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Development of an imaging gas correlation spectrometry based mid-infrared camera for two-dimensional mapping of CO in vehicle exhausts

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Abstract

Real-time imaging of CO in vehicle exhaust was demonstrated using a gas correlation spectrometry based mid-infrared camera for the first time. The novel gas-correlation imaging technique is used to eliminate the spectral interferences from background radiation and other major combustion products, and reduce the influences of the optical jitter and temperature variations, thereby identifying and quantifying the gas. We take several spectral factors into account for the instrument design, concentration calibration and data evaluation, including atmospheric transmission, radiation interference, as well as the spectral response of infrared camera, filter and gas cell. A calibration method based on the molecular spectroscopy and radiative transfer equation is developed to identify the numerical relationship between the CO concentration × length and the measured image intensity. Two-dimensional CO distribution of vehicle exhaust with a time resolution of 50 Hz and detection limit of 20 ppm × meter is achieved when the distance between optical equipment and engine nozzle is 3 m. The gas correlation spectrometry based mid-infrared camera shows a great potential as a future technique to monitor vehicle pollution emissions quantitatively and visually.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The impact of vehicle exhaust on atmospheric pollution has aroused increasing public attention and scientific interest over the past decades. The emissions of automobiles play a central role in damaging human health and sensitive ecosystems for their great contribution to photochemical smog and acid deposition. Among the main regulated vehicle emissions, such as carbon monoxide (CO), hydro carbons (HCs), nitrogen oxides (NOx), and particulate matter, CO is of special significance and interest. The concentration of CO in the automobile emissions fluctuates a lot at different vehicle running states because CO is mostly generated through lack of oxygen in the fuel/air mixture. CO emissions emanating from mobile vehicles account for more than 80% of the total national emission of CO in major cities, such as New York (94%), Los Angeles (85%), Cook County (91%) and Dallas County (90%) [1]. Beyond-standard of CO content may threaten human health seriously for its toxicity in reducing oxygen transport efficiency by competitively binding to oxygen transporting molecules in the human body [2]. Additionally, increased CO in the earth’s atmosphere may also indirectly intensify global warming and break the chemical and radiation balance by depleting tropospheric OH radicals and perturbing the stratospheric ozone layer [3, 4].

A wide variety of spectroscopic techniques have been developed to monitor CO pollution escaped from automobiles that fail to meet the requirements for pollutant discharge. Non-dispersive infrared sensors have been widely used in the on-road remote sensing systems such as Fuel Efficiency Automobile Test and Remote Sensing Devices products, with an accuracy of about ± 1% CO in the vehicle exhaust [5]. The gas phase Fourier Transform Infrared spectrometers have been developed for quantitative analysis of CO, as well as several other components in the automotive exhaust gases simultaneously [6]. The tunable diode laser absorption spectroscopy (TDLAS) instruments show great advantages for on-road remote sensing of vehicle exhausts, for their large dynamic ranges and fast time responses [7, 8]. The recent commercial quantum cascade lasers (QCLs) operating at room temperature provide access to mid-infrared spectrum region where CO are strongly absorbing [9, 10]. Greatly enhanced sensitivity and accuracy have been achieved for real-time, in situ CO detection by using QCL absorption spectroscopy of CO fundamental transitions to probe the exhaust of a laboratory flame, which shows enormous potential for on-road remote sensing of CO in vehicle exhausts [11, 12].

However, those traditional remote sensing technologies by point- or line-moniting generally have problem of test data scattering [13]. Recent advances in optical gas imaging techniques (OGITs), such as UV [14], infrared [15] or laser assisted cameras [16], offer an efficient solution to these problems by covering a wider area. Via those new techniques, much better determinations of trace gas fluxes will be obtained instead of only measuring the total column density along a single line of sight. Additionally, OGITs enable the taking of two-dimensional images of trace gas distributions and give much better insight into chemical composition and chemical variability, as well as into chemical transformations within gas plumes [17, 18].

Imaging gas correlation spectrometry (IGCSP) technique [19], developed for the imaging of a certain gas by employing gas filter correlation techniques and infrared cameras, is a new kind of OGITs. IGCSP technique typically offers the opportunity for high spectral resolution as well as high signal to noise, by using a sample of the gas being measured as a spectral filter. Superior sensitivity is achieved with the help of gas filter to eliminate infrared radiation absorbed or emitted by interference component and exploit the spectral information of the target gas from entire spectral bands. Lund Institute of Technology described the IGCSP technique for real-time gas leakage detection and visualization [19–21]. And more recently,much effort has been invested in taking the optical gas imaging from detection and quantification to flow rate estimation [22]. The effectiveness of IGCSP technique also makes it competent on numerous platforms including aircraft, satellites, and the space shuttle for different applications, such as pollution monitoring [23, 24], trace gas detection [25] and wind observations [26].

