# Fileset

[7880239.pdf](https://mdr.nims.go.jp/filesets/0146a878-7c82-4e72-a53e-a660b9599fc7/download)

## Creator

[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)

## Rights

© 2026 Optica Publishing Group. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[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)

## Fulltext

Supplemental DocumentGas temperature measurement based on contrastreversal in mid-infrared CO2 images: supplementHIDEKI 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.jpThis supplement published with Optica Publishing Group on 19 May 2026 by The Authors underthe terms of the Creative Commons Attribution 4.0 License in the format provided by the authorsand unedited. Further distribution of this work must maintain attribution to the author(s) and thepublished article’s title, journal citation, and DOI.Supplement DOI: https://doi.org/10.6084/m9.figshare.32071797Parent Article DOI: https://doi.org/10.1364/OE.596786https://orcid.org/0000-0003-4152-1171https://orcid.org/0000-0002-1976-8760https://orcid.org/0000-0003-2933-0014http://creativecommons.org/licenses/by/4.0/https://doi.org/10.6084/m9.figshare.32071797https://doi.org/10.1364/OE.5967861Gas temperature measurement based on contrast reversal in mid-infrared CO2 images: supplemental documentHIDEKI 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.jpA. Supplementary discussion on the basics of radiative transferA.1 Calculation of CO₂ absorption spectrum based on HITRANThe absorption cross section 𝑘ν derived from HITRAN [1] forms the basis of all CO₂ absorption values in this study. By considering all CO₂ isotopologues and assuming the Voigt lineshape, 𝑘ν was calculated at various gas temperatures under a pressure of 101,325 Pa. Figure 2(a) in the main text shows 𝑘ν for a gas temperature 𝑇g = 50°C, which is used in Fig. 2(c), (d), Fig. 3(a), and (d) (main text). For the calculations in Fig. 3(b) and (c) (main text), 𝑘ν spectra at various temperatures were used.A.2 Quantification of responsivity spectrum of CO2 imaging cameraThe responsivity spectrum 𝑅ν (Fig. 2(b), main text) of the CO₂ imaging camera used in this study was measured using the step-scan function of a Fourier transform infrared spectrometer (FTIR). An optical system was mounted at the specimen stage for extracting a collimated light beam from the FTIR, and the infrared light modulated by the interferometer was irradiated across the entire image sensor. The temporal waveform (interferogram) of the average brightness was Fourier-transformed, and the quantitative responsivity spectrum was determined by comparison with the results of a calibrated detector, with a resolution of 2 cm⁻¹, placed at the same position.A.3 Details of discussion in Sec. 2.3In this section, we prepare a framework of the radiative transfer equation based on Eq. (5) in the main text, which is applicable to general cases including nonuniform gases as well as uniform ones. To achieve this, it is first necessary to return to the monochromatic radiative transfer equation at frequency (wavenumber) ν (Eq. (3), main text). In Eq. (3), the gas temperature 𝑇g can be a function of position 𝑧. As shown in Eq. (2) of the main text, the optical thickness κν is determined by 𝑘ν, the total volume number density of the gas 𝑛, and the concentration (the mole fraction) of the gas 𝑐. The concentration 𝑐 can also be a function of 𝑧, and both 𝑘ν and 𝑛 depend on 𝑇g. Therefore, κν can be influenced by the spatial distribution of 𝑇g as well as that of 𝑐.By defining an effective temperature 𝑇effνg  for each frequency ν, the blackbody radiation term 𝑖νbb can be separated from the integral over κ∗ν in Eq. (3):𝑖𝜈(κν) = 𝑖νbb(𝑇s)exp( ― κν) + ∫κν0 𝑖νbb 𝑇g exp[ ― (κν ― κ∗ν)]dκ∗ν mailto:*MIYAZAKI.Hideki@nims.go.jp2= 𝑖νbb(𝑇s)exp( ― κν) + 𝑖νbb 𝑇effνg ∫κν0 exp[ ― (κν ― κ∗ν)]dκ∗ν = 𝑖νbb(𝑇s)exp( ― κν) + 𝑖νbb 𝑇effνg [1 ― exp( ― κν)], (S1)where 𝑇s is the light source (background) temperature, and𝑖νbb 𝑇effνg = ∫κν0 𝑖νbb 𝑇g exp[ (κν κ∗ν)]dκ∗ν∫κν0 exp[ (κν κ∗ν)]dκ∗ν. (S2)There are two remarks regarding Eqs. (S1) and (S2). First, for a gas with uniform temperature and concentration, 𝑇effνg  = 𝑇g, and Eq. (S1) reduces to Eq. (4) in the main text. Second, 𝑇effνg  as given in Eq. (S2) corresponds to the contrast reversal temperature 𝑇revs  at frequency ν. This is because, the intensity difference Δ𝑖ν due to the presence of gas,Δ𝑖ν = 𝑖ν(κν) ―𝑖ν(0) = 𝑖νbb 𝑇effνg ― 𝑖νbb(𝑇s) [1 ― exp( ― κν)] = 𝐴νg 𝑖νbb 𝑇effνg ― 𝑖νbb(𝑇s) ,where 𝐴νg is the absorptivity, becomes zero when 𝑇s = 𝑇effνg ; this is the definition of the contrast reversal temperature 𝑇revs . Detailed results are discussed in the next Sec. B and Fig. S2 for both uniform and nonuniform cases.Using the relation in Eq. (S1), Eq. (5) in the main text defining the intensity signal 𝐼R(𝑢) (𝑢: column number density) can be written in a more concise form:𝐼R(𝑢) = ∫∞0 𝑅ν𝑖ν(κν)dν = ∫∞0 𝑅ν𝑖νbb(𝑇s)exp( ― κν) dν +∫∞0 𝑅ν𝑖νbb 𝑇effνg [1 ― exp( ― κν)]dν. (S3)For the convenience of practical applications, consider a scheme to approximate a nonuniform gas with spatial distribution of temperature and concentration, as a uniform gas with an effective temperature 𝑇effg  and the same column number density 𝑢. Equation (S3) can be expressed in terms of two components: blackbody radiation and gas absorption. The blackbody radiation function and the responsivity spectrum (except for its sharp edges) vary slowly with respect to ν, so they can be separated from the gas absorption terms. Then, separated terms are described by experimentally measurable quantities for a uniform gas with an effective temperature 𝑇effg :𝐼R(𝑢) = ∫∞0 𝑅ν𝑖νbb(𝑇s)exp( ― κν) dν + ∫∞0 𝑅ν𝑖νbb 𝑇effνg [1 ― exp( ― κν)]dν ≈ 𝑅ν0𝑖ν0bb(𝑇s)Δν × ∫ν2ν1exp( ― κν) dν∆ν+ 𝑅ν0𝑖ν0bb 𝑇effν0g 𝛥𝜈 × ∫ν2ν1[1 ― exp( ― κν)] dν∆ν ≈ ∫∞0 𝑅ν𝑖νbb(𝑇s)dν × ∫∞0 𝑅ν exp κν 𝑇effg ,𝑢 dν∫∞0 𝑅νdν+ ∫∞0 𝑅ν𝑖νbb 𝑇effg dν ×∫∞0 𝑅ν 1 exp κν 𝑇effg ,𝑢 dν∫∞0 𝑅νdν = 1 ― 𝐴g 𝑇effg ,𝑢 𝐼Rbb(𝑇s) + 𝐴g 𝑇effg ,𝑢 𝐼Rbb 𝑇effg ,where ν0 is the center frequency in the bandwidth Δν (Δν =  ν2 ― ν1),𝐼Rbb(𝑇) = ∫∞0 𝑅ν𝑖νbb(𝑇)dν,and𝐴g(𝑇,𝑢) =∫∞0 𝑅ν 1 exp( κν(𝑇,𝑢)) dν∫∞0 𝑅νdν. (S4)3Thus, the approximate expression of Eq. (6) in the main text is obtained. This approximation was justified by confirming the following relation numerically:∫∞0 𝑅ν𝑖𝜈bb(𝑇)[1 ― exp( ― κν)]dν ≈ ∫∞0 𝑅ν𝑖νbb(𝑇)dν ×∫∞0 𝑅ν 1 exp( κν) dν∫∞0 𝑅νdν,and an agreement within 7% accuracy was confirmed.Here, 𝐼Rbb(𝑇) can be determined by calibration experiments, measuring a uniform blackbody at various temperatures 𝑇 by the detector with responsivity 𝑅ν. 𝐴g(𝑇,𝑢) is the absorptivity of a uniform CO2 gas with a temperature 𝑇 and column number density 𝑢. While 𝐴g can also be obtained experimentally, this study uses the 𝐴g values based on HITRAN. We confirmed the consistency between HITRAN and our experimental results. N₂-diluted CO₂ gases with various column densities of ζ = 0–1.04×10⁵ ppm m (25°C) were encapsulated in a gas cell with CaF₂ windows and a length of 𝐿 = 104 mm, and absorptivity 𝐴g at 𝑇g = 25°C was determined. The results are shown as open circles in Fig. S1(a). Figure S1(a) also shows 𝐴g values for representative temperatures derived from HITRAN. The experimental results and those by HITRAN at 𝑇g = 25°C show reasonable agreement. Using HITRAN, it is possible to obtain 𝐴g values at any gas temperature. Figure S1(a) shows that the 𝐴g–𝑢 relationship has a small temperature dependence.Here, the signal difference due to the presence of the gas is∆𝐼R = 𝐼R(𝑢) ― 𝐼R(0) ≈ 𝐴g 𝑇effg ,𝑢 𝐼Rbb 𝑇effg ― 𝐼Rbb(𝑇s) ,which is a generalized expression of Eq. (7) in the main text. When 𝑇s = 𝑇effg  , ∆𝐼R = 0. Thus, we can experimentally determine the effective gas temperature 𝑇effg  as the contrast reversal temperature 𝑇revs . For a gas with uniform