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[Hideki T. Miyazaki](https://orcid.org/0000-0003-4152-1171), [Takeshi Kasaya](https://orcid.org/0000-0002-1976-8760), Masahiro Saito, Kazuya Kimoto, Yutaro Tsuiki, [Tetsuyuki Ochiai](https://orcid.org/0000-0003-2933-0014)

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[Gas temperature measurement based on contrast reversal in mid-infrared CO                    <sub>2</sub>                    images](https://mdr.nims.go.jp/datasets/5edc28d9-68ba-48cc-a85e-c82f200664e4)

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Gas temperature measurement based on contrast reversal in mid-infrared CO2 imagesResearch Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19701Gas temperature measurement based oncontrast reversal in mid-infrared CO2 imagesHIDEKI T. MIYAZAKI,* TAKESHI KASAYA, MASAHIRO SAITO,KAZUYA KIMOTO, YUTARO TSUIKI, AND TETSUYUKI OCHIAINational Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047, Japan*MIYAZAKI.Hideki@nims.go.jpAbstract: We demonstrate noninvasive measurement of gas temperature based on the opticalgas imaging. Gas flows containing carbon dioxide (CO2) appear as either bright or dark images,depending on the relative temperatures of the background and the gas, when using a narrowbandmid-infrared camera tuned to the CO2 absorption wavelength at 4.3 µm. When the backgroundtemperature is varied continuously, the gas image vanishes transiently and then the contrastreverses. The specific background temperature at the point when the gas image disappearsprovides the gas temperature. This technique is an evolved implementation of the classical linereversal method, made possible by advanced infrared devices. We also apply this techniqueto two-dimensional temperature mapping and to dynamic emissions from engine exhaust andhuman breathing.© 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement1. IntroductionThe measurement of gas temperature continues to be a challenging problem [1,2] due to the poorthermal conductivity and boundary heat transfer of gases. The most straightforward method is toexpose a solid probe, such as a thermocouple, to the gas. However, in using this simple method,it is difficult to obtain reliable results due to thermal conduction through the probe and radiationfrom the probe’s surface. Therefore, various noninvasive methods have been developed, such asinfrared radiation computed tomography [3], Rayleigh [4] or Raman scattering [5], and coherentanti-Stokes Raman spectroscopy [6]. Recently, it has become possible to determine temperaturefrom a single absorption lineshape using quantum cascade lasers [7]. However, these techniquesrequire precise optical systems, making them unsuitable for applications outside the laboratory.Among the many noninvasive techniques for gas temperature measurement, there is anexceptionally simple method: line reversal [1,2,8]. The line reversal method was widely studiedin the early 20th century as a way to determine flame temperature (1000–2800 K). In this approach,a thermal radiation light source with variable temperature (intensity) is placed behind the flame,and its light passing through the flame is observed with a spectrometer while changing thetemperature of the light source. The flame temperature is determined as the temperature of thelight source when the bright lines turn to dark lines [9,10]. Although the reversal of the D linesof Na atoms is well known [11], the use of absorption lines of carbon dioxide (CO2) and watervapor (H2O) in the mid-infrared region has also attracted interest from an early stage [10,12,13].In 1928, the temperature of CO2 contained in a flame was measured by the line reversal methodin the 4-µm region [14].Recent advances in infrared detectors have permitted optical gas imaging (OGI) [15,16]. Byrestricting the observation wavelength to a narrowband tuned to the absorption of a specificgas, that gas can be selectively visualized remotely. Dispersive OGI based on Fourier transforminfrared spectroscopy is versatile but slow in image acquisition [17]. In contrast, nondispersiveOGI without a spectrometer allows dynamic tracking of specific gas movements [18–21], whichis the topic of this study. While the sensitivity band of the imaging device itself is used for#596786 https://doi.org/10.1364/OE.596786Journal © 2026 Received 12 Mar 2026; revised 18 Apr 2026; accepted 20 Apr 2026; published 19 May 2026https://orcid.org/0000-0003-4152-1171https://orcid.org/0000-0002-1976-8760https://orcid.org/0000-0003-2933-0014https://doi.org/10.1364/OA_License_v2#VOR-OAhttps://crossmark.crossref.org/dialog/?doi=10.1364/OE.596786&amp;domain=pdf&amp;date_stamp=2026-05-19Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19702visualizing gases in some cases [22], band-pass filters or gas cells matched to the gas of interestare usually employed [20]. In particular, filters cooled at cryogenic temperatures [21] provideimages with higher quality than uncooled, room-temperature filters [18,19]. In either case, theuse of a cooled camera is necessary for satisfactory results because faint intensity changes innarrow bands must be captured.OGI technology has been used for detecting hazardous gas leaks [18–20] and visualizing gasflows [21–24]. In addition, since the COVID-19 pandemic, there has been growing interest invisualizing human exhalation [25–29].This paper presents a noninvasive method for gas temperature measurement based on theprinciple of line reversal and use of the OGI technique. A temperature-variable thermal radiationlight source is placed behind a gas containing CO2, and its light passing through the gas isobserved with a CO2 imaging camera while changing the temperature of the light source. In thismethod, instead of the reversal of line spectra, black and white gas appearances are reversed intwo-dimensional (2D) images; here, we call this phenomenon contrast reversal. Accordingly,the gas temperature is determined as the temperature of the light source at the point when thecontrast reverses.A few works have reported on gas temperature measurement using OGI [17,30,31]. However,they all determined temperature based on the assumed theoretical temperature dependence ofthe gas absorption coefficient. On the other hand, the contrast reversal method is a null method,where the gas temperature is determined as the background temperature at the moment the gasbecomes invisible. The accuracy of the measurement is mainly determined by the accuracy ofthe light source temperature, rather than by the assumed absorption properties of the gas.The evolution from classical line spectra reversal to 2D image contrast reversal brings strongadvantages. With the aid of advanced image processing techniques, the rich information in theimages can be fully exploited, permitting accurate temperature determination even from imageswith poor contrast. Moreover, this approach can obtain 2D temperature distribution. Using ahigh frame rate, typically 30 frames per second, makes it possible to measure the temperature oftime-varying targets such as engine exhaust and human breath. In addition, both the camera andlight source are portable, thus facilitating application outside the laboratory.With the growing demand for reducing CO2 emissions and the transition to new fuels,monitoring gas emissions into the atmosphere is becoming increasingly important. Techniques ofquantitatively measuring gas emissions using OGI are thus promising [16,32]. However, becausethe appearance of gas in OGI strongly depends on the gas temperature [32–34], the first step inquantifying gas emissions is to measure the temperature of a gas, and this challenge is the primarymotivation of this work. Because emitted gas contains CO2 in most cases, the method presentedhere can usually be applied as is; moreover, by seeding emissions with CO2, this method can beapplied to any gas.The remainder of this paper is structured as follows. Section 2 discusses the theoreticalfoundation of contrast reversal. Section 3 introduces the equipment used as well as the imagemeasurement method. Section 4 verifies the basic principle by measuring gases with knowntemperatures. Section 5 applies this technique to target gases of unknown temperature. Section 6provides a discussion and summary. Further details are discussed in Supplement 1.2. Fundamentals of contrast reversal in gas imaging2.1. Radiative transfer equation and blackbody radiationIn this section, we clarify how the temperature of a gas is reflected in infrared optical images.Suppose that radiation from a light source at temperature Ts passes through a gas at temperatureTg and is detected by a camera (Fig. 1(a)). The spectral radiation intensity iν (W/(m2 sr cm−1)) atfrequency (wavenumber) ν (cm−1) along the coordinate z from the light source to the camerahttps://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19703follows the radiative transfer equation:diνdκν= −iν(κν) + isourceν (κν). (1)Here, κν is the optical thickness (dimensionless) and isourceν (κν) is the source function repre-senting the radiation from the gas. We basically follow the definitions of Siegel and Howell [35]and the HITRAN database [36]. Gas scattering can be neglected [23]. Furthermore, stimulatedemission can be ignored in the range Tg = 0–200°C, which is used in this work. Throughout thisstudy, pressure is assumed to be constant (standard pressure: 101,325 Pa).Fig. 1. Overview of gas temperature measurement based on contrast reversal. (a) Proposedsystem: arrangement of light source, gas, and camera, coordinate system, temperature ofeach part, and observed image. Inset: variation of light source temperature Ts crossing thegas temperature Tg. (b) Change in intensity IR profile along a line just after the emission inthe gas image, according to the change (increase in this figure) of light source temperatureTs.The optical thickness isκν = ∫∞0 aνdz = ∫∞0 kνncdz, (2)where aν (cm−1) is the absorption coefficient, kν (cm2/molecule) is the absorption cross section,n = T0NA/(TV0) (molecules/cm3) is the total volume number density of the gas, T0 is thestandard temperature (273.15 K), V0 is the volume occupied by 1 mol of gas at standard state(2.24× 104 cm3), NA is the Avogadro constant, T is temperature, and c is the mole fraction(concentration) of the gas. As an indicator of gas concentration, the column number density u(molecules/cm2) is considered [36]:u = ∫∞0 ncdz.For practical convenience, the product of concentration and thickness ζ (ppm m), referred tosimply as the column density, is often used [16]:ζ = ∫∞0 cdz.The incident light is assumed to be blackbody radiation at temperature Ts. Since there is noscattering, the source function corresponds to the blackbody radiation of the gas at temperatureTg. The blackbody radiation intensity iνbb(T) (W/(m2 sr cm−1)) is given as [37]iνbb(T) =2hc20ν3exp(hc0ν/kBT) − 1,where h is the Planck constant, c0 is the speed of light in vacuum, and kB is the Boltzmannconstant. The radiative transfer equation (Eq. (1)) can be written in an integrated form usingResearch Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19704blackbody radiation intensity:iν(κν) = iνbb(Ts) exp(−κν) + ∫κν0 iνbb(Tg)exp[−(κν − κ∗ν)]dκ∗ν. (3)2.2. Radiative transfer at a single frequency in uniform gasLet us consider radiative transfer at a single frequency ν for a simple situation, where thetemperature and concentration of the gas are uniform and the thickness L (m) is clearly defined.It is assumed that only the target gas exhibits absorption. In this case, Eq. (2) is simplified toκv = kvncL = kvu, where u = ncL. Equation (3) is also simplified asiν(κν) = (1 − Aνg)iνbb(Ts) + Aνgiνbb(Tg), (4)where Aνg = 1 − τνg is absorptivity and τνg = exp(−κν) is transmissivity.Typical spectra are shown in Fig. 2. The CO2 absorption cross section kν is a collection ofsharp absorption lines as seen in Fig. 2(a). The absorption spectrum for CO2 in this study followsHITRAN [36]. For details on the spectra in Fig. 2 and equations in Sec. 2.2 and 2.3, refer toSupplement 1, Sec. A.Fig. 2. Spectra related to radiative transfer for gases with uniform temperature andconcentration. (a) Absorption cross section spectrum kν of CO2 gas at temperature Tg = 50°C.(b) Responsivity spectrum Rν of CO2 imaging camera used in study. (c) Radiation intensityspectrum iν and blackbody radiation intensities iνbb at gas temperature Tg = 50°C, lightsource temperature Ts = 75°C, and column density ζ (50°C)= 102, 103, 104 ppm m. (d)Similar results at Tg = 50°C and Ts = 25°C. In all panels, vertical lines indicate full width athalf maximum of responsivity spectrum Rν.The responsivity Rν of the CO2 imaging camera used in this study (Fig. 2(b)) covers a muchbroader bandwidth, with a full width at half maximum of ∆ν = ν2−ν1, than individual absorptionlines. Therefore, the experimentally observed signal is an integration over many absorption lines,as discussed below (Sec. 2.3, Fig. 3(d)). For Tg = 50°C, Ts = 75°C, and several column densitiesζ, iν obtained from Eq. (4) is shown in Fig. 2(c); iν for Ts = 25°C is shown in Fig. 2(d).https://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19705Fig. 3. Contrast reversal behavior for CO2-containing gas at temperature Tg = 50°C observedby a CO2 imaging camera with responsivity Rν and a finite bandwidth. (a) Relationshipof signal difference ∆IR to light source temperature Ts for uniform gas with temperatureTg = 50°C and various column densities ζ (50°C) shown in legend. (b) ∆IR–Ts relationfor nonuniform gas with Gaussian-distributed temperature and concentration: peak gastemperature Tpeakg = 50°C, concentration corresponding to the values of ζ (25°C) in thelegend of (a). (c) Relationship between contrast reversal temperature Trevs and ζ for Gaussian-distributed CO2-containing gas with Tpeakg = 50°C and concentration corresponding to ζin the horizontal axis. The 1/e-width average temperature T1/eg is also indicated. (d)Relationship between absorptivity Ag and ζ (50°C) for CO2-containing uniform gas at Tg =50°C. (e) Relationship between Tpeakg and T1/eg for gas with Gaussian-distributed temperatureat ambient temperature Ta = 25°C.While column density ζ is a convenient parameter simply based on gas concentration cand thickness, absorptivity cannot be specified with only ζ. The essential parameter definingabsorptivity is the column number density u. Since u also depends on temperature T due to the nterm, absorptivity is determined by both ζ and T. Therefore, whenever ζ is specified in this paper,the temperature, at which the value of ζ is defined, is also noted.When the background is hotter than the gas (Fig. 2(c)), background radiation is absorbed bythe gas, and the signal detected by the camera decreases as the gas becomes thicker (highercolumn density); the gas appears dark in contrast to the background (negative image). However,even when the gas is so dense as to be completely opaque, the detected intensity does not reachzero. The minimum intensity is limited by the blackbody radiation at the gas temperature.Conversely, when the background is colder than the gas (Fig. 2(d)), the radiation from thegas is added to the background radiation, and the gas appears brighter as it becomes denserResearch Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19706(positive image). Here, the maximum brightness is limited by the blackbody radiation at the gastemperature. Accordingly, Fig. 2(c) and (d) show gas images with reversed contrast.2.3. Radiative transfer in uniform gas over a finite bandwidthFor a gas with column number density u, the intensity signal IR(u), which is actually detectedby the camera, is given by integrating iν(κν) multiplied by the responsivity spectrum Rν of thecamera (Fig. 2(b)) over ν:IR(u) = ∫∞0 Rνiν(κν)dν= ∫∞0 Rνiνbb(Ts) exp(−κν)dν + ∫∞0 Rν ∫κν0 iνbb(Tg)exp[−(κν − κ∗ν)]dκ∗νdν.(5)For the convenience of practical applications, Eq. (5) can be described in a simpler form, asEq. (4) for a single frequency case:IR(u) ≈ (1 − Ag)IRbb(Ts) + AgIRbb(Tg). (6)Refer to Supplement 1, Sec. A.3 for the derivation. Here,IRbb(T) = ∫∞0 Rνiνbb(T)dνis the signal measured by the detector with responsivity Rν for blackbody radiation at temperatureT, which can be determined by calibration experiments.Ag =∫∞0 Rν[1 − exp(−κν)]dν∫∞0 Rνdνis the CO2 absorptivity measured by the detector with responsivity Rν; this depends not only onthe column number density u but also on the gas temperature Tg. While Ag can also be obtainedexperimentally, this study uses the Ag values calculated by HITRAN. Ag based on HITRAN wasconfirmed to be consistent with experimental results (Fig. S1(a)). Equation (6) is the fundamentalformula, and it is used below for practical corrections.In the absence of gas,IR(0) = IRbb(Ts),and thus the radiation signal difference due to the presence of the gas is∆IR = IR(u) − IR(0) ≈ Ag[IRbb(Tg) − IRbb(Ts)]. (7)When the background temperature Ts and the gas temperature Tg are equal, ∆IR = 0 (i.e., the gasbecomes invisible), regardless of Ag (i.e., regardless of the concentration or absorption propertiesof the gas).This is demonstrated for Tg = 50°C (as in Fig. 2) and the representative column densities inFig. 