Our motivation for this work is to develop an IGCSP based mid-infrared camera for two-dimensional mapping of CO in vehicle exhausts. Our system is capable of separating the spectral signal of the gas of interest out from the overall signal by using a sample of the gas being measured as a spectral filter. Therefore, the IGCSP based mid-infrared camera is insensitive to background radiation and spectral interference from other major combustion products. The motion variations of gas images caused by position changes of cameras or automobiles can also be avoided with simultaneous captures of the direct and the gas-filtered images. Here we report, to the best of our knowledge, the first demonstration of vehicle exhausts quantification and visualization by using IGCSP based mid-infrared camera.

2. Spectral consideration

Several spectral factors, such as atmospheric transmission, background radiation, spectral response of infrared (IR) camera, spectral line intensities of the species of interest and spectral interference from other major combustion products, should be taken into account for the optimum selection of operating wavelength for passive detection. There are three major vibrational absorption bands in the infrared part of CO molecule spectrum. Compared with the first overtone (Δυ = 2) and second overtone (Δυ = 3) at approximately 2.3μm and 1.55 μm, the fundamental band (Δυ = 1) near 4.6 μm with the strongest spectral line intensity is promising for better detection sensitivity [27]. However, other emissions in the exhaust plume, such as H2O, CO2 and particulate matter, are emitting and absorbing infrared signal simultaneously in the spectral region of CO fundamental band. In Fig. 1 we report the atmosphere transmittance through of urban air with an optical path length of 3 meters and spectral resolution of 0.001 cm−1, the background radiation including radiance emitted by surface and the reflected solar radiation, as well as the spectral behavior of CO, H2O and CO2 in vehicle exhausts at concentration × length values of 50, 16,000 and 5,000 ppm·m, respectively, for a typical exhaust temperature of 400 K. The method of calculating atmosphere transmittance and spectral radiance of vehicle exhausts is based on the molecular spectroscopy database HITRAN2016 [28].

 figure: Fig. 1

Fig. 1 Top traces: atmosphere transmittance through 3 meters of urban air. Middle traces: background radiance emitted by surface, as well as the reflected solar radiation. Bottom traces: the spectral response of the IR camera, spectral transmission curve of the filter, and spectral radiance of vehicle exhausts and blackbody, which is calculated based on HITRAN [28].

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As can be seen from Fig. 1, H2O and CO2 absorption block part of the spectrum and limit the effective range of optical measurements. The reflected solar radiation and radiance emitted by surface have a significant influence on passive detection in the wavelength region shorter and longer than 4 μm, respectively. Taken these spectral considerations into account, we choose a medium-wave infrared refrigeration camera with a normalized spectral response shown in the bottom of Fig. 1 for vehicle exhaust imaging. An infrared narrow bandpass filter is used in conjunction with this thermal camera to achieve a good signal-to-noise ratio by blocking the spectral interference of infrared radiation from H2O, CO2 and background radiation. The spectral transmission curve of the bandpass filter is also shown in the bottom of Fig. 1.

Exhaust gases and particulate matters escaped from automobile engines are of high temperature and emit electromagnetic radiation in the thermal infrared wavelengths. The spectral density of thermal infrared radiation emitted by a black body in thermal equilibrium at a given temperature T is described by Planck function

Bυ(T)=2hυ3c21(ehυκBT1)

Here h is Planck's constant, c is the speed of light, υ is electromagnetic wavenumber and kB is the Boltzmann constant.

The distribution of gases concentration and temperature in vehicle exhausts is nonuniform and varies with the engine's working conditions and air flow of the surrounding environment. Every single particle or gas molecule radiates as a function of its temperature and material properties. At the same time, part of the emitted radiation is absorbed by surrounding particles and gas molecules. The net transmitted radiation due to the balance between emission and absorption is expressed by Schwarzschild's equation [29]

Iυ(L)=I0eτυ(L)+0Ldτυ(s)dsBυ(s)eτυ(s)ds
Where Iυ(L) is the net transmitted radiation along the optical path of L, I0 is the background radiation of surface both emitted by itself and reflecting the solar radiation, and τυ(s) is the optical thickness from the sensor to layer s, defined as
τυ(s)=0Lj=1mαυj(s)Xj(s)ds
Where αυj(s) and Xj(s) are the absorption coefficient and concentration of the exhaust gases layer s, and j=PM,H2O,CO is the number of exhaust gases in the column of vehicle exhausts that absorb or emit in the spectral region of measurement system.