temperature and concentration, 𝑇revs = 𝑇effg = 𝑇g simply holds. For a nonuniform gas, as discussed in Sec. 2.4 and Fig. 3 in the main text, these temperatures are close to the 1/𝑒-width average temperature 𝑇1/eg  (Fig. S1(d)): 𝑇revs = 𝑇effg ≈𝑇1/eg .4 Fig. S1. (a) Relationship between absorptivity 𝐴g and column number density 𝑢 at several gas temperature 𝑇g values. Experimentally determined 𝐴g (open circles) at 𝑇g = 25°C and values calculated using Eq. (S4) based on HITRAN at representative 𝑇g values are shown. Upper axis shows corresponding column density ζ for gas at 𝑇g = 25°C as a reference. (b) Relationship between absorption and transmission bands within the sensitivity band of the camera. Lower panel shows responsivity spectrum 𝑅ν with bandwidth Δν of CO2 imaging camera used in study, retrieved from Fig. 2(b), main text. Upper panel shows radiation intensity spectrum 𝑖ν and blackbody radiation intensities 𝑖νbb at 𝑇g = 50°C, light source temperature 𝑇s = 75°C, and 𝜁 (50°C) = 104 ppm m, retrieved from Fig. 2(c), main text. The sensitivity bandwidth Δν can be clearly divided into absorption (width: 𝑟absΔν) and transmission bands (width: (1 ― 𝑟abs)Δν). (c) Concentration profile of gas assumed in Fig. 3, main text. Gaussian distributions to achieve specific values of column density ζ given in legend are considered, assuming a uniform temperature of 25°C. (d) Temperature profile of gas assumed in Fig. 3, main text. A Gaussian distribution is considered with peak temperature 𝑇peakg  = 50°C, converging to ambient temperature 𝑇a = 25°C at a sufficiently large distance. In (c) and (d), thickness 𝑧𝑛𝑜𝑟𝑚 is normalized by the distance at which Gaussian function decays to 1/𝑒 of the peak value. In (d), the region within the 1/𝑒 width is colored red. 𝑇1/eg  is the average value in this region, and it is indicated by the horizontal red dashed line.B. Radiative transfer at a single frequency in nonuniform gasFigure S2 systematically shows radiative transfer at a single frequency ν for a gas with Gaussian distributions of temperature (Fig. S2(b)) and concentration (Fig. S2(a)). A frequency corresponding to the wavelength of 4.26 μm (center of the CO2 absorption band) is assumed. The relationships between the intensity difference Δ𝑖ν due to the presence of the gas and the light source temperature 𝑇s are very similar to those for the finite bandwidth results in Fig. 3(a) 10-1100101102103104105106107Concentrationc-4 -2 0 2 4Normalized position znorm 100 ppm m 101 ppm m 102 ppm m 103 ppm m 104 ppm m 105 ppm m 106 ppm mζ (25°C)cpeak0.70.60.50.40.30.20.10AbsorptivityAg1016 1017 1018 1019 1020Column number density u (molecules cm-2)100 101 102 103 104 105Column density ζ (ppm m, 25°C)TgExperiment 25°CHITRAN 25°C 50°C 100°C43210ResponsivityRν(104  counts ms-1 nW-1)2500240023002200Wavenumber ν (cm-1)1612840Intensityi ν(10-3 W m-2 sr-1 cm)ν1 ν2iνiνbb(Ts)iνbb(Tg) rabsΔνΔν(1−rabs)Δν(a) (b)50403020TemperatureT g (°C)-4 -2 0 2 4Normalized position znormTgpeakTg1/eTa(c) (d)5and (b) in the main text for both the uniform (Fig. S2(c)) and nonuniform distributions (Fig. S2(d)). The relationship between gas concentration (optical thickness κν) and contrast reversal temperature 𝑇revs  (= 𝑇effνg ) for various peak gas temperature 𝑇peakg  values is shown in Fig. S2(e). While absorption is low (i.e., concentration is low), 𝑇revs  remains constant and is close to the 1/𝑒-width average temperature 𝑇1/eg  shown by the dashed lines at any temperature. The deviation of 𝑇revs  from 𝑇1/eg  begins around κν ~ 2, i.e., where absorptivity 𝐴νg starts to saturate (Fig. S2(f)). Consequently, the behavior in a finite bandwidth discussed in the main text (Fig. 3) is essentially identical to the monochromatic case. The fact that 𝑇revs  is close to 𝑇1/eg  suggests the universal importance of the 1/𝑒-width average value in systems with a temperature distribution.  