Hyperspectral quantitative imaging of gas sources in the mid-infrared M. A. Rodríguez-Conejo and Juan Meléndez* LIR—Infrared Laboratory, Departamento de Física, Universidad Carlos III de Madrid, Leganés (Madrid), Spain *Corresponding author: [email protected] Received 5 June 2014; revised 6 October 2014; accepted 17 November 2014; posted 19 November 2014 (Doc. ID 213489); published 5 January 2015
An imaging Fourier transform spectrometer operating in the medium infrared (1800–5000 cm−1 ) has been used to image two gas sources: a controlled CO2 leak at room temperature and the exhaust of a combustion engine. Spectra have been acquired at a resolution of 0.5 cm−1 using an extended blackbody as the background. By fitting them with theoretical spectra generated with parameters from the High-Resolution Transmission Molecular Absorption database, quantitative maps of temperature and gas column density (concentration·path product) for the gas plumes have been obtained. Spectra are related to gas plume parameters by means of a radiometric model that takes into account not only gas absorption, but also its emission and the atmospheric absorption, as well as the instrument lineshape function. Measurements for the gas leak show very good agreement between retrieved and nominal values of temperature and CO2 column density. This result has direct application to obtain quantitative imaging of exhaust emissions from automobiles and other mobile sources, as shown here with measurements of exhaust gases in a diesel engine. © 2015 Optical Society of America OCIS codes: (110.3080) Infrared imaging; (110.4234) Multispectral and hyperspectral imaging; (010.1120) Air pollution monitoring; (120.0280) Remote sensing and sensors; (300.6300) Spectroscopy, Fourier transforms; (120.1740) Combustion diagnostics. http://dx.doi.org/10.1364/AO.54.000141
1. Introduction
The recent development of commercially available imaging Fourier transform spectrometers (IFTS) has opened a new range of possibilities in the field of remote sensing of pollutants. While the use of Fourier transform spectrometry to measure gas effluents from smokestacks and other industrial sources already has a long history [1–3], the spatial resolution provided by imaging instruments adds a new dimension to this technique, making it much more powerful [4]. Not only column densities of pollutants and plume temperature can be mapped, but also, since the small instantaneous field of view (IFOV) of each pixel minimizes spatial averaging of inhomogeneous regions, simpler models can be used for data analysis and quantification is much more accurate. 1559-128X/15/020141-09$15.00/0 © 2015 Optical Society of America
The study of the time evolution of images even makes it possible to track the gas flow and estimate effluent mass flow rates [5]. Previous IFTS studies of pollutant sources have focused on emission from smokestacks of power plant facilities. Although some mobile sources like ships [6] or aircraft engines [7] have been measured, remote measurement of automobile exhaust emissions has been limited to nonimaging methods, that, furthermore, provide only ratios of pollutants rather than absolute values [8]. In this work, we explore the ability of IFTS to provide quantitative images of temperature and gas column density of this kind of gas sources. This problem poses some specific difficulties since the amount of gases involved is much smaller and the temperatures are typically lower, whereas measurement distances will be usually shorter. In order to obtain the temperature and column density values from experimental spectra, an accurate modelization must be made from both the scene 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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and the instrument. Therefore, a radiometric model has been developed, which is described in detail in Section 2. This model dictates the relationship between the ideal radiance spectra at the sensor’s location and the temperature and composition of the gas plume. These ideal spectra have been obtained with a line-by-line method using the High-Resolution Transmission Molecular Absorption (HITRAN) spectroscopic database [9]. In order to compare them with the measured spectra, however, instrumental effects must be taken into account. They are summarized in an instrument lineshape function that is convolved with the ideal spectra. The widened spectra are compared then with the measured spectra for each pixel, by a fitting algorithm that explores temperature (T) and column density (Q) values until it finds the optimal agreement, thus providing the measured (T, Q) couple. Computation of the simulated spectra, instrumental widening, and the fitting procedure are explained in Section 3. The method developed in Sections 2 and 3 is applied to experimental measurements in Section 4. A Telops Hypercam IFTS instrument [10] operating in the medium infrared has been used in two measurement campaigns; first in the laboratory with a controlled CO2 leak and then measuring emissions from the diesel engine of an automobile. Finally, conclusions and guidelines for future work are drawn in Section 5. 2. Radiative Model
In a typical experimental setup for IFTS gas measurement (Fig. 1), the instrument images a gas plume against a background and provides a measurement of the spectral radiance incoming to each pixel. In order to relate this radiance with the plume parameters, a radiative model of the measurement configuration is needed. We will make the following simplifying assumptions: 1. For each pixel, the exhaust plume is modeled by a single temperature and a single value of concentration for each gas; i.e., the plume is assumed to be homogeneous in the IFOV and these values are considered as line-of-sight averages. With this approximation we can ignore internal absorption of radiation emitted by the plume, and characterize it by a single transmittance τpl and emittance εpl 1 − τpl at each pixel.
