":"2011","journal-title":"J. Lightwave Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.jqsrt.2015.06.023","article-title":"Measurement of water vapor line strengths in the 1.4\u20132.7 \u00b5m range by tunable diode laser absorption spectroscopy","volume":"165","author":"Klein","year":"2015","journal-title":"J. Quant. Spectrosc. Radiat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.jqsrt.2014.11.008","article-title":"Diode-laser measurements of linestrength and temperature-dependent lineshape parameters for H2O transitions near 1.4 \u00b5m using Voigt, Rautian, Galatry, and speed-dependent Voigt profiles","volume":"152","author":"Goldenstein","year":"2015","journal-title":"J. Quant. Spectrosc. Radiat."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.jqsrt.2013.06.008","article-title":"Diode laser measurements of linestrength and temperature-dependent lineshape parameters of H2O-, CO2-, and N2-perturbed H2O transitions near 2474 and 2482 nm","volume":"130","author":"Goldenstein","year":"2013","journal-title":"J. Quant. Spectrosc. Radiat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.jqsrt.2007.05.008","article-title":"Diode laser measurements of temperature-dependent collisional-narrowing and broadening parameters of Ar-perturbed H2O transitions at 1391.7 and 1397.8 nm","volume":"109","author":"Li","year":"2008","journal-title":"J. Quant. Spectrosc. Radiat."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/s00340-003-1380-7","article-title":"Wavelength modulation absorption spectroscopy with 2f detection using multiplexed diode lasers for rapid temperature measurements in gaseous flows","volume":"78","author":"Liu","year":"2004","journal-title":"Appl. Phys. B-Lasers Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"19951","DOI":"10.1364\/OE.21.019951","article-title":"VCSEL-based, high-speed, in situ TDLAS for in-cylinder water vapor measurements in IC engines","volume":"21","author":"Witzel","year":"2013","journal-title":"Opt. Express"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s00340-004-1643-y","article-title":"Line-shape study of water vapor by tunable diode laser spectrometer in the 822-832 nm wavelength region","volume":"79","author":"Ray","year":"2004","journal-title":"Appl. Phys. B-Lasers Opt."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"29550","DOI":"10.1364\/OE.26.029550","article-title":"High-accuracy sinewave-scanned direct absorption spectroscopy","volume":"26","author":"Du","year":"2018","journal-title":"Opt. Express"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1364\/OL.33.001566","article-title":"Wavelength modulation spectroscopy with a widely tunable InP-based 2.3 \u00b5m vertical-cavity surface-emitting laser","volume":"33","author":"Hangauer","year":"2008","journal-title":"Opt. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6728","DOI":"10.1364\/AO.42.006728","article-title":"Wavelength modulation spectroscopy: Combined frequency and intensity laser modulation","volume":"42","author":"Schilt","year":"2003","journal-title":"Appl. Opt."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1364\/AO.45.001052","article-title":"Extension of wavelength-modulation spectroscopy to large modulation depth for diode laser absorption measurements in high-pressure gases","volume":"45","author":"Li","year":"2006","journal-title":"Appl. Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s00340-017-6780-1","article-title":"Measurement of the absolute absorbance based on wavelength modulation spectroscopy","volume":"123","author":"Du","year":"2017","journal-title":"Appl. Phys. B-Lasers Opt."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s00340-002-0984-7","article-title":"Handheld, battery-powered near-IR TDL sensor for stand-off detection of gas and vapor plumes","volume":"75","author":"Wainner","year":"2002","journal-title":"Appl. Phys. B-Lasers Opt."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3482","DOI":"10.1364\/OE.383216","article-title":"A high-accurate and universal method to characterize the relative wavelength response (RWR) in wavelength modulation spectroscopy (WMS)","volume":"28","author":"Du","year":"2020","journal-title":"Opt. Express"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0584-8547(02)00220-3","article-title":"Improved detectability of wavelength modulation diode laser absorption spectrometry applied to window-equipped graphite furnaces by 4th and 6th harmonic detection","volume":"58","author":"Gustafsson","year":"2003","journal-title":"Spectrochim. Acta B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"23104","DOI":"10.1364\/OE.19.023104","article-title":"Calibration-free wavelength modulated TDLAS under high absorbance conditions","volume":"19","author":"Peng","year":"2011","journal-title":"Opt. Express"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1364\/AO.53.000356","article-title":"Fitting of calibration-free scanned-wavelength-modulation spectroscopy spectra for determination of gas properties and absorption lineshapes","volume":"53","author":"Goldenstein","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"125203","DOI":"10.1088\/0957-0233\/24\/12\/125203","article-title":"Analysis of calibration-free wavelength-scanned wavelength modulation spectroscopy for practical gas sensing using tunable diode lasers","volume":"24","author":"Sun","year":"2013","journal-title":"Meas. Sci. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5546","DOI":"10.1364\/AO.48.005546","article-title":"Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments","volume":"48","author":"Rieker","year":"2009","journal-title":"Appl. Opt."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2844","DOI":"10.1002\/adma.200801060","article-title":"High-speed color-switching silicon LEDs","volume":"20","author":"Kuai","year":"2008","journal-title":"Adv. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1109\/JLT.2007.912519","article-title":"Tunable diode laser spectroscopy with wavelength modulation: A phasor decomposition method for calibration-free measurements of gas concentration and pressure","volume":"26","author":"McGettrick","year":"2008","journal-title":"J. Lightwave Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"107801","DOI":"10.1088\/1674-1056\/ab3e44","article-title":"Optoelectronic properties analysis of silicon light-emitting diode monolithically integrated in standard CMOS IC","volume":"28","author":"Chen","year":"2018","journal-title":"Chin. Phys. B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"11976","DOI":"10.1364\/OE.20.011976","article-title":"Odd harmonics with wavelength modulation spectroscopy for recovering gas absorbance shape","volume":"20","author":"Peng","year":"2012","journal-title":"Opt. Express"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"23724","DOI":"10.1364\/OE.21.023724","article-title":"First harmonic with wavelength modulation spectroscopy to measure integrated absorbance under low absorption","volume":"21","author":"Peng","year":"2013","journal-title":"Opt. Express"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/s00340-014-5866-2","article-title":"Multi-harmonic measurements of line shape under low absorption conditions","volume":"117","author":"Lan","year":"2014","journal-title":"Appl. Phys. B-Lasers Opt."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"9263","DOI":"10.1364\/OE.26.009263","article-title":"Wavelength modulation spectroscopy for recovering absolute absorbance","volume":"26","author":"Du","year":"2018","journal-title":"Opt. Express"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.jqsrt.2017.06.038","article-title":"The HITRAN2016 molecular spectroscopic database","volume":"203","author":"Gordon","year":"2017","journal-title":"J. Quant. Spectrosc. Radiat."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1016\/j.jqsrt.2012.02.010","article-title":"A Predoi-Cross. Spectral line parameters including temperature dependences of self- and air-broadening in the 2\u21900 band of CO at 2.3 \u00b5m","volume":"113","author":"Mantz","year":"2012","journal-title":"J. Quant. Spectrosc. Radiat."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/681\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:44:41Z","timestamp":1760363081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/3\/681"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,26]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["s20030681"],"URL":"https:\/\/doi.org\/10.3390\/s20030681","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,26]]}}}