Fig. S2. (a) Gas concentration profiles with Gaussian distributions having various optical thicknesses κν (legend in (c)). (b) Gas temperature profiles with Gaussian distributions having various peak temperatures 𝑇peakg  at ambient temperature 𝑇a = 25°C. (c) Contrast reversal at a certain frequency ν for uniform gases with gas temperature 𝑇g = 50°C and various κν, during sweeping of light source (background) temperature 𝑇s. (d) Contrast reversal at a certain ν for nonuniform gases with Gaussian distributions of temperature (𝑇peakg  = 50°C) and concentrations (κν in (c)), in 𝑇s sweeping. (e) Relationship between contrast reversal temperature 𝑇revs  and concentration (κν) at a certain ν for gases with various 𝑇peakg  (legend in (b)) with Gaussian distributions. Dashed lines show 1/𝑒-width average temperature 𝑇1/eg . (f) Relationship between absorptivity 𝐴νg and κν for gases with various 𝑇peakg  in (e).C. Correction considering the influence of background layerC.1 Influence of optical properties of light sourceA correction that considers the influence of the background layer is discussed here based on Fig. S3. The space is divided into three layers: the background layer between the light source -0.4-0.20.00.20.4Intensity differenceΔiν(10-3 W m-2 sr-1 cm)7060504030Background temperature Ts (°C) 0.01 0.1 1 10 100κνTg = 50°CTg-0.4-0.20.00.20.4Intensity differenceΔiν(10-3 W m-2 sr-1 cm)7060504030Background temperature Ts (°C)Tgpeak = 50°CTg1/e3002001000TemperatureT g (°C)-4 -2 0 2 4Normalized position znormTgpeak 300 200 100 50 25 0Ta10-310-210-1100101102Absorption coefficienta ν-4 -2 0 2 4Normalized position znorm300250200150100500Temperature (°C)0.01 0.1 1 10 100Optical thickness κν1.00.80.60.40.20AbsorptivityAνgTsrevTg1/e(a) (c)(b) (d)(e)(f)6surface and the gas layer, the gas layer itself, and the foreground layer between the gas layer and the camera [2–5]. The intensity signal at the end of each region, giving consideration to the responsivity spectrum of the camera, is defined as 𝐼0, 𝐼1, 𝐼2, and 𝐼3 at the emission surface of the light source, the end of the background layer, the end of the gas layer, and the entrance of the camera lens, respectively. Moreover, the light source may have an internal structure. For example, the light source B and C used in this study had an anti-reflection-coated Si window for vacuum encapsulation. The light source temperature 𝑇s discussed so far should be regarded as the equivalent temperature at the emission surface. The true emissivity and temperature of the internal radiating surface of the light source are εs and 𝑇orgs , and the window transmissivity is τs. The emission signal from the surface of a light source without a window (like the light source A in this study) is 𝐼0 = εs𝐼Rbb 𝑇orgs . For a light source with a window, 𝐼0 = τsεs𝐼Rbb𝑇orgs + (1 ― τs)εenv𝐼Rbb(𝑇a). The second term shows the component where the environmental radiation is reflected by the window surface and directed toward the camera. εenv and 𝑇a are the emissivity (assumed to be ~1) and temperature of the surrounding environment. So far, such a value of 𝐼0 has been regarded as 𝐼Rbb(𝑇𝑠).Fig. S3. Schematic diagram of three-layer model for considering atmospheric CO2 absorption/emission and optical system characteristics. Transmissivity, emissivity, and temperature of each part are shown.C.2 Influence of atmospheric CO2 in background spaceConsider the transmissivities τb and τf for the background and foreground layers, respectively, and suppose that their temperatures are equal to the ambient temperature 𝑇a. The transmissivity of the gas τg is also used (𝐴g = 1 ― τg). The intensity signals at the end of each region are given as𝐼1 = τb𝐼Rbb(𝑇s) + (1 ― τb)𝐼Rbb(𝑇a),𝐼2 = τg[τb𝐼Rbb(𝑇s) + (1 ― τb)𝐼Rbb(𝑇a)] + 1 ― 𝜏𝑔 𝐼Rbb 𝑇1/eg ,and𝐼3 = τf τg[τb𝐼Rbb(𝑇s) + (1 ― τb)𝐼Rbb(𝑇a)] + 1 ― τg 𝐼Rbb 𝑇1/eg + (1 ― τf)𝐼Rbb(𝑇a).In the absence of gas,𝐼no gas3 = τf[τb𝐼Rbb(𝑇s) + (1 ― τb)𝐼Rbb(𝑇a)] + (1 ― τf)𝐼Rbb(𝑇a).The signal difference due to the presence of the gas is∆𝐼3 = τf𝐴g 𝐼Rbb 𝑇1/eg ― τb𝐼Rbb(𝑇s) ― (1 ― τb)𝐼Rbb(𝑇a) . (S5)The property of the foreground τf has no effect on the contrast reversal temperature at ∆𝐼3 = 0.