3(a). When the background (light source) temperature Ts is varied, ∆IR(Ts) = 0 at Ts = Tg,regardless of the column density ζ. In this manner, the gas temperature can be determined fromimages. The Ts that gives ∆IR(Ts) = 0 is called the contrast reversal temperature T revs .Here, let us summarize the concept of the contrast reversal method with reference to Fig. 1.A planar infrared light source with controllable temperature is placed behind the gas, and thebackground (light source) is observed through the gas (Fig. 1(a)). We then consider the intensityprofile in the image just after the gas emission (Fig. 1(b)). When the light source temperature Tsis varied (e.g., increased) across the expected gas temperature Tg (Fig. 1(a), inset), the imageintensity signal IR basically increases in accordance with Ts, but the signal difference of the gasagainst the background, ∆IR, changes gradually from positive to negative. During this process,there is a moment when the gas and background intensity match, resulting in a flat profile wherethe gas becomes invisible. Consequently, the unknown gas temperature Tg can be determined asthe light source temperature T revs at which this contrast reversal occurs.https://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 197072.4. Radiative transfer in nonuniform gas over a finite bandwidthThe aim of this study is to quantify the temperature of gas plumes released into free space, whichwould be beneficial for real-world applications. Accordingly, the above discussion must beextended to general cases where the temperature and concentration are not uniform.Conventional line reversal methods have also been applied to nonuniform gases. Flames in freespace are essentially nonuniform; a hot core is surrounded by cold boundary layers. Therefore, theline reversal temperature should be regarded as an average or effective temperature [1,8]. Strictlyspeaking, the line reversal method is a null technique for determining the effective temperature offlames or gases [38]. Although the relationship between the temperature distribution of a flameand the line reversal temperature has been discussed [39], different temperature distributions wereassumed for each case [40,41], and no generalized theory has been found. Here, we consider a gaswhose temperature and concentration are distributed in a Gaussian manner along the thicknessdirection, which would be a sufficiently general assumption.We assume that the temperature and concentration profiles of the gas are described by respectiveGaussian functions with a common width. The gas concentration profile is assumed to have apeak value cpeak and to be zero in the environment. The peak concentration is set to achievea specific value of column density ζ (Fig. S1(c)), assuming a uniform temperature of 25°C.The temperature profile is assumed to have a peak gas temperature Tpeakg = 50°C in an ambienttemperature Ta = 25°C (Fig. S1(d)). As shown in Eq. (2), the optical thickness κν is determinedby kν, n, and c. Since both kν and n depend on Tg, κν is influenced by the spatial distributionof Tg as well as that of c. Taking into account all of these spatial distributions in Eq. (5), thedetected signal IR(u) for nonuniform gas is obtained for various light source temperatures Ts.The relationship between the signal difference ∆IR due to the presence of the gas and thelight source temperature Ts is shown in Fig. 3(b) for various column densities ζ. Unlike theuniform case (Fig. 3(a)), the gas becomes invisible at Ts lower than 50°C. Furthermore, thecontrast reversal temperature T revs decreases as ζ increases. The relationship between T revs and ζ issummarized in Fig. 3(c). While ζ is low, T revs remains nearly constant and close to the 1/e-widthaverage temperature T1/eg (Fig. S1(d)) shown by the dashed line. However, T revs starts to decreaseat ζ ∼ 1000 ppm m, corresponding to the region where Ag begins to saturate (Fig. 3(d)). For asufficiently dense gas, radiation from the light source is attenuated due to the high opacity ofthe gas, and only radiation from the surface layer at the exit side of the gas reaches the camera.Consequently, in the high ζ limit, the determined T revs approaches the environmental temperatureat the edge of the Gaussian distribution.This behavior is essentially identical to the single-frequency, nonuniform case presented in Fig.S2 (see Supplement 1, Sec. B). From these findings, it seems to be a universal nature that thecontrast reversal method gives a temperature value close to T1/eg for relatively low-density gases.In summary, Eqs. (6) and (7) can also be applied to nonuniform gas flows in free space. Anonuniform gas with Gaussian temperature and concentration distributions should be regardedas a uniform gas with an equivalent temperature of T1/eg . For such nonuniform gases, thecontrast reversal temperature T revs gives the 1/e-width average temperature T1/eg . The relationshipbetween the measured T1/eg and the peak temperature Tpeakg is analytically denoted as T1/eg =0.746Tpeakg + 0.254Ta, as shown in Fig. 3(e). For more complicated gas distributions, specialconsiderations are necessary. However, such cases are outside the scope of this study.2.5. Necessary corrections considering the influence of atmospheric CO2The CO2 discussed in this study also exists in the atmosphere at approximately 400 ppm, and itsabsorption cannot be ignored. The properties of the optical system have also been neglected inprevious sections. Here, we discuss necessary corrections for gas temperature measurements inreal situations. For details, see Supplement 1, Sec. C and Fig. S3.https://doi.org/10.6084/m9.figshare.32071797https://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19708Two factors must be considered. The first is the radiative transfer in the background space. Inall of the above discussions, IRbb(Ts) should be replaced with IRbb(Teffs ), whereIRbb(Teffs ) = τabsb IRbb(Ts) + (1 − τabsb )IRbb(Ta). (8)Due to the transmissivity τabsb of the background space between the light source and the gas, theintensity of light that actually irradiates the gas is reduced from the original intensity. Meanwhile,radiation from atmospheric CO2 at temperature Ta is added. As a result, the light incident on thegas corresponds to blackbody radiation at an effective temperature Teffs .The second factor is the bandwidth over which transmissivity is defined. Here, the transmissivityτabsb is for the local band where the camera’s sensitivity overlaps the gas absorption band, and thesuperscript indicates that this is for the absorption band. When considering signal difference∆IR in Eq. (7), which is used to extract the effect of the presence of the gas, the signals in IR(u)and IR(0) within the transparent band cancel each other out. Therefore, only the transmissivitywithin the absorption band must be considered (for detailed derivation, see Supplement 1, Sec.C and Fig. S1(b)). In all subsequent cases, a τabsb correction determined by the ambient CO2concentration and background distance was applied to each measurement.3. Experimental methods3.1. CO2 imaging narrowband infrared cameraFor use in our experiments, we adopted a custom-made InSb camera equipped with a built-incooled filter for CO2, FLIR A6796 (Fig. 4(a) and (b)). Both the image sensor and the filter werecooled to 80 K. The camera’s main features included image resolution of 640× 512 pixels, framerate up to 480 fps, and intensity resolution at 14 bits. The responsivity spectrum (Fig. 2(b)) had acenter wavelength of 4.21 µm and a full width at half maximum of 0.21 µm. This band was shiftedto the shorter wavelength side relative to the CO2 absorption (Fig. 2(a)). Consequently, even forhighly dense CO2, a certain amount of incident light could always be detected, ensuring someamount of image output. More detailed information on this camera is provided in Supplement 1,Sec. D. While many OGI cameras with cooled filters are available for hydrocarbon molecules[15], those for CO2 are limited [21,25,26,28,29]. However, with the growing interest in carbonemissions and CO2 storage, the demand is expected to increase.3.2. Temperature-variable thermal radiation light sourcesThree custom-made planar blackbody light sources were used, depending on the requiredtemperature range. Light source A (Fig. 4(a)) has an effective area of 130× 130 mm square, atemperature control range of 5–105°C using a Peltier element, and temperature changing ratesof 0.4°C/s for heating and –0.15°C/s for cooling. Light source B (Fig. 4(b)) has an effectivediameter of 177 mm, a temperature control range from room temperature (25°C) to 430°C,and temperature rates of 0.7°C/s (heating) and –0.05°C/s (natural cooling). At high surfacetemperatures, buoyant flows of heated atmospheric CO2 near the surface create flickering inthe background image. In addition, when airflow hits the surface, temperature inhomogeneityon the surface exhibits nonuniformity in background radiation. To address these problems,the blackbody is encapsulated in a vacuum (< 50 Pa), and the infrared radiation is emittedthrough a double-sided, anti-reflection-coated Si window. Finally, light source C has nearlythe same appearance as light source B and is similarly vacuum-sealed, but it uses a water-cooled Peltier element instead of a simple heater for its temperature control range from –20°Cto 80°C and temperature changing rates of 0.11°C/s (heating) and –0.06°C/s (cooling). Allradiation surfaces are coated with blackbody paint (0.986 emissivity in the CO2 camera band).In this study, the surface temperature of these light sources serves as the absolute standardfor gas temperature measurement. Therefore, the surface temperature was calibrated using ahttps://doi.org/10.6084/m9.figshare.32071797https://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19709Fig. 4. Measurement system. (a) Setup for measuring gas temperature Tg near roomtemperature using light source A and gas temperature controller A; both are Peltier-controlled.