Fig. 1. Schematics of the radiative model. 142
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2. The emission of the atmosphere is negligible. This approximation is justified as long as the atmospheric temperature is much lower than those of the plume and/or the background. 3. The background emissivity εb is large, so that the reflection of ambient radiation in the background is negligible. 4. The plume is in local thermal equilibrium (so that Boltzmann distribution holds), and the effects of absorption and scattering by particulate matter are negligible. These assumptions, usually made for smokestacks effluents [4], are even more justified for combustion engine emissions, usually cleaner (with less particles) and at lower temperatures. With these approximations, the incoming radiance at the radiometer is Lin LBB T b · εb · τa1 τpl τa2 LBB T pl · 1 − τpl τa2 ; (1) where τpl , τa1 , and τa2 are, respectively, the transmittances of the plume and the first and second atmospheric paths (atm1 and atm2 in Fig. 1), LBB stands for Planck’s blackbody radiance, and T b , T pl are, respectively, the temperatures of the background and the plume. For each wavenumber, transmittance depends on temperature, optical path, and concentrations of each chemical species. It will be assumed also that Lambert–Beer’s law holds, i.e., that for a single chemical absorbing species, with an optical path L, τ is given by τν; C; T e−kν;TL e−αν;TCL ;
(2)
where the absorption coefficient k has been written in terms of the absorptivity α and the concentration C, k αC, and the dependence of k and α on wavenumber and temperature has been shown explicitly. Absorptivities are generally well known and can be extracted from spectroscopic databases like HITRAN [9]. If there is more than one absorbing species, τν is just a product of terms like Eq. (2), one for each species. Our aim is to obtain values of plume concentration Cpl and temperature T pl from experimental measurements of Lin ν. In fact, since only the product Cpl L appears in the equations, our result will be the column density Qpl ≡ Cpl L rather than the concentration Cpl , and we will measure the amount of gas, as usual in spectroscopic remote sensing methods, in units of ppm · m (parts per million per meter). The final products of our measurement method will be a “column density image” and a “temperature image” with values of, respectively, Qpl ≡ Cpl L and T pl at each point in the field of view. To solve Eq. (1) for the plume column density and temperature is not possible because both parameters are coupled in the Lambert–Beer expression of transmittance [Eq. (2)], where the absorptivity α depends on T pl in a nontrivial way. Instead, they will be
determined by a fitting process: we will calculate theoretical spectra and assign to each pixel the concentration and temperature values which provide the best fit to the experimental spectra. This process can be somewhat simplified for the extreme cases of very hot or very cold backgrounds. A.
Solving the Model: Absorption Mode
When the background is much hotter than the plume, the second term in Eq. (1), accounting for the plume emission, can be neglected. This is the so-called absorption (or active) mode. Equation (1) becomes BB a1 pl a2 Lin on;abs ≈ L T b · εb · τ τ τ :
(3)
The subindex on, abs has been added to indicate that the plume is “on” and measurement is in absorption mode. The plume transmittance is then (showing explicitly the dependencies on wavenumber, temperature, and column densities) τpl ν; Qpl ; T pl ≈
Lin on;abs ν LBB ν; T b · εb · τa ν; Qa ; T a
;
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where τa stands for the total atmospheric transmittance, and τa τa1 · τa2 (it will be assumed that temperature is the same for the atmospheric paths 1 and 2). If the background temperature and atmospheric transmittance are known [so that the denominator in Eq. (4) is known], values of plume column density Qpl and temperature T pl can be determined by fitting the theoretical τ [Eq. (2)] to this experimental value. All the terms in Eq. (4) can be measured experimentally if it is possible to turn off the plume, in order to have a reference spectrum BB Lin ν; T b · εb · τa ν; Qa ; T a off ;abs ν ≈ L
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where τpl0 stands for the transmittance of the region of atmosphere that was occupied by the plume when it was “on”. Since it will be assumed that τpl0 ≈ 1 (thin plume), the plume transmittance is simply τpl ν; Qpl ; T pl ≈ B.