τf, Taτg, Tg1/eτb, Taτs, εs, TsorgForegroundlayerGaslayerBackgroundlayerLight sourceI3I1I1I0, TsEnvironment εenv, TaCamera7C.3 Influence of transmission/absorption regions within imaging bandwidthFor the CO₂ camera used in this study, another factor must be considered. As shown in Fig. 2(a) and (b) in the main text, there is a designed mismatch between the responsivity band of the camera and the absorption band of the CO₂ gas. Therefore, even if the column density of the gas is sufficiently high and the gas becomes totally opaque, a certain amount of light still enters the camera through the transmission band. As a result, gas absorptivity 𝐴g does not reach 1. Since the signal due to the transmission band does not change regardless of the presence or absence of the gas, it is canceled when obtaining the difference between 𝐼3 and 𝐼no gas3  and does not contribute to ∆𝐼3. Therefore, intensity signal 𝐼3 must be further divided into absorption and transmission band components, denoted with superscripts abs and tra, respectively. The absorption and transmission bandwidths within the total camera bandwidth Δν are written as 𝑟absΔν and (1 ― 𝑟abs)Δν, respectively (Fig. S1(b)). At 𝑇g=25°C, based on 𝐴g for ζ = 10⁶ ppm m in Fig. S1(a), 𝑟abs is taken as 0.636. Within 𝐼3, the intensity signal of the absorption and transmission bands are 𝑟abs𝐼3 and (1 ― 𝑟abs)𝐼3, respectively. Here, it is assumed that the blackbody radiation intensity spectrum has a flat ν dependence (Fig. S1(b), upper). For the absorptivity 𝐴 and transmissivity 𝜏 (𝐴 =  1 ― 𝜏) for the total bandwidth Δν, the absorptivity 𝐴abs and transmissivity τabs within the absorption band are expressed as 𝐴abs = 𝐴/𝑟abs and τabs = 1 ― 𝐴/𝑟abs, respectively.𝐼3 can be separated into each band as follows:  𝐼abs3 = τabsfτabsg τabsb 𝑟abs𝐼Rbb(𝑇s) + 1 ― τabsb 𝑟abs𝐼Rbb(𝑇a) + 1 ― τabsg 𝑟abs𝐼Rbb 𝑇1/eg +1 ― τabsf 𝑟abs𝐼Rbb(𝑇a),𝐼tra3 = (1 ― 𝑟abs)𝐼Rbb(𝑇s).In the absence of gas,𝐼abs,no gas3 = τabsf τabsb 𝑟abs𝐼Rbb(𝑇s) + 1 ― τabsb 𝑟abs𝐼Rbb(𝑇a) + 1 ― τabsf 𝑟abs𝐼Rbb(𝑇a),𝐼tra,no gas3 = (1 ― 𝑟abs)𝐼Rbb(𝑇s) = 𝐼tra3 .Therefore, the signal difference due to the presence of the gas is∆𝐼3 = 𝐼abs3 + 𝐼tra3 ― 𝐼abs,no gas3 + 𝐼tra,no gas3= τabsf 𝐴absg 𝑟abs 𝐼Rbb 𝑇1/eg ― τabsb 𝐼Rbb(𝑇s) ― 1 ― τabsb 𝐼Rbb(𝑇a)= τabsf 𝐴g 𝐼Rbb 𝑇1/eg ― τabsb 𝐼Rbb(𝑇s) ― 1 ― τabsb 𝐼Rbb(𝑇a) . (S6)In comparing this Eq. (S6) with Eq. (S5), even after correction for the transmission and absorption bands, 𝐴g remains the same (absorptivity defined for total bandwidth Δν). However, τf and τb must be replaced by τabsf  and τabsb . By defining𝐼Rbb 𝑇effs = τabsb 𝐼Rbb(𝑇s) + 1 ― τabsb 𝐼Rbb(𝑇a),as in Eq. (8) in the main text, Eq. (7) is modified as∆𝐼3 = τabsf 𝐴g 𝐼Rbb 𝑇1/eg ― 𝐼Rbb 𝑇effs .When ∆𝐼3 = 0, we can determine the 1/𝑒-width average temperature of the gas as 𝑇1/eg = 𝑇effs . In summary, if the effective transmission source temperature 𝑇effs  is considered according to Eq. (8) in the main text to account for the effect of background CO₂, the conclusion stands that the contrast reversal temperature 𝑇revs  can be regarded as the gas temperature 𝑇1/eg .8In this study, the 𝐼Rbb(𝑇) needed for Eq. (8) was measured at various temperatures for the system, including the camera lens. Therefore, 𝐼R in the main text is equivalent to 𝐼3 in this section, which can thus be read as 𝐼R.The transmissivity of the background layer in the absorption band τabsb  can be determined from absorptivity 𝐴b, corresponding to column density ζ in the background layer (Fig. S1(a)) and then by applying τabsb = 1 ― 𝐴b/𝑟abs.The contrast reversal method is essentially a