(b) Setup for measuring a higher gas temperature Tg using vacuum-sealed light source B andgas temperature controller B. (c) Nozzle and thermocouple for measuring gas temperature.Thermocouple in this photograph is 50 µm in diameter; the 13-µm-diameter thermocouplemainly used in the experiments is too thin to clearly show in the photograph. Coordinates(X, Z) are defined with the nozzle tip center as the origin. (d) Temperature distribution indepth (Z) direction at X = 5.5 mm. Red curve shows Gaussian fitting. Gray vertical linesshow 1/e-width, and red dashed line denotes 1/e-width average temperature T1/eg .manufacturer-calibrated sensor. During the temperature scanning, the surface temperature ismonitored in real time by a radiation thermometer with up to 10-ms time resolution, and it isconverted to the equivalent blackbody temperature Ts, corrected for surface emissivity and Siwindow transmissivity. Radiation thermometers for light sources B and C are installed inside thevacuum chamber.3.3. Gas supply systemFor proof-of-concept experiments, a system was built to supply CO2 gas with controlledconcentration, flow rate, and temperature. For concentration adjustment, CO2 diluted with N2was used, since N2 is infrared inactive and does not affect images. The required concentration andflow rate of CO2 were generated by a mixed gas generator equipped with mass flow controllers(HORIBA, MU-3314). Two gas cylinders—a pure CO2 cylinder and one with 4.0% CO2 dilutedin N2—were used for supply. The temperature was controlled just before emission from thenozzle. Two custom-made gas temperature controllers were used according to the requiredtemperature range. Gas temperature controller A (Fig. 4(a)) uses a Peltier element and iscontrollable in the 15–60°C range; gas temperature controller B (Fig. 4(b)) uses a heater andcan control temperatures from room temperature (25°C) to 150°C. To release a sheet-like gasResearch Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19710flow of constant thickness and column density, we used a flat stainless-steel nozzle with innerdimensions of 12.55× 1.65 mm at the tip (Fig. 4(c)). The coordinate system (X, Z) was definedas shown in Fig. 4(c), with the nozzle center as the origin. Gas temperature control is not easy:Temperature rapidly converges to room temperature after ejection from the nozzle. Consequently,it is important to know the actual temperature of the emitted gas. However, in this study, the onlyavailable gas temperature sensors were thermocouples.As discussed in Sec. 1, thermocouples are not considered reliable for gas temperaturemeasurement due to thermal conduction through the probe and radiation from the probe’s surface.Therefore, to maximize the reliability of the obtained values, we used an ultrafine thermocouplewith minimized heat capacity. The temperature of the outflowing gas was monitored with a 13-µm-diameter thermocouple (Anbe SMT Co., KFT-13-200-100). An example of the temperaturedistribution measured with this thermocouple is shown in Fig. 4(d). This distribution is reasonablyfit by a Gaussian function, confirming that the temperature distribution assumed in Sec. 2.4 wasjustified for this nozzle.3.4. Experimental procedureA temperature-variable light source (Sec. 3.2) was placed behind the gas to be measured. TheCO2 imaging camera (Sec. 3.1), equipped with a 50-mm F2.5 lens, was properly positioned forobserving the gas and the light source. For measuring gas having a known temperature, a gassupply system (Sec. 3.3) was used to emit CO2 at the specified concentration c and flow rateQ. For the demonstrations of engine exhaust and exhaled breath, the target gas contained CO2.When the CO2 in the gas was insufficient, pure CO2 was inserted at the inlet to reach the requiredconcentration. In all experiments, the CO2 column density was within the effective range for thetemperature measurement ( <∼ 1000 ppm m) discussed in Sec. 2.4. Appropriate exposure time texp(2.5–40 ms) and frame rate f (24.9–30 fps) were selected depending on the target, and the movierecording started simultaneously with the start of the temperature change. The data acquisitionof the radiation thermometer of the light source was synchronized with that of the camera image,assigning a light source (background) temperature Ts to each frame. The equivalent temperatureTeffs could be determined from Ts by taking account of the transmissivity τabsb of the backgroundCO2 based on Eq. (8). To determine the signal difference ∆IR due to the presence of gas, areference region on the image periphery unaffected by the gas was selected, and its averageintensity was designated as IR(0). Occasional residual gas in the reference region was excludedusing a median filter in the time domain. In the ∆IR image, the background always exhibits aconstant intensity, and the gas appears either brighter or darker relative to the background. Morecomplex image processing was applied as needed, as discussed in the following sections. Imageprocessing was performed by original software written in Python.As discussed in the previous section, we had no other choice than to use a thermocoupleto confirm the gas temperature in this study. Basically, the abovementioned 13-µm-diameterthermocouple was used, but when this one was bent by the flow, we adopted a 50-µm-diameterthermocouple (Anbe SMT, KFT-50-200-100).Due to the uncertainty of the results from these thermocouples for gas temperature measurement,the absolute accuracy of the gas temperature determined by contrast reversal cannot be verifiedwithin this study. Confirmation of absolute accuracy must await comparison with other techniquesin the future. Nevertheless, a thermocouple is a practically useful standard. Therefore, in thisstudy, we compare the contrast reversal temperature with the gas temperature measured by theultrafine thermocouple. Various other instruments were also used to clarify the experimentalconditions (details described in Supplement 1, Sec. D).https://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 197114. Proof-of-concept experiments4.1. Moderate-concentration CO2 gas at room temperatureTo verify whether known temperatures could be reasonably measured, three proof-of-conceptexperiments were conducted. First, the simplest case—a gas at room temperature—was chosen,since there is no heat exchange with the surrounding environment and the gas temperaturecan be maintained uniformly. Under an ambient temperature of Ta = 24.5°C, CO2 gas witha concentration of c= 10% and a flow rate of Q= 1 L/min was ejected from gas temperaturecontroller A, which was set at 25°C in the setup of Fig. 4(a). The column density ζ at the nozzleoutlet was 165 ppm m, and the gas temperature was measured as Tg = 24.8°C with a thermocouple.Using light source A, a movie was recorded during the process where Teffs increased from 20°Cto 30°C (assuming τabsb = 0.874 for 64 ppm m) under conditions of texp = 40 ms and f = 24.9 fps.The results are shown in Fig. 5 and Visualization 1.Fig. 5. Gas temperature determination by contrast reversal for a 10% CO2 gas at roomtemperature. (a) Signal difference ∆IR image at effective light source (background)temperature Teffs = 20.6°C, (b) at 24.5°C, and (c) at 28.5°C, displayed with a commonbrightness scale (see Visualization 1). Yellow line shows position for intensity profilemeasurement. As in conventional image processing, positive Y axis is defined downward.