Lin on;abs ν : in Loff ;abs ν
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Solving the Model: Emission Mode
If, on the other hand, the background is much cooler than the plume, its contribution to the measured radiance will be negligible. This is the emission (or passive) mode. In this case, Eq. (1) becomes BB Lin T pl · 1 − τpl · τa on;emi ν ≈ L
(7)
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: (8)
This is formally similar to Eq. (4), but there is a crucial difference. While the denominator in Eq. (4) can be measured with a reference spectrum, or, in any case, can be estimated if the background temperature and atmospheric data are known, the denominator in Eq. (8) contains the plume temperature, which is precisely what has to be determined. So, transmittance cannot be measured experimentally, and it is the measured radiance which must be fitted by the calculated right-hand side of Eq. (7). This means that the radiometer must be accurately calibrated in radiance, and values of Qa2 and T a2 must be known. The only simplification, as compared to the general case, is that the parameters of the background (T b ) and the atmospheric path between the background and the plume (Qa1 , T a1 ) do not appear in the equations. C.
Approach of This Work
In our case, the temperature of the exhaust gases was expected to be relatively low, about 140°C. In the spectral region of the CO2 emission/absorption band, at 4.2 μm, even for a very thick flame with ε 1 the emitted radiance at 140°C is more that 15 times smaller than the radiation of a 350°C background. This fact, together with the complications just described for the emission mode, suggested to focus on measurements in the absorption mode. Two radiance spectra are measured against the hot background: Lmeas on;abs ν with the plume “on” and Lmeas off ;abs ν with the plume “off.” According to Eq. (6), an experimental plume transmittance spectrum, τpl exp , has been defined as τpl exp ν ≡
Lmeas on;abs ν : meas Loff ;abs ν
(9)
This spectrum must be fitted by theoretical transmittance spectra τpl th ν; Qpl ; T pl , calculated with Eq. (2), to obtain Qpl and T pl as the parameters which provide the best fit. 3. Theoretical Spectra and Fitting Procedure A. Ideal, High-Resolution Transmittance Spectra
In order to generate theoretical spectra, the starting point is to know the fundamental spectroscopic parameters of the molecules. There exist several databases with this information. We have used HITRAN [9], which catalogs the line center positions and intensities of a great variety of gas molecules in the IR region. A very convenient web implementation, HITRAN on the Web [11], computes, by summing up the standard lineshapes of single absorption lines (“line-by-line method”), the spectra of absorption coefficient (k αC, [cm−1 ]), and transmittance (τ). However, in order to fit the experimental spectra, many iterations have to be performed, and therefore theoretical spectra must be generated in a fast way, without having to recourse to the web application each time the concentration or temperature is varied. The main difficulty lies in the temperature 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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Absorptivivity as a function of temperature for different wavenumbers 20
B.