null method: The measurement error is determined by the accuracy of the light source temperature. However, only in the case of CO₂ measurement, background correction in Eq. (8) (main text) becomes necessary due to the substantial amount of CO₂ contained in the atmosphere. Therefore, temperature accuracy could be affected by the estimation of τabsb  discussed here. The correction by Eq. (8) in this work ranged from 0.1°C (at 𝑇1/eg  ~ 25°C) to 8°C (at 𝑇1/eg  ~ 100°C). Temperature error due to improper estimation of τabsb  would be only a fraction of these values (a few °C at most).D. Experimental methodsD.1 Details of CO2 imaging cameraThe FLIR A6796 is an InSb camera equipped with a bandpass filter having the transmission profile shown in Fig. 2(b), main text. Although both the image sensor and filter require cooling to 80 K, the camera can be operated by battery power. The image resolution is 640×512 pixels, and the maximum frame rate is 480 fps. A variety of FLIR lenses (F2.5) can be mounted, and various data analyses are possible. The intensity resolution is 14-bit, and signals exceeding 105 counts can be obtained without saturation. On the other hand, signal differences as small as ≲  10 counts can be distinguished. Therefore, the dynamic range of intensity is 103 or higher. The signal can be adjusted to fit this range by selecting the exposure time 𝑡exp. The noise equivalent differential temperature (NEDT), an important metric for infrared cameras, was measured at 28 mK at 25°C. This value is inferior to that of the original InSb camera (18 mK), but it is reasonable considering the reduction in signal due to the bandwidth limitation.Although a CO2 imaging camera, the GF343 from FLIR [6,7], is commercially available, it has limitations in pixel count, available settings, and lens choices. Therefore, we asked FLIR to provide a custom-made A6796 that combines a scientific-grade InSb camera with a built-in cooled filter for CO2 [8].D.2 Instruments used in this workTwo types of thermocouples, with 13-μm and 50-μm diameters, were used (Anbe SMT, KFT-13-200-100 and KFT-50-200-100, respectively). Thermocouple temperatures were recorded with a data logger (Hioki, LR8431). The following CO2 sensors were used depending on the target: Hodaka, HT-1300Z type D and Kane, KANE455 for concentration and temperature of hot and high-density CO2, Vaisala, GMP252/MI70 for environmental CO2 concentration, and a capnometer, Medtronic, Capnostream35 for CO2 concentration in human breath. We also used a spirometer, Chest, HI-801 for emission rate of human breath and a radiation thermometer, Tanita, BT-54X for body temperature. The blackbody radiation surface temperature was calibrated with a calibrated temperature sensor (Lake Shore, DT-670-CU-HT-1.4H). The emissivity (absorptivity) of the blackbody paint and the transmissivity of the silicon window were measured using FTIR (JASCO, FT/IR-6200) equipped with a microscope unit, IRT-5000.E. Temperature measurement of intermittently emitted gas9The intensity in the CO2 image of intermittently ejected gas is discussed in accordance with Sec. 2.3 in the main text. For simplicity, it is assumed that gas with constant CO₂ concentration and temperature is emitted as rectangular pulses. As shown in the bottom and middle panels of Fig. S4(a), the absorptivity changes between 0 and its maximum value, and the temperature changes between room temperature 𝑇a and its maximum. Under these conditions, according to Eqs. (6) and (7) in the main text, the signal difference Δ𝐼R varies in a rectangular manner between 0 and a certain peak value, as shown in the top panel. When the gas is not being emitted, the concentration and thus the absorptivity are 0, so Δ𝐼R becomes 0. The height of nonzero Δ𝐼R, as shown in Eq. (7) (main text), is given by the difference between the blackbody radiation functions