(d) Variation in intensity profile IR immediately past the nozzle as Teffs increases. (e)Relationship of ∆IR to Teffs , shown by a color map (bottom) and the transition of its RMS(top). Black curve shows the quadratic fitting for accurately determining the contrast reversaltemperature Trevs .When Teffs < Tg, the gas appears bright (Fig. 5(a)), but when Teffs > Tg, the gas appears dark(Fig. 5(c)). In addition, there is a momentary transitional point when the gas becomes invisible(Fig. 5(b)). To discuss this process quantitatively, the line profile just behind the nozzle wasexamined. Figure 5(d) shows the transition of the line profile in the original IR image.As predicted in Fig. 1(b), while Teffs is low, the gas exhibits a positive contrast: As Teffs increases,the contrast decreases, and at a certain Teffs , the image vanishes. At higher Teffs , the contrasthttps://doi.org/10.6084/m9.figshare.31638049https://doi.org/10.6084/m9.figshare.31638049Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19712reverses to negative. The baseline of the profile, except for the center region showing the ejectedgas, presents the background intensity IR(0). However, it is not necessarily flat. This is mainlybecause the ejected CO2 gas flowed in reverse due to changes in the environmental airflow. Inthe lower panel of Fig. 5(e), the change in the line profile of ∆IR is illustrated as a color map.Here, the fluctuation of the baseline was removed by subtracting the original IR(0) fitted to apolynomial function.The root mean square (RMS) of that profile is shown in the upper panel of Fig. 5(e). Thecontrast reversal temperature T revs (24.5°C) was obtained as the light source temperature at whichthe RMS reaches a minimum (i.e., the most featureless). This was regarded as the gas temperatureT1/eg , and it agreed with the result obtained by the thermocouple Tg within 0.3°C. The obtainedT1/eg value was closer to Ta than Tg, which can be interpreted that the gas converged to the ambienttemperature Ta immediately after ejection.4.2. Low-concentration CO2 gas at room temperature: contrast enhancementNext, we confirmed that the contrast reversal method could also be applied to gases of lowerconcentrations. Under ambient temperature Ta = 21.9°C, CO2 gas at c= 1% (ζ= 16.5 ppm m atnozzle outlet) and Q= 1 L/min was emitted from gas temperature controller A set at 25°C. Thesetup was the same as that in Sec. 4.1, but this experiment was conducted on a different day at alower room temperature. Regardless of the set value of the gas temperature controller (25°C), thegas temperature was determined as Tg = 22.2°C with a thermocouple. The temperature of thenozzle itself was confirmed to be close to the ambient temperature (Ta) by thermocouple. Sincethe body of the temperature controller around the nozzle was exposed to the room environment, itis reasonable that the nozzle temperature deviated from the set value (25°C). Using light sourceA, a movie was recorded (Teffs from 13°C to 27°C, τabsb = 0.874 for 64 ppm m, texp = 40 ms, andf = 24.9 fps).In this case, the line profile just behind the nozzle showed large fluctuations, and clear resultslike those in Fig. 5(e) could not be obtained. According to the Ag–ζ relationship for Tg ∼25°C (Fig. S1(a)), the absorptivity of CO2 at the column density ζ= 16.5 ppm m is Ag ∼ 0.02.Considering the camera’s dynamic range (103), visualizing this absorption is not difficult. Theissue lies in the CO2 originally present in the environment. The distance from the camera to thebackground light source was 0.9 m. Considering the atmospheric CO2 concentration of 400 ppm,the column density in the atmosphere itself is 360 ppm m, 20 times higher than that from thenozzle (16.5 ppm m). Fluctuation due to air currents in the room obscured the intensity changecaused by the gas emitted from the nozzle. Therefore, it is difficult to extract only the contributionof the target gas by observing solely the line profile at the nozzle exit.However, the environmental CO2 and the emitted gas from the nozzle behave differently.Therefore, we attempted to visualize only the gas from the nozzle based on differences in theimage features. The gas from the nozzle changes more abruptly compared with the environmentalCO2. Therefore, it can be extracted by a time derivative. However, the simple difference fromthe previous frame introduces considerable noise. Therefore, to clarify the change in the imagewhile reducing random noise, we evaluated the difference from the average of 30 surroundingframes (past 15 frames and next 14 frames; for about 1 second) at each moment. This is referredto as an enhanced difference image.The results are shown in Fig. 6(a)–(c). At low Teffs , the gas motion is clearly visible (Fig. 6(a)).At a certain time, it disappears (Fig. 6(b)). Then, with a further increase in Teffs , the gas motionbecomes visible again (Fig. 6(c)). As a quantitative indicator, the standard deviation of theenhanced difference image in the measurement box shown in the figure was investigated for eachframe (Fig. 6(d)). The minimum value was observed at T revs = 22.2°C, indicating that the imageis the most featureless at this Teffs . This is regarded as the gas temperature T1/eg , and it matchedthe result by thermocouple within 0.1°C. By making full use of 2D image information in thisResearch Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19713way, the temperature of the gas from the nozzle could be identified even in an environment with a20-times-higher column density of CO2 (360 ppm m vs 16.5 ppm m).Fig. 6. Gas temperature determination by contrast reversal for a 1% CO2 gas at roomtemperature. (a) Enhanced difference image of intensity IR at effective light source(background) temperature Teffs = 18.1°C, (b) at 22.2°C, and (c) at 26.2°C, displayed with acommon brightness scale (see Visualization 2). Yellow box indicates region for standarddeviation measurement. Nozzle outline is shown by white dashed line. (d) Variation instandard deviation of enhanced difference image in measurement region as Teffs increases.Visualization 2 shows the original (signal difference ∆IR) and enhanced difference images sideby side. The environmental flow is also visible in the enhanced difference images, but the flowfrom the nozzle is dominant. Therefore, it was possible to identify the moment at which the gasof interest vanished, as shown in Fig. 6(d).4.3. Hot CO2 gas with moderate concentration: 2D mappingIn the final proof-of-concept experiment, it was revealed how contrast reversal occurs in gas at asubstantially higher temperature than room temperature. Under ambient temperature Ta = 24.6°C,CO2 gas with c= 10% (ζ= 165 ppm m (100°C) at the nozzle outlet) and Q= 3 L/min wasejected from gas temperature controller B set at 100°C. The gas temperature was measured asTg = 106.6°C by thermocouple.Using the setup in Fig. 4(b) and light source B, a movie was recorded (Teffs from 27°C to 111°C,τabsb = 0.880 for 60 ppm m, texp = 5 ms, and f = 30 fps). The gas temperature was continuouslyconnected with surrounding Ta and had a distribution in the Z (depth) direction. Figure 4(d) showsthe temperature distribution at X = 5.5 mm during this experiment. The gas temperature alsoconverges to Ta as it moves farther away from the outlet in the +X direction. Representative ∆IRimages at three different Teffs values are shown in Fig. 7(a)–(c) and Visualization 3. Nevertheless,different from the previous cases, we could not find any moment when the gas completelydisappeared.https://doi.org/10.6084/m9.figshare.31638055https://doi.org/10.6084/m9.figshare.31638055https://doi.org/10.6084/m9.figshare.31638046Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19714Fig. 7. Gas temperature determination by contrast reversal for a 10% CO2 gas at ∼ 100°C.(a) Signal difference ∆IR image at the effective light source (background) temperatureTeffs = 30°C, (b) at 70°C, and (c) at 110°C, displayed with a common brightness scale (seeVisualization 3). (d) Variation in average ∆IR of the square region just past the nozzle shownin (a)–(c) as Teffs increases. (e) 2D temperature distribution by obtaining the contrast reversaltemperature Trevs (°C) at each pixel. Invalid region is shown by black. (f) Temperatureprofile at representative positions in (e).The variation in the average intensity of the square region just past the nozzle (shown as boxesin Fig. 7(a)–(c)) is shown in Fig. 7(d). To exclude rapid fluctuations in gas, a moving averageof N = 30 points (for 1 s) is shown, but abrupt negative spikes are still remarkable. This resultsfrom the backward flow of dense CO2 into the measurement region due to changes in airflow inthe environment; here, the cooled, previously ejected CO2 appears dark, so these spikes alwaysappear as negative. On the other hand, in regions far from the nozzle, the gas flutters randomly;the presence and absence of the gas are randomly repeated. These stochastic fluctuations canbe removed with a median filter of suitable length N in the time domain, which gives the mostrepresentative value among N continuous frames by excluding exceptional frames. Here, N = 5was chosen. Smooth trends for each pixel were obtained by fitting a polynomial function. TheTeffs when this trend crosses ∆IR = 0 was determined to be T revs for each local region. In areaswithout the gas, the background IR(0) is visible most of the time, so ∆IR is always ≈0 and thecorrelated trend with Teffs as in Fig. 7(d) is not observed. Therefore, as a first step, abnormalpoints where the ∆IR trend does not cross 0 and areas of the nozzle itself or those outside thelight source window were excluded. Furthermore, we excluded points where the width W ofthe change (Fig. 7(d)) over the entire experiment duration was lower than a certain threshold.The resulting temperature distribution for each valid pixel is shown in Fig. 7(e). In this way, therepresentative gas temperature at each pixel could be determined, even for dynamically flutteringgas.Two representative T revs profiles at X = 0.5 mm and 5.5 mm at the nozzle center extracted fromFig. 