Instrumental Widening
The spectra constructed thus far are high-resolution, ideal spectra, with absorption features of intrinsic width. In order to be compared to the measured spectra, they need to be previously processed to take into account instrumental effects. Specifically, they must be convolved with the instrumental lineshape function (ILS) to account for finite instrument resolution. In our case, a triangular apodization was used, and therefore the ILS is a squared sinc function [12]. However, when calculating the theoretical transmittance spectrum τpl th ν, it is not correct to simply convolve the ideal spectrum with the ILS. The reason is that τpl th ν is going to be compared to the experimental transmittance spectrum τpl exp ν, and this is not measured directly, but rather as a ratio [Eq. (9)] of two radiance spectra measured by our inmeas strument, Lmeas on;abs and Loff ;abs . While in Eq. (6) the atmospheric transmittance and blackbody radiance terms cancel out for ideal spectra, this is no longer true for the experimental spectra, because they are affected by the instrumental resolution. Therefore, the correct spectrum τpl th ν must be calculated as a ratio of widened radiances R τpl th ν
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αT; ν p3 ν · T 3p p2 ν · T 2p p1 ν · T p p0 ν: (10) The dependence of absorptivities on temperature for each gas has been thus parametrized in the region from 2000 to 2400 cm−1 , with a spectral resolution of 0.01 cm−1. Althoug this step is not enough to reproduce accurately the shape of some individual lines, that can be as narrow as 0.05 cm−1 for CO2, the effect is very small on the widened spectra used for fitting. An example of the dependence of the absorptivity on temperature for CO2 at some specific wavenumbers is shown in Fig. 2. With this parametrization it is easy to construct transmittance spectra for arbitrary values of T and CL, using Eq. (2).
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dependence of the absorptivity. The strategy that we have followed consists in approximating that temperature dependence with a known function. In order to do that, many simulations of k, at different temperatures and at the highest resolution available, have been calculated for each gas of interest with HITRAN on the Web. Pressure was fixed at 1 atm and gas abundance at 100%, so that, since k αC, the k thus calculated is numerically equal to α if concentrations are measured in % at atmospheric pressure. These values of α have been fitted by third-order polynomial functions. In this way, all the information needed to generate spectra is reduced to four parameters per wavenumber
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R τpl th ν
LBB ν0 ; T b · εb · τa ν0 · τpl ν0 · ILSν − ν0 dν0 R BB 0 ; L ν ; T b · εb · τa ν0 · ILSν − ν0 dν0 (11)
where τpl ν and τa ν stand for the ideal transmittance spectra of the plume and the atmosphere, respectively, as provided by HITRAN. They are functions (not explicitly displayed) of the temperatures (T pl , T a ) and column densities (Qpl , Qa ). Since the blackbody has a relatively flat spectral profile, and the same can be expected for εb, they can be simplified out with very good approximation R τpl th ν
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In contrast, the effect of the atmospheric term τa ν0 cannot be simplified. Therefore, through instrumental widening, values of T a and Qa affect somewhat the measured spectra. The effect is small for the usual values of concentrations and distances, although not generally negligible (in particular when measuring CO2 concentrations in the plume, since CO2 is a component of the unpolluted atmosphere). C.
Effects of Plume Emission
If the emission of the plume is not negligible, the approximations used in the absorption mode will be no longer valid, and the full radiometric model must be considered. Equation (12) should be changed to
LBB ν0 ; T b · εb · τa ν0 · τpl ν0 LBB ν0 ; T pl · 1 − τpl ν0 · τa ν0 · ILSν − ν0 dν0 R BB 0 : L ν ; T b · εb · τa ν0 · ILSν − ν0 dν0
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Temperature (K)
(13)
The emitted plume radiance becomes relevant when two conditions hold: gas plume temperatures are comparable to those of the background and transmittance in the spectral band used for fitting is small (i.e., emissivity is high). Thus, the importance of emission can be minimized by a proper selection of the spectral region. In any case, taking into account the emission factor simply makes calculations longer, but has no significant effects on the convergence of the fitting algorithm. D.