We now assume that the path is homogenous, concentration and temperature do not vary with position in the plume, and the plume is in thermodynamic equilibrium. Equation (2) and Eq. (3) could be reduced to the following expressions for a single homogenous layer:

Iυ=(I0Bυ)eτυ+Bυ=(BυI0)(1eτυ)+I0
τυ=j=1mαυjXjL
Here, the quantity, BυI0, is called the thermal contrast, which plays a key role in the determination of the ultimate detection limit and sensitivity of the gas correlation spectrometry based mid-infrared imager.

The gas correlation spectrometry based mid-infrared imager has a nominal passband of 2000 cm−1 to 2250 cm−1 that is defined by an infrared narrow bandpass filter, which covers both P and R branches of the CO fundamental band. The gas correlation technique used in the mid-infrared imager serves to make the sensor particularly sensitive to the gas being measured and improves its signal-to-noise ratio considerably. However, in this spectral region of CO fundamental band, there are contaminating signals that are due to the presence of bands of other major combustion products, particularly H2O. The spectral interference from background radiance also exits in this spectral region. This contamination can be reduced at utmost if the channel passband of the filter is carefully designed. The spectral radiances of H2O, CO and background, as well as the total radiance are shown in Fig. 2.

 figure: Fig. 2

Fig. 2 Spectral radiances of H2O, CO, background (BG) and the total radiance.

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The typical temperature range of the vehicle exhausts is from about 500 K to ambient temperature, spanning 200 K. The radiation intensity of vehicle exhausts varies with the distance from the exhaust nozzle. Generally, the closer from the nozzle, the higher the temperature is, and the stronger the radiation intensity is. Figure 3 shows the spectral radiance of vehicle exhausts at typical exhaust temperatures of 300, 330, 360, 390, 420 and 450 K. When exhaust temperature is 300 K, close to ambient temperature condition, the radiation intensities of vehicle exhausts and background are of the same order of magnitude, while for exhaust temperature at 450 K, the radiation intensities of vehicle exhausts is more than 30 times stronger. It is worth noting that the detection limit of the gas correlation spectrometry based passive method is strongly influenced by the temperature difference (ΔT) between the background and the exhaust gas of interest. The noise equivalent concentration length (NECL) as a function of ΔT is nonlinear. The minimum resolvable gas concentration (MRGC) model established by Li et al. [30] was used to determine a detection limit of 20 ppm·m (ΔT = 40 K) in the present set-up.

 figure: Fig. 3

Fig. 3 Spectral radiance of vehicle exhausts at typical exhaust temperatures of 330, 360, 390, 420 and 450 K with a spectral resolution of 0.001 cm−1.

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3. Instrumentation and principle

As can be seen from Fig. 4, the gas correlation spectrometry based mid-infrared imager is a remote sensing instrument with two optical channels focused on an overlapping area where vehicle exhausts pass through. The two channels, a reference and correlation, use band pass filters with the same spectral transmission curve to isolate the same spectral region of interest. Each channel also includes a 20 mm thick cell in front of their imaging optics. The cell of the correlation channel is filled with pure CO gas with a total pressure of 150 mbar as a spectral selective filter. While, the cell of the reference channel contains a gas with no features, such as N2, in the spectral range of measurement to compensate the optical attenuation caused by the cell windows of the correlation channel. The two gas cells are held at a constant temperature of 294 K. Light passing through the two cells is sent to two thermal video cameras as identical as possible to form images at their respective focal planes. Identical imaging optics make the two similar images, same in shape but different in intensity.

 figure: Fig. 4

Fig. 4 Schematic diagram of detection of vehicle exhausts using gas correlation spectrometry based mid-infrared imager.

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The cooled thermal camera used in our imaging system has a low noise-equivalent temperature difference of 20 mK (@ 300K & 3ms), and produces 320 × 256 pixels calibrated temperature images with 14-bit digitization at 50 frames/s. Its normalized spectral response is shown in the bottom of Fig. 1. The camera is portable (18.5 cm × 10.0 cm × 10.0 cm, 1.1 kg), requires 24 VDC and consumes a maximum of 30 W. The IR lens of the IR camera produces an angle of view of 11° × 8.8° with F number of 2. The filter is carefully selected to match pre-determined specifications for optimal sensing of CO gas in vehicle exhausts. The spectral transmission curve of the bandpass filter is also shown in the bottom of Fig. 1. For the windows of correlation and reference cells, several materials with transmission in the 2-8 µm wavelength region were considered. We choose CaF2 for measurements of CO gas and coat the CaF2 window surfaces to reduce the reflection loss, yielding more than 98% transmittance in the transmission spectral region of the band pass filter.