of the gas temperature 𝑇g and the light source temperature 𝑇s. As shown in Fig. 9(d), main text, when 𝑇s (𝑇effs ) is varied, the height of the rectangular signal changes and the sign of Δ𝐼R reverses at a certain 𝑇effs . This 𝑇effs  is equal to the gas temperature 𝑇g. Therefore, by selectively observing the nonzero Δ𝐼R, the same discussion as the contrast reversal method for continuous gas emissions applies.Next, the exhaust gas of the internal combustion engine in Sec. 5.2, main text, is considered. Each cylinder of a diesel engine completes one cycle in two rotations (720 degrees). Assuming that the exhaust valve is open during the final 180 degrees of the second rotation, the timing of gas emission during one cycle of a three-cylinder engine is shown in Fig. S4(b). The image exposure cycle at 30 fps is also shown. The exhaust frequency (22.5 Hz) for 900 rpm rotation and this frame rate have similar values. The exposure time is sufficiently shorter than the exhaust cycle, so each frame captures either the emission or halt phase. It is probabilistically determined whether an emission or halt scene is captured; in the case of Fig. S4(b), about 75% of frames (33.3 ms/44.4 ms) are expected to capture the emission phase and 25% (11.1 ms/44.4 ms) the halt phase.  Individual frames are displayed in Fig. S5. Of the 30 frames captured in one second, 7 did not capture any gas (23%). Two were transitional. The discussion given in Fig. S4(b) closely corresponds to the actual situation.Figure S4(c) is a schematic representation of exhalation, which produces slow intermittent emissions. In each emission and halt period, a number of images are recorded; consequently, a clear selection of only those images during exhaust is possible.10 Fig. S4. Fundamental discussion on temperature measurement of intermittently emitted gas. (a) Changes in gas absorptivity 𝐴g (corresponding to concentration) and temperature 𝑇g are presented in bottom and middle panels, respectively. Absorptivity is assumed to change between 0 and its maximum value, and temperature between ambient temperature 𝑇a and its maximum value, both in a rectangular shape. Light source (background) temperature 𝑇s is shown as a blue line in middle panel. Corresponding signal difference ∆𝐼R is shown in top panel. (b) Time chart showing engine gas emission and image acquisition. Cylinders C1, C2, and C3 emit gas sequentially at equal intervals. Images are acquired at a similar frequency. (c) Time chart for exhaled breath emission and image acquisition. Breathing is slow relative to image acquisition.0.30.20.10AbsorptivityAg2000150010005000Time t (arb. unit)100500Temperature (°C)1050-5Signal ΔI (arb. unit)Tg(t)TsTa150100500Time (ms)7203600Image exposureGas emissionCrank angle (deg.)C1 C2C2 C3C11086420Time (s)Gas emissionImage exposure(a) (b)(c)11Fig. S5. Consecutive images (frames 1–30) of diesel engine exhaust at effective light source temperature 𝑇effs  = 31.8°C as discussed in Sec. 5.2, main text. Gas is nearly absent in seven frames 1, 7, 14, 16, 18, 27, and 29. Thin residual gas is seen in two frames 12 and 25. Mushroom-shaped emission patterns in frames 2, 4, 15, 17, 28, and 30 suggest origin of temperature peak at 30 mm from exhaust outlet.F. Detailed discussion related to human exhalationThe temperatures of exhaled breath measured at a position 10 mm from the mouth or nose using a 50-μm thermocouple are shown in Fig. S6. The measurement results for mouth exhalation (Fig. S6(a)) were stably obtained. In contrast, the temperature of the nasal exhalation (Fig. S6(b)) fluctuated greatly. We considered the average of the top 20% data points (shown in red, measured from the valleys defining individual peaks) as the exhalation temperature. The average was 31.9°C for the mouth and 31.0°C for the nose. The result that exhalation from the mouth was 0.9°C higher than