Experimental Spectra and Fitting Procedure
For clarity of exposition, we describe here the procedure assuming that there is a single gas with absorption lines in the measured spectral region. The generalization to several gases is straightforward: simply, there is an additional unknown value of column density to be determined for each additional gas. As already explained, our aim is to find for each pixel the couple of values (Qpl , T pl ) for which the theoretical spectrum τpl th ν; Qpl ; T pl provides the best fit to the experimental spectrum τpl exp ν; i.e., one that minimizes the sum of squared errors (SSE) between pl τpl th and τ exp . Experimental spectra have been acquired with a Telops Hypercam IFTS system. In this instrument, the incoming radiance is modulated by a Michelson interferometer, and then is detected by an InSb 320 × 256 focal plane array (IFOV 0.35 mrad), sensitive in the medium infrared (1800 to 5000 cm−1 ). An interferogram is acquired at each pixel, which, after processing, provides spectra with a maximum resolution of 0.25 cm−1, although in this work all spectra have been measured at 0.5 cm−1 in order to reduce acquisition time. Technical details on the instrument can be found in the literature [10,13]. In order to compare two spectra, both must have the same number of points and they must correspond to the same wavenumbers. For the 0.5 cm−1 nominal resolution of experimental spectra, separation between consecutive wavenumbers is 0.417 cm−1. However, this resolution is poor for theoretical spectra, and therefore the interferograms have been padded with zeros to a length seven times larger, so that the step in the wavenumber axis of τpl exp ν was reduced to 0.0595 cm−1 . The wavenumber axis of the experimental spectra must be corrected also because in the Michelson interferometer the angular deviation from the optical axis affects by a multiplicative factor the wavenumber values [14]. The correction factor for each pixel can be estimated using as a wavenumber reference a well-defined absorption line at a known spectral position; in our case, the 1918 cm−1 water line was employed. This means that the experimental spectra take values at slightly different wavenumbers for different pixels. In order to have a common wavenumber axis for the whole image, interpolated spectra with values at the wavenumbers of the optical axis have been used in the fitting process.
At each pixel, the fitting procedure is as follows. We start by assuming a value for the couples Qpl ; T pl and Qa ; T a . The ideal transmittance spectra τpl , τa are calculated with Eqs. (10) and (2) at the points of the wavenumber axis of the experimental spectra. Then the theoretical spectrum τpl th is calculated with Eq. (12) [or with Eq. (13) if plume emission is not negligible]. The differences with τpl exp for each wavenumber are summed up in quadrature to get the SSE. The Nelder–Mead minimization algorithm, as implemented in MATLAB software, is used then to find the value of Qpl ; T pl for the next iteration, until convergence is reached [recalculation of Qa ; T a is usually not necessary, but is also possible]. The process is repeated for each pixel to obtain the images of column density and temperature. E. Spectral Region for Fitting and Error Estimation
The full spectra provided by the Telops Hypercam range approximately from 1800 to 5000 cm−1 . With a spectral step of 0.0595 cm−1, as described in the previous section, this means ≈ 53; 800 points for each pixel. Even using a subwindow instead of the whole image, the fitting process requires a lot of computing resources, in particular because of the convolutions of the ideal spectra with the ILS performed at each iteration. In addition, for each gas there may be regions with very strong or very weak absorption features, that are scarcely sensitive to gas concentrations. Therefore, it is advisable to select an optimal spectral subregion for the fitting process. For the particular case of CO2, the region with strongest absorption lines in the medium IR ranges from 2280 to 2400 cm−1 . However, this strong absorption means that for long optical paths, the response can be saturated even with the atmospheric CO2 . This can be appreciated in Fig. 3, which is the spectrum of a blackbody at T 350°C seen through 2.75 m of nominally clean atmosphere (no plume), at a 0.5 cm−1 resolution. Even for a relatively short path, the region of the strong absorption peak at ∼2350 cm−1 has low signal and should be avoided,
Fig. 3. Typical reference spectrum (no gas plume), measured for a 350°C blackbody with 0.5 cm−1 resolution, at a distance of 2.75 m. The inset shows the region of the CO2 medium infrared absorption band. 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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4. Experimental Results
In order to test the results of the measurement method in a controlled laboratory environment, a series of validation experiments was performed . A.
Laboratory Setup and Measurements
B. Analysis of Results
The column density results of the iterative fitting procedure, performed in the 2240 to 2280 cm−1 spectral region, are shown in Fig. 5, for the first horizontal line of pixels above the exhaust pipe. Results have been obtained assuming a 400 ppm concentration [15] for ambient CO2 and the measured T a 25°C. Two column density profiles are shown: circles have been obtained using the absorption approach, whereas for squares the full radiometric model, including plume emission effects, has been employed. Both profiles are compared with the optical path for each pixel (plotted with a different vertical axis), estimated from the tube diameter through a simple geometrical calculation. Since a CO2 concentration of 100% is being used, it is easy to compare magnitudes: the column density should be Q 15700 ppm · m at the tube center (where the path is 15.7 mm) and should follow elsewhere the optical path profile.