The spectral responses of the reference channel are the convolution of the transmission spectrum of the reference cell, camera optics and the filter. While, for the correlation channel, the the transmission spectrum of CO gas in the correlation cell needs to be taken into account for the spectral responses calculation. The spectral responses of the reference and correlation channels, as well as the equivalent spectral response (ESR) function of the gas correlation spectrometry based mid-infrared imager are shown in Fig. 5. The ESR function is obtained by differencing the two spectral responses and can be given by

ΔF=FrcFcc=f(υ)τ(υ)[1eα(υ)]
Where f(υ) and is the spectral transmission curve of the bandpass filter, τ(υ) is the convolution of the transmission spectrum of the cell windows and camera optics, and α(υ) is the optical depth of CO gas in the correlation cell.

 figure: Fig. 5

Fig. 5 Top traces: The spectral response of the reference channel (Frc). Middle traces: The spectral response of the correlation channel (Fcc). Bottom traces: the ESR function of the gas correlation spectrometry based mid-infrared imager (ΔF).

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As can be seen in Fig. 5, wavelengths transmitted by the the reference channel are strongly affected by the presence of target gas, while those transmitted by the the correlation channel are not. This difference is the fundamental source of sensitivity to target gas. The correlation channel attenuates the spectrum only in the absorbance bands unique to the targeted gas, the reference channel is highly sensitive to the presence of the target gas along the instrument line of sight, and the ESR function is largely independent of spectral interference from exhaust gases and background radiation.

The ratio of the correlation signal ΔS and the reference signal S can be define as the normalized correlation ΔSS and expressed by

ΔSS=SrcSgcSrc=AΩξΔFIυdvAΩξFrcIυdv=ΔFIυdvFrcIυdv
Where AΩξ is the opto-electronic conversion factor of the gas correlation spectrometry based mid-infrared imager.

For visual analysis of the influence from the temperature variation of vehicle exhausts, we carried out calculations of the normalized correlation ΔSS for different temperature and CO concentration × length values. The left image in Fig. 6 shows a 3D representation of the result. As anticipated, the value of normalized correlation ΔSS is mainly determined by CO concentration × length. In order to show its insensitivity to temperature more clearly, the normalized correlation varying with temperature at CO concentration × length of 1000 ppm·m is presented in the right image of Fig. 6. As can be seen, the impact of the temperature variation on the normalized correlation is negligible even in a relatively high exhaust temperature of 400 K.

 figure: Fig. 6

Fig. 6 Left: 3D representation of normalized correlation for different temperature and CO concentration × length values. Right: normalized correlation varies with temperature at CO concentration × length of 1000 ppm·m.

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For the gas correlation spectrometry based mid-infrared camera, the infrared images of two optical channels are captured simultaneously with the same path length, same background radiation, and same temperature and CO concentration distribution. The differential nature makes the difference images independent of variations in optical properties of the scene, such as interference radiation from other exhaust gases, emissivity and scattering of particulate matters, and absorption by atmospheric species. By using the difference method and the ratio method, the distribution of CO concentration could be obtained from correlation images, which are determined from the ratio of the experimentally determined difference images and reference images.

4. Methods and measurements

The discrimination and quantification of CO in vehicle exhausts requires high-fidelity thermal images from gas correlation spectrometry based mid-infrared camera. The mid-infrared camera consists of the following main components, gas cell, imaging optics, sensor arrays, filter and processor-based camera electronics. Both these components and the calibration process play an especially crucial role in ensuring the quality of an IR camera.

Due to the limitations of existing technology, the individual pixels of the sensor arrays have uniquely different spectral responses and sensitivities, and thus differing characteristics. For correction of this non-uniformity, two black body sources are located very close to the front-end optics alternately to convert all pixels onto the standard characteristic curve by using two-point correction method. The temperature values of the two black body sources are is kept at 300 K and 350 K respectively by a temperature controller. The temperature of each blackbody is stable to ~0.5 K. The vehicle exhaust of a gasoline engine was selected to experiment object. It is worth to note that the filter needs to be placed behind the lens, while the black body sources should be placed in front of the gas cell. This design concept ensures that radiation from the gas cell and imaging optics is properly accounted for during the process of calibration.