7(e) are shown in Fig. 7(f) and, in Table 1, compared with the temperature profiles in theZ direction measured by thermocouple. For the thermocouple measurements, both Tpeakg andT1/eg are displayed. T revs is the value at the position of the white circle (center line) in Fig. 7(f).https://doi.org/10.6084/m9.figshare.31638046Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19715While the temperature T revs obtained from the contrast reversal was closer to T1/eg than to Tpeakg asexpected, a discrepancy of 5–7°C was found between T revs and T1/eg . Nevertheless, consideringthat the temperature of a dynamically fluctuating gas was evaluated remotely and noninvasively,the advantage of the contrast reversal method proved to be sufficient. There could also beunderestimation in the results of the thermocouple due to heat escape. Figure 7(e) also illustrateshow high-temperature gas at ∼ 100°C ejected into a room-temperature environment rapidly coolsdown; here, the gas temperature is below 40°C after traveling 50 mm.Table 1. Representative temperatures at different X positions for a 10%CO2 gas at ∼ 100°C. Comparison of the peak gas temperature Tpeakg andthe 1/e-width average value T1/eg , both determined from Z-directiontemperature distribution measured by thermocouples, and contrastreversal temperature Trevs , determined from signal difference ∆IRimages.Position X (mm)Thermocouple CO2 imageTpeakg (°C) T1/eg (°C) Trevs (°C)0.5 106.6 88.2 93.55.5 97.7 80.3 87.2This procedure for measuring temperature distribution was adopted in all of the followingcases as well. Only the appropriate value of N for the median filter was adjusted for each case.5. Application experiments5.1. Hair dryerThe method described in the previous section was applied to various forms of gases at unknowntemperatures. As an example of continuous high-temperature gas, we measured the temperatureof the air blown from a hair dryer (Panasonic EH534, power: 900 W). With our CO2 camera, itwas possible to visualize the air emitted from the hair dryer as is, since the atmospheric CO2at 400 ppm (0.04%) is heated and appears bright. However, the contrast was insufficient todetermine the gas temperature. Therefore, pure CO2 gas as a tracer was mixed into the intake air.By mixing CO2 gas at 23.5 L/min, the emitted CO2 concentration increased to c= 3.8%. Fromthe CO2 flow rate and concentration, the total flow rate of the hair dryer is estimated to be Q= 620L/min. The outlet has an opening of 21 mm in the depth (Z) direction, and the column density isestimated at ζ= 800 ppm m (100°C). The setup is shown in Fig. 8(a). Using light source B, amovie was recorded (Ta = 25.8°C, Teffs = 31–156°C, τabsb = 0.880 for 60 ppm m, texp = 2.5 ms, andf = 30 fps).Typical images at low and high Teffs are presented in Fig. 8(b) and (c), respectively, as wellas in Visualization 4. As described in Sec. 4.3, the temperature distribution for each pixelshown in Fig. 8(d) was determined (N = 5 for median filter). The maximum T revs at the outletwas 107°C; the temperature was distributed asymmetrically in the vertical direction, and theupper side was hotter. The temperature measured with a 50-µm thermocouple exhibited themaximum temperature of 140°C near the upper end, and T1/eg was estimated at 111°C. Thisresult is consistent with the contrast reversal method (107°C). From the obtained temperaturedistribution, at a distance of 100 mm, reflecting a typical position for drying hair, the temperaturewas estimated at T1/eg ∼ 65°C and Tpeakg ∼ 80°C.5.2. Exhaust gas of a diesel engine: quick intermittent emissionNext, we measured the temperature of exhaust gases from a diesel engine vehicle. This differsfrom previous cases in that the gas is ejected intermittently. Additionally, the camera and lighthttps://doi.org/10.6084/m9.figshare.31638058Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19716Fig. 8. Temperature measurement of air from a hair dryer. (a) Measurement setup. Acylinder was fixed at the intake of the dryer, and pure CO2 gas was introduced from theside. (b) Signal difference ∆IR image at effective light source (background) temperatureTeffs = 35°C and (c) at 135°C, displayed with a common brightness scale (see Visualization 4).(d) 2D distribution of the contrast reversal temperature Trevs (°C).source were taken outside the laboratory for measurement, making this experiment meaningfulas a practical demonstration.We used an agricultural tractor, the John Deere 1750 (2.940 L, 3 cylinders). The exhaust pipewas modified to protrude to the side, making observation more convenient. Below the exhaustpipe with an elliptical cross section (inner diameter: 50 mm horizontally, 45 mm vertically),light source B was placed facing upward, and the CO2 camera was set above facing downward(Fig. 9(a)).In an environment at Ta = 12.8°C, the engine speed was maintained at 900 rpm (idling). Theaverage exhaust flow was estimated to be Q= 22 L/s. The exhaust gas sensor (thermocouple) gaveTpeakg = 80°C (T1/eg = 66°C) and c= 1.9% (ζ= 855 ppm m (80°C)) at the center of the exhaustpipe’s end. A movie was recorded during the rise of Teffs from 32°C to 133°C (τabsb = 0.853 for80 ppm m, texp = 3.5 ms, and f = 30 fps). Typical ∆IR images at low and high Teffs are shown inFig. 9(b) and (c), respectively, and in Visualization 5.In Supplement 1, Sec. E and Fig. S4, we discuss how the temperature of such intermittentlyemitted gas is measured by the contrast reversal method. For simplicity, it was assumed that gaswith constant CO2 concentration and temperature was emitted as rectangular pulses. A schematicof contrast reversal for this case is shown in Fig. 9(d). Initially, when Teffs is low, the gas looksbright in most frames but occasional frames without a gas image give negative spikes. When Teffsis high, the gas is mostly dark, but some frames without a gas yields positive spikes. Therefore,even for intermittently emitted gases, by excluding frames where the gas was absent, the gastemperature can be determined using the contrast reversal method.More specifically, a 4-stroke, 3-cylinder engine rotating at 900 rpm exhausts gas 22.5 timesper second [42–44]. As discussed in detail in Supplement 1, Sec. E, by assuming the exhaustvalve opening angle as 180 degrees, phases of producing emission for 33.3 ms and halting itfor 11.1 ms were alternately repeated. Since texp is sufficiently shorter than these periods, someframes did not capture exhaust gases (Fig. S5). This is because the engine and the frame ratehttps://doi.org/10.6084/m9.figshare.31638058https://doi.org/10.6084/m9.figshare.31638061https://doi.org/10.6084/m9.figshare.32071797https://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19717Fig. 9. Temperature measurement of exhaust gas from a diesel engine. (a) Measurementsetup. (b) Signal difference ∆IR image at effective light source (background) temperatureTeffs = 31.8°C and (c) at 107.8°C, displayed with a common brightness scale (see Visualiza-tion 5). (d) Variation in ∆IR with respect to Teffs based on a model of intermittently emittedgas. (e) 2D distribution of the contrast reversal temperature Trevs (°C).were not synchronized, and the frame rate was not fast enough to track all engine processes.Consequently, frames without gas appeared randomly with a probability of 25%.Again, a temporal median filter is effective here. By choosing N = 31 (about 1 s), the influenceof gas-free frames could be excluded. By fitting the median-filtered ∆IR–Teffs for each pixel to apolynomial function to obtain a smoothed trend, the Teffs at which ∆IR = 0 was determined as T revs .As in Sec. 4.3, the temperature distribution for each pixel was determined as shown in Fig. 9(e).At the center just after the outlet, T revs was 63.5°C, consistent with the T1/eg (66°C) estimatedby the exhaust gas sensor. A notable feature of this case is that the maximum temperature is notlocated immediately after the outlet. The maximum temperature point appears about 30 mm awayfrom the outlet. This feature was common to other engine speeds (not shown). As shown in Fig.S5 and Visualization 5, gas released from the pipe does not flow away smoothly at a constantspeed but forms mushroom-shaped vortices and exhibits halted motion around this position.As a result, the high-temperature gas at the center flows outward by the vortex and stagnatesthere, causing the maximum temperature region to appear slightly ahead of the outlet. However,intensive discussion on combustion engineering is out of the scope of this work. In addition,Fig. 9(e) shows that at 90 mm from the outlet, the gas cools to T1/eg ≈ 40°C (Tpeakg ≈ 45°C).5.3. Human breath: slow intermittent emissionAs a relatively slow intermittent case, human breath was also measured. The subject was a62-year-old male, with a body temperature of 36.0°C. The CO2 concentration in the subject’sbreath was c= 4.5% (end-tidal carbon dioxide (EtCO2): 34.5 mmHg by a capnometer), and totalexhaled air was Q= 6.1 L/min (minute volume (MV): 12.2 L/min by a spirometer). From hismouth and nostrils dimensions in the depth (Z) direction, typical column density was estimatedat ζ= 900 ppm m (35°C) for the mouth and 1125 ppm m (35°C) for the nose (both nostrils).https://doi.org/10.6084/m9.figshare.31638061https://doi.org/10.6084/m9.figshare.31638061https://doi.org/10.6084/m9.figshare.31638061Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19718Fig. 10. Temperature measurement of human breath. (a) Measurement setup. (b) Signaldifference ∆IR image at effective light source (background) temperature Teffs = 34.8°C, (c) at33.0°C, and (d) at 30.9°C, displayed with a common brightness scale (see Visualization 6).Black boxes in (c) indicate measurement ROIs for the mouth (A) and nose (B). (e) Rawintensity signal IR of the mouth versus time. Vertical gray lines indicate timing of exhalationstart and end. Invalid regions due to inflow of previously exhaled, cooled breath into ROI areshown by black curves. Red curves indicate valid regions. Numbers at representative breathsare denoted. Blue curve represents background intensity signal IR(0). (f) Relationship ofvalid ∆IR with Teffs for nose (top) and mouth (bottom). Black dots represent average ∆IR foreach breath (B1–B21) plotted at the midpoint between start and end of exhalation. Theirquadratic fittings are shown by black curves; their intersection with ∆IR = 0 indicates thecontrast reversal temperature Trevs .The setup is illustrated in Fig. 10(a). Using light source C, in an environment of Ta = 25.2°C, amovie was recorded as Teffs dropped from 38°C to 28°C (τabsb = 0.829 for 100 ppm m, texp = 40 ms,and f = 24.9 fps). To achieve uniform temperature distribution on the light source surface, wesearched for T revs while lowering Teffs . The subject placed his chin on a fixed rod to keep the headposition constant.∆IR images at three representative Teffs values are shown in Fig. 10(b)–(d) and in Visualization 6.The subject breathed through both the nose and mouth. At first (high Teffs ), the exhaled breathfrom both the mouth and nose appeared dark (Fig. 10(b)). At the end (low Teffs ), both appearedbright (Fig. 10(d)). At an intermediate state, however, there was a moment where the exhaledhttps://doi.org/10.6084/m9.figshare.31638052https://doi.org/10.6084/m9.figshare.31638052Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19719breath from the mouth appeared bright while that from the nose was dark (Fig. 10(c)). Thisindicates that the exhaled breath temperature from the mouth differs from that from the nose.As in Sec. 5.2, this is an intermittent gas, but the cycle is sufficiently slower than the framerate; therefore, emission and halted phases are clearly distinguished (Fig. S4(c)). There were21 breaths during the recording, and these were called B1, B2, . . . , B21. Measurement regionsof interest (ROIs) were set approximately 3 mm from both the mouth and nose (see boxesin Fig. 10(c)), and the average intensity IR within each ROI was evaluated. ROI sizes were1.7× 0.85 mm for the mouth and 2.7× 2.7 mm for the nose.Overall, stagnated gas originated from the previous exhalation tended to disturb the measure-ment. Each ROI was minimized to avoid such disturbances. Figure 10(e) shows the raw intensitysignal IR of the mouth from B1 to B21. The times of the start and end of each exhalation weredetermined from the change in the image around the ROI for the mouth; these are shown asvertical gray lines. The intensity value where the IR curve intersects the gray line is assumed toindicate the background intensity. A smooth polynomial fit through these points (blue curve inFig. 10(e)) is regarded as IR(0). Within the raw intensity IR, some parts were excluded as invalid(black curve) due to the overlap with the previous exhalation. The remaining part (red curve)was valid, and its difference from IR(0), ∆IR was used for temperature determination. A similarprocedure was done for the nose (not shown).Figure 10(f) shows the ∆IR–Teffs relation for exhaled breath from the mouth and nose. Theaverage ∆IR for each breath (B1–B21), from start to end of the exhalation, is plotted as blackdots. The intersection of the quadratic fit to these points with ∆IR = 0 was defined as the contrastreversal temperature T revs , which was found to be 33.7°C for the mouth and 32.8°C for the nose.The peak temperatures Tpeakg are estimated to be 36.5°C for the mouth and 35.3°C for the nose,which are both close to body temperature.Breath temperature was also measured with a 50-µm thermocouple (Fig. S6, see Supplement 1,Sec. F for details). Those temperatures were lower than those derived from CO2 imagingby ∼ 2°C: 31.9°C for the mouth and 31.0°C for the nose. These values are consistent withpast reports [45]. The discrepancy of ∼ 2°C can be attributed to the difference in measuringpoint. The thermocouple was positioned 10 mm from the mouth or nose, since it was difficult toposition fragile probes any closer to a moving human subject. In the CO2 image in Fig. 10(c),exhaled bright air from the mouth changes to dark just 10–20 mm beyond the mouth, supportingthe expectation of rapid temperature drop over a short distance. Moreover, thermocouplemeasurements may be underestimated due to heat loss. However, the finding that mouth breath is∼ 1°C warmer than nasal breath is consistent for both imaging and thermocouple measurements.Given that nose surface temperature is particularly low in the facial region [46–48], it isreasonable that breath exhaled through the nasal cavity is cooler than that through the mouth.Additionally, as seen in Supplement 1, Sec. F (Figs. S7–S8), interesting findings could bederived from our results, but further medical discussion is beyond the scope of this work. In thisstudy, it was necessary to use complex manual processing to obtain T revs from breath images; thisshould be automated in the future. Nevertheless, the capability to successfully determine breathtemperature based on contrast reversal is a significant achievement.6. Discussion6.1. Temperature measurement accuracyIn previous temperature measurement based on the OGI technique [17,30], the temperaturedistribution of the gas in the depth direction was neglected and treated as a line-of-sight averageor path-integrated temperature. In contrast, this study explicitly considered the temperaturedistribution in the depth direction and showed that the proposed method provides a temperaturehttps://doi.org/10.6084/m9.figshare.32071797https://doi.org/10.6084/m9.figshare.32071797Research Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19720T revs c lose to the 1/e-width average temperature T1/eg for a gas with temperature and concentrationdistributed according to a Gaussian function.Within this study, we could not confirm the absolute accuracy of the gas temperature obtainedby the contrast reversal method. In actual experiments, at around 100°C (Sec. 4.3), there was adiscrepancy of up to 7°C between T revs and T1/eg measured by the thermocouple. However, wecannot discuss true accuracy as long as it relies on comparison with thermocouple measurements,which are not necessarily reliable. While the contrast reversal method was applied to targets suchas engine exhaust and human breath in the application experiments, it is not clear whether theiractual temperature distributions can be approximated by a Gaussian function. Further discussionon accuracy would require direct comparison of measurements from the contrast reversal methodand advanced three-dimensional laser spectroscopy on the same targets.6.2. Required CO2 concentration for contrast reversal methodIn the hair dryer example in Sec. 5.1, application of the contrast reversal method was judgedto be difficult without the addition of CO2. The original column density was estimated to beζ= 8 ppm m (100°C). However, in Sec. 4.2, contrast reversal could be applied to a similarlylow ζ of 16.5 ppm m (25°C) by making full use of the overall image fluctuations. From theseresults, we can conclude that this method is applicable to ζ >∼ 10–15 ppm m. Based on the Ag–ζrelationship (Fig. S1(a)), for ζ= 8 ppm m (100°C) and 16.5 ppm m (25°C), Ag = 0.018 and 0.031,respectively. Therefore, when absorptivity is ∼ 3%, the contrast reversal can be applied. On theother hand, Fig. 3(c) suggests that when ζ >∼ 1000 ppm m, the discrepancy between T1/eg andT revs becomes substantial, leading to reduced accuracy of temperature measurement.The contrast reversal method can also be applied to the measurement of other gases, with anOGI camera tailored to each target gas. For a variety of gases besides CO2, this method shouldbe applicable at even lower concentrations, since the presence of atmospheric CO2 fluctuationslimited the minimum application range in the case of measuring CO2.6.3. Comparison with classical line reversal methodThe line reversal method in the 4-µm band for temperature measurement of CO2-containinggases (flames) was demonstrated nearly 100 years ago by Henning et al. They placed anintensity-variable light source behind the flame and monitored the intensity at 4.4 µm using amonochromator and a thermocouple. Here, we employed a narrowband infrared camera. Thisled to four essential innovations. First, the use of high-sensitivity cameras permitted temperaturemeasurement of gases of moderate temperatures, including those around room temperature.Traditionally, application of the line reversal method was limited to combustion gases of ∼1000 K or higher. However, due to the complexity of combustion processes, the interpretationwas not straightforward. There has been a debate over the presence of temperature error dueto the chemical reactions [1,10,13]. In contrast, the gases in this study (∼ 100°C) are simplythermodynamically hot, ensuring reliability of the determined temperature. Second, by leveragingestablished image processing techniques, rich image information could be fully exploited toenhance the accuracy of temperature determination, even from images with poor contrast. Third,2D temperature distribution measurements were achieved. Finally, use of high-speed camerasmade it possible to apply the method to dynamic targets such as internal combustion engines andhuman respiration.6.4. Significance of current studyThe ability to measure 2D temperature distributions simply by capturing images with a camerais expected to find many applications. The gas from the flat nozzle in Sec. 4.3 rapidly cooled,but in Sec. 5.1, the gas from a hair dryer was delivered efficiently over a greater distance. Thisconfirmed that the hair dryer was well-engineered to satisfy its functional requirements. ThisResearch Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19721technique is expected to play an important role in the development of such fluidic devices. Section5.2 suggests the technique’s usefulness for the development of internal combustion engines.Section 5.3 demonstrated that this approach can also provide valuable insights in the medicalfield. It not only clearly illustrated the temperature differences in exhaled breath but also clarifiedthe fast and complex dynamics of human breathing.Another important objective is the quantitative measurement of CO2 emissions. Equation (7)shows that Ag can be obtained from the intensity difference ∆IR if the gas temperature is known.Once Ag is determined, the column density and thus the total amount of gas can be estimated[16,32]. Therefore, gas temperature measurement is the first step to remotely quantifying CO2emission. Toward realizing a low-carbon society, CO2 emission measurement based on gasimaging will make significant contributions to the detection of CO2 leaks and estimation ofemission volumes.6.5. Required mid-infrared devicesA current challenge in applying this method is the time required. The temperature scanning forcontrast reversal typically takes several minutes due to the slow response of thermal radiation lightsources. Recently, LEDs in this wavelength range have become available; however, their operationis limited to pulsed mode and their intensity is insufficient. Consequently, implementation ofelectroluminescent planar light sources is highly anticipated [49]. This would enable not onlyhigh-speed scanning, but also eliminate the need for vacuum encapsulation, allowing a simplersystem for gas temperature measurement compared with the present work.In addition, OGI cameras usually require cooling to below 80 K, and thus they are expensive.However, the development of narrowband infrared detectors with higher operation temperature ismaking significant progress, based on optimally engineered quantum wells [50–52]. Therefore,the development of inexpensive OGI cameras is also anticipated.6.6. Comparison with conventional technologies and future challengesAmong various laser spectroscopy techniques for temperature measurement, tunable diode laserabsorption spectroscopy (TDLAS) is particularly well developed. Through comparison withTDLAS, we would like to clarify the future challenges of the method proposed in this study.The essential difference between TDLAS and the contrast reversal method (or OGI) derivesfrom their underlying technologies: narrow-linewidth lasers or image sensors. TDLAS is anactive technique based on near-infrared semiconductor laser technology [53]. The laser lighthas a linewidth much narrower than individual absorption lines of the gas, and its intensityis overwhelmingly higher than the thermal radiation from the background or gas. Therefore,discussion on a specific transition of a particular gas species is theoretically straightforward, andhigh-speed measurements are also possible. While the temperature determined with TDLAS wasinitially limited to line-of-sight average temperature [54,55], nowadays tomographic determinationof temperatures or gas concentrations at specific points in space has been achieved. For example,tomographic imaging of aircraft engine exhaust [56] and combustion diagnosis of temperatureand multiple gas concentrations have been demonstrated [57].On the other hand, OGI is a fundamentally passive technique based on mid-infrared imagesensor technology. The intensity observed is comparable with the thermal radiation of room-temperature objects or gases, and there are even cases where the radiation from the gas exceedsthat from the light source (background). In addition, the linewidth of interest is broad, observingthe integration of many absorption lines. In this study, we discussed nondispersive OGI, i.e., OGIthat does not use precise spectroscopic elements. Compared with dispersive OGI, this has theadvantage of being able to dynamically track the movement of specific gases. However, comparedwith state-of-the-art laser spectroscopy techniques like TDLAS, the supporting fundamentaltechnologies are still immature. As discussed in Sec. 6.5, mid-infrared devices have not advancedResearch Article Vol. 34, No. 11 / 1 Jun 2026 / Optics Express 19722as much as near-infrared devices. Nevertheless, with the recent spread of infrared cameras andthe growing attention towards greenhouse gas emissions, OGI-based technology is expected toattract greater interest in the future.For the establishment of the contrast reversal method, it is necessary to verify the temperaturemeasurement accuracy by comparison with established methods such as TDLAS, to clarify thecontrast reversal temperature for arbitrary temperature distributions, and to develop mid-infrareddevices for achieving high-speed temperature (intensity) scanning, system simplification, andbroadened range of applicable gases. Attempts at three-dimensional measurements using multipleOGI cameras have already begun for concentration measurements [58,59]. As discussed in Sec.6.4, temperature measurement based on the contrast reversal would be particularly useful as astep toward quantitative measurement of gas emission based on OGI.7. SummaryThis study demonstrated a noninvasive method for measuring the temperature of CO2-containinggases released into free space, based on the image contrast reversal produced by a temperature-variable light source and a CO2 imaging narrowband mid-infrared camera. By sweeping thetemperature of the light source placed behind the gas, the gas temperature is determined as thetemperature of the light source when the gas body’s image contrast reverses. For a gas plumewith Gaussian-distributed temperature and concentration, the contrast reversal temperature yieldsa value close to the 1/e-width average temperature. The method was applied to various CO2gases with temperatures ranging from 25°C to 100°C and concentrations (column densities)ranging from 15 to 1000 ppm m, achieving gas temperature determinations consistent with theresults by the thermocouple within a range of 0.1–7℃. The measurement of 2D temperaturedistributions and its application to dynamically emitted gases are also possible. Moreover, thismethod can be applied to gases lacking sufficient CO2 by simply adding CO2. The minimumrequired CO2 concentration was reduced by leveraging established image processing technologies.Applications to various target sources, including outdoor combustion engines and humans, werealso demonstrated. The proposed method is also expected to be effective for quantitative CO2emission measurements.Funding. National Institute for Materials Science (Sensors and Actuators Research Project); Cabinet Office (PRISM);Ichimura Foundation of New Technology; Steel Foundation for Environmental Protection Technology; Japan Societyfor the Promotion of Science (JP22K18990, JP23K26576, JP23H01883); New Energy and Industrial TechnologyDevelopment Organization (JPNP14004).Acknowledgments. The authors are thankful for insightful discussion with H. Fujita, and for technical support byK. 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