Column density (ppm·m)
A hollow copper pipe, with an internal diameter of 15.7 mm, was disposed vertically, as is shown in Fig. 4, and connected to a calibrated gas bottle with a 100% CO2 concentration. A radiant heater, with a high emissivity surface of 29.5 × 29.5 cm at T 600°C (not shown in Fig. 4), was placed close to the bottom of the tube in order to heat the copper
pipeline and, consequently, the gas flow. This heating procedure has been preferred to a combustion device (as a blow torch or similar) since CO2 and H2 O produced in combustion could interfere with the experiment. An extended area (6 × 6 in.) blackbody, with nominal emissivity ε 0.94 and temperature T 350°C, was placed as a background behind the pipe outlet. A thermocouple was also positioned at the mouth of the tube. The Telops Hypercam was placed at a distance of 3.10 m and collected four interferograms for both reference (in the absence of flow) and CO2 gas flow. The spectral resolution was 0.5 cm−1 and the spatial subwindowing 120 × 100 pixels. Each set of four acquired interferograms was preprocessed by calculating its median, and then Fourier-transformed to meas obtain the Lmeas on;abs ν and Loff ;abs ν spectra necessary to calculate the experimental transmittance spectrum.
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since transmittances obtained with Eq. (9) will be very noisy. On the contrary, it has been found that transmittances in the interval from 2240 to 2280 cm−1 (corresponding to the fundamental transition of 16 O13 C16 O) show a good sensitivity to the concentration variations of CO2 in the whole range studied. At the same time, the relative weakness of absorption lines in that region implies that results are less sensitive to atmospheric CO2 concentration and temperature. For these reasons, this region has been selected to apply the fitting procedure. An estimation of the uncertainties in T pl and Qpl associated with the fitting method has been made by performing radiometric simulations of τpl ν, calculated with Eq. (13). A range of noise levels was added to the ideal radiance spectra, from the value measured in a reference spectrum (∼1 mW∕m2 sr in the 2280 to 2400 cm−1 region) to a value ten times higher. For each noise step, τ was calculated for 100 random values of temperature and column density. The mean relative error of the retrieved values ranged from 1.6% to 1.8% for T pl (measured in K), and from 0.2% to 0.5% for Qpl. Therefore, for the noise levels expected in our measurements, expected errors are small and the method is quite robust.
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Fig. 4. Experimental setup employed in the validation measurements, as viewed from the IFTS. CO2 comes out of the copper pipe placed vertically at the center, and is observed against the background of the extended blackbody. A horizontal thermocouple is seen at the right-hand side, with its tip at the mouth of the tube. 146
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Fig. 5. Two retrieved column density profiles at the pipe outlet, both compared with the optical path estimated for each pixel. One of the profiles (squares) is retrieved by employing the full radiometric model, taking into account the emission term. The second profile (circles) is based on the absorption approach, neglecting self-emission effects.