The reference and correlation channels are focused on an overlapping area where vehicle exhausts pass through. Two signal images are captured simultaneously with the same integration time of 2 ms by the reference and correlation channels of the gas correlation spectrometry based mid-infrared imager respectively when vehicle exhausts appear in the field of view. Two background images are also recorded against the road background without vehicle exhausts. We subtract the two background images from their corresponding signal images to remove the interference factors from imaging optics and gas cell self-emission. We also reduce the salt and pepper noise with image smoothing and median filtering. The reference and CO gas-filtered images with background image subtracted and noise reduced are shown in the top and middle of Fig. 7, respectively. The correlation image is obtained by divide the reference image with the CO gas-filtered image, which is shown in the bottom of Fig. 7.

 figure: Fig. 7

Fig. 7 The reference, CO gas-filter and correlation images. Top: the direct image. Middle: the CO gas-filter image. Bottom: the correlation image.

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5. CO quantifying and imaging

As can be seen from Eq. (4) and Eq. (7), the normalized correlation ΔSS is obviously a function of the CO concentration × length, LXCO. It is important to note that the dependency of ΔSS on LXCO is generally non-linear. Only for a single layer of target gas at a uniform temperature and small optical depth, the normalized correlation ΔSS can be written as:

ΔSS=LMα¯COXCO
Where α¯CO is the spectrally averaged absorption coefficient of CO over the transmission bandpass of the interfetence filter.

In this exceptional case, the normalized correlation ΔSS is proportional to LXCO. Therefore, this instrument is in principle calibration free, for the relationship of the measured value of ΔSS and LXCO which is defined by Eq. (8). However, Eq. (8) does not take the effects of noise and interfetence into account, which may greatly affect the accuracy of the gas correlation method for the determination of CO concentration. In all other cases, LXCO cannot be easily obtained from Eq. (7) because the spectral radiance of vehicle exhausts, as well as the background radiance are not well known.

There are three possibilities to derive the CO concentration from CO images. The standard addition methods are to accurately measure the net transmitted radiation Iυ(L), or conducte an empirical instrument calibration to determine the relationship between ΔSS and LXCO. However, accurate measurement of net transmitted radiation is very difficult, especially for the spectral radiance of vehicle exhausts, which are constantly changing. This calibration methodology is also not used because the calibration curve is non-linear and the spatial variations of the external gas may destroy the calibration. Gas concentration calibration method developed by Lund Institute of Technology [20] is adopted by this work for practical considerations.

The relationship between ΔSS and LXCO, as well as the temperature is simulated numerically based on the molecular spectroscopy and radiative transfer equation, as shown in Fig. 6. The normalized correlation ΔSS is mainly determined by CO concentration × length, and insensitive to temperature, as well as the background radiation and spectral interference from other major combustion products. Therefore, the CO concentration × length of vehicle exhausts could be obtained by using this numerical relationship from the measured ΔSS. Figure 8 shows the spatial two-dimensional concentration × length of CO in vehicle exhausts. Its concentration levels are set by threshold values obtained from numerical simulations in Fig. 6.

 figure: Fig. 8

Fig. 8 Two-dimensional concentration × length of CO in vehicle exhausts (Visualization 1).

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6. Discussion and conclusions

It has been demonstrated that the gas correlation spectrometry based mid-infrared camera was preliminarily achieved for visualization and quantification of vehicle exhausts, as we believe, for the first time. This instrument is capable of providing 320 × 256 pixel images and gives two-dimensional CO distributions at time resolutions as high as 50 Hz. A detection limit of 20 ppm × meter for CO composition was accomplished in this setup when the optical equipment was placed at a distance of 3 m from the engine nozzle.

The gas correlation spectrometry based mid-infrared camera is a novel device for the remote sensing of vehicle exhausts using infrared radiation of pollution gases in the vehicle exhausts as a light source for the measurements. Strong spectral interference from water vapour and other combustion products in the 4.6 μm wavelength region is eliminated cleverly by using the difference between the CO gas cell and the clear one as a spectral filter. Simultaneous capture of the direct and the gas-filtered images achieves video image stabilization. The influence from the temperature variation of vehicle exhausts is also reduced effectively though normalized correlation of the difference and direct image. Therefore, the IGCSP based mid-infrared camera is insensitive to spectral interferences, optical jitter and temperature variations and is capable of retrieving the CO concentration × length with high accuracy after instrument calibration. The main advantage of the passive gas correlation imaging method over the active methods is the ability of providing two-dimensional CO distributions.