that from the nose was consistent for both imaging and measurement by thermocouple.Careful observation of the signal difference Δ𝐼R of exhalation from the mouth and nose revealed a number of interesting findings, as shown in Figs. S7 and S8. Breathing starts between frames 1 and 10, and frames 10–44 show monotonic exhalation. Exhaled breath from both the 1 2 3 4 56 7 8 9 1011 12 13 14 1516 17 18 19 2021 22 23 24 2526 27 28 29 3012mouth and nose appear bright in Fig. S8. However, at frame 45, nasal emission stops once (A, Fig. S7), although the mouth continues exhalation. In the next moment (frame 46), nasal emission resumes and exhibits a large, bright exhaust from the nose at frame 47 (B, Fig. S8). Then, at frame 49, both nasal and oral emissions stop (C), as indicated by the vertical line in Fig. S7. Nevertheless, exhalation from both the nose and mouth resumes at frame 50, reaching another peak in frame 53 (D, Fig. S7). After this, exhalation weakens and emission ends. Previously exhaled breath remains in the nasal area as a dark cloud (Fig. S8). This corresponds to the invalid region of the nose shown in gray in the upper panel of Fig. S7.Sudden stops and resumptions of breath occurred within a single frame, i.e., within only 40 ms. Such quick changes within a single frame were frequently observed. Although medical discussion is beyond the scope of this paper, it is important to note that these observed phenomena, which can only be captured by this method, merit further study.Fig. S6. Results of measuring breath temperature by thermocouple: (a) mouth and (b) nose, both at a distance of 10 mm.Fig. S7. Temporal variation in mouth and nose signal difference ∆𝐼R for breath B21. Representative frame numbers corresponding to Fig. S8 are denoted. For the nose after 77.6 s, values are invalid due to overlapping with previously emitted, cooled breath (gray). Other clear features, A, B, C, and D, represent meaningful findings.32302826Temperature (°C)1612840Time (s)Mouth32302826Temperature (°C)20151050Time (s)Nose(a) (b)1000-100Signal difference ΔI R (counts)787776Time (s)1000-100ABCDFrame 1 6049MouthNose13Fig. S8. Representative images during breath B21 at effective light source temperature 𝑇effs  = 30.9°C. Correspondence between important features in Fig. S7 and frame numbers are as follows: A: frame 45, B: 47, C: 49, and D: 53.References1. I. E. Gordon, L. S. Rothman, R. J. Hargreaves, et al., “The HITRAN2020 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 277, 107949 (2022).2. M. L. Polak, J. L. Hall, and K. C. Herr, “Passive Fourier-transform infrared spectroscopy of chemical plumes: an algorithm for quantitative interpretation and real-time background removal,” Appl. Opt. 34(24), 5406–5412 (1995).3. A. Ben-David and C. E. Davidson, “Probability theory for 3-layer remote sensing radiative transfer model: univariate case,” Opt. Express 20(9), 10004–10033 (2012).4. M. A. Rodríguez-Conejo and J. Meléndez, “Hyperspectral quantitative imaging of gas sources in the mid-infrared,” Appl. Opt. 54(2), 141–149 (2015).5. N. Hagen, “Survey of autonomous gas leak detection and quantification with snapshot infrared spectral imaging,” J. Opt. 22(10), 103001 (2020).6. B. Murphy, R. Cahill, C. McCaul, et al., “Optical gas imaging of carbon dioxide at tracheal extubation: a novel technique for visualising exhaled breath,” Br. J. Anaesth. 126(2), e77–e78 (2021).7. Y. Peng and M. Yao, “Quantitatively visualizing airborne disease transmission risks of different exhalation activities through CO2 imaging,” Environ. Sci. Technol. 57(17), 6865–6875 (2023).8. M. Morioka, Y. Takamura, H. T. Miyazaki, et al., “Relationship between surgical field contamination by patient's exhaled air and the state of the drapes during eye surgery,” Sci. Rep. 13, 5713 (2023).1 10 20 30 4041 42 43 44 4546 47 48 49 5051 52 53 54 5556 57 58 59 60