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The figure shows clearly that the emission term has a small but appreciable contribution, and if it is taken into account, retrieved column densities agree very well with their nominal values in a wide region around the center of the tube, with errors smaller than 1%. Discrepancies appear at tube edges, where the optical path abruptly falls down to zero, while the retrieved concentration suffers a smooth variation. This effect can be explained by the nonideal modulation transfer function of the optical system, since defocusing, lens aberrations, and other effects attenuate high spatial frequencies. The results of the measurement method are shown in Fig. 6, where both column density [Fig. 6(a)] and temperature [Fig. 6(c)] images are displayed. In order to speed up calculations, a preclassification has been made, excluding pixels with very high transmittance (therefore, with negligible CO2 concentration) from the fiting process. In Figures 6(b) and 6(d) there have been also plotted, respectively, several column density and temperature profiles, taken at the same rows, marked in the respective images (the line named as “Row 86” corresponds to the profiles in Fig. 5). Results for density column agree with the expected gas dilution, as peak values
fall down as the plume moves away from the tube outlet. It is difficult to estimate properly the accuracy of the retrieved temperature values, since thermocouple measurements in gas flows are affected by important uncertainties and, in any case, provide only a point measurement. Despite this fact, the horizontal temperature profiles at different heights shown in Fig. 6(d) are very plausible, since they depict a thermal structure that agrees with the heating procedure employed, where the walls of the pipeline are responsible for heating the gas flow, and the absolute values also agree with those given by the thermocouple, of about T 100°C. The quality of the fit can be appreciated also by looking directly to the spectra. Figure 7 shows experimental and theoretical transmittance for a pixel above the tube center, in the middle of the gas plume. It is clear that there is a very good agreement between both data sets, especially in the fitted region, from 2240 to 2280 cm−1 . The relative error between empirical and theoretical fitted transmittance, depl pl fined as jτpl th − τexp j∕τexp , is also represented; the graph shows how it becomes larger for those wavenumbers outside the fitted bandwidth. 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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C.
Engine Measurements
After the proposed method was checked through the validation tests just described, it was applied to measurements of the exhaust duct of an automobile diesel engine. Four interferograms were averaged for each measurement, with a total acquisition time of nearly five minutes. Given the turbulent nature of the plume it would have been advisable to average more interferograms, but stabilization of the engine was imperfect and appreciable drifts appeared for longer times. Figures 8 and 9 show the obtained maps of CO2 column density and temperature. Fitting was performed, as previously, in the 2240 to 2280 cm−1 region. Errors in this case are bound to be larger than in the controlled CO2 leak since spectra are noisier noise due to turbulence. However, although we have no independent measurements of Q and T to estimate errors, we can be reasonably sure that these errors are small, since simulation of noisy spectra has shown that the fitting algorithm is quite
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robust: a tenfold increase in the noise of radiance spectra (measured in the fitting region) only increased the average error from 1.6% to 1.8% for T (measured in K) and from 0.2% to 0.5% for Q. Since variability of the exhaust plume during the acquisition time is larger than this, we conclude that errors should not be significant for our measurement conditions. In addition to carbon dioxide, several gases are expected in the exhaust emission of an internal combustion engine. Water, carbon monoxide, and hydrocarbons could be observed in the medium infrared, and even (if present in large concentrations) nitrogen oxides or sulfur dioxide. However, although pixels in the exhaust plume were analyzed in the full spectral range, only CO2 and H2 O were identified during this measurement campaign. In fact, this is to be expected in our case, since typical concentration values in the exhaust of a state-of-the-art diesel engine are quite small, with mean values for CO, total hydrocarbons, NOx , and SO2 below the detection limits estimated from the experimental spectra [16]. Nevertheless, the proposed methodology is suitable for all the mentioned species if present in high enough concentrations (as in gross pollutant vehicles), and its application might be even simpler than in the CO2 case, since they are absent in a typical atmosphere. 5. Conclusions and Future Work
A method to remotely quantify pollutant effluents, using an imaging Fourier transform spectrometer (IFTS) to provide “maps” of column density and temperature of the gas plumes, has been developed, tested in the laboratory for a controlled CO2 leak, and applied to the exhaust emissions of a diesel engine. Using as single input the raw data provided by the Telops Hypercam IFTS (interferograms at each pixel), the full FTIR spectral processing has been worked out. Radiative propagation, from the IR source to the sensor, has been modeled including
instrument effects, and a routine to create synthetic spectra from the HITRAN database parameters and to fit experimental spectra to them has been created. These procedures have been integrated into a methodology that is based on the calculation of ratios of spectra in the absorption mode (i.e., an active method that uses a hot background). These ratios are equivalent to transmittances in the simple case of negligible emission (low plume temperature), but plume emission is also taken into account if necessary. The use of ratios implies that a strict radiometric calibration is not required. This leads to a robust measurement method, with a low sensitivity to many influence factors, such as detector spectral responsivity or atmospheric transmittance. Validation measurements have been carried out with highly successful results in terms of both temperature and gas concentration retrieval in the case