A theoretical basis for the pertinent aspects of working with the IGCSP based mid-infrared camera systems is given in detail, including the spectroscopic theory, measurement principle, instrument design, concentration calibration and data evaluation. A calibration method based on the molecular spectroscopy and radiative transfer equation is developed to identify the numerical relationship between the CO concentration × length and the measured image intensity. Several issues are identified that influence instrument performance. For one, decreasing in temperature of vehicle exhausts lead to a poor signal to noise ratio, and therefore reduce the measuring accuracy. Secondly, unclear or unknown of the spectral radiance of vehicle exhausts, or the background radiance makes it a difficult problem to determine the precise relationship between the normalized correlation ΔSS and the CO concentration × length, LXCO. Thirdly, small distance between imaging lens and vehicle exhausts lead results in a difference in shooting angle between the direct and the gas-filtered images, which may influence CO imaging and quantifying.

Several areas for improvement in the present design can be identified. Firstly, there is an obvious need to improve the automation for routine observations. Secondly, cooled infrared filters is required to eliminate the radiation noise of infrared optical system to achieve higher sensitivity. Thirdly, several gases in vehicle exhausts such as CO2, HCs and NOx could also be monitored though this instrument by swapping the filter and CO cell for the gas of interest. Finally, the system described here is operated on the ground, but it is quite feasible to be used on an airborne platform to meet the surveillance requirements for a broader area.

Funding

National Key Research and Development Plan of China (2017YFC0211900); National Natural Science Foundation of China (NSFC) (61705253); Open Research Fund of Key Laboratory of Spectral Imaging Technology, Chinese Academy of Sciences (LSIT201701D).

Acknowledgments

Prof. Chiao-Yao She of Colorado State University is acknowledged for his suggestion and encouragement.

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Supplementary Material (1)

NameDescription
Visualization 1       Movie of two-dimensional concentration × length of CO in vehicle exhausts for Visualization 1.

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Figures (8)

Fig. 1
Fig. 1 Top traces: atmosphere transmittance through 3 meters of urban air. Middle traces: background radiance emitted by surface, as well as the reflected solar radiation. Bottom traces: the spectral response of the IR camera, spectral transmission curve of the filter, and spectral radiance of vehicle exhausts and blackbody, which is calculated based on HITRAN [28].
Fig. 2
Fig. 2 Spectral radiances of H2O, CO, background (BG) and the total radiance.
Fig. 3
Fig. 3 Spectral radiance of vehicle exhausts at typical exhaust temperatures of 330, 360, 390, 420 and 450 K with a spectral resolution of 0.001 cm−1.
Fig. 4
Fig. 4 Schematic diagram of detection of vehicle exhausts using gas correlation spectrometry based mid-infrared imager.
Fig. 5
Fig. 5 Top traces: The spectral response of the reference channel (Frc). Middle traces: The spectral response of the correlation channel (Fcc). Bottom traces: the ESR function of the gas correlation spectrometry based mid-infrared imager (ΔF).
Fig. 6
Fig. 6 Left: 3D representation of normalized correlation for different temperature and CO concentration × length values. Right: normalized correlation varies with temperature at CO concentration × length of 1000 ppm·m.
Fig. 7
Fig. 7 The reference, CO gas-filter and correlation images. Top: the direct image. Middle: the CO gas-filter image. Bottom: the correlation image.
Fig. 8
Fig. 8 Two-dimensional concentration × length of CO in vehicle exhausts (Visualization 1).

Equations (8)

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B υ ( T ) = 2 h υ 3 c 2 1 ( e h υ κ B T 1 )
I υ ( L ) = I 0 e τ υ ( L ) + 0 L d τ υ ( s ) d s B υ ( s ) e τ υ ( s ) d s
τ υ ( s ) = 0 L j = 1 m α υ j ( s ) X j ( s ) d s
I υ = ( I 0 B υ ) e τ υ + B υ = ( B υ I 0 ) ( 1 e τ υ ) + I 0
τ υ = j = 1 m α υ j X j L
Δ F = F r c F c c = f ( υ ) τ ( υ ) [ 1 e α ( υ ) ]
Δ S S = S r c S g c S r c = A Ω ξ Δ F I υ d v A Ω ξ F r c I υ d v = Δ F I υ d v F r c I υ d v
Δ S S = L M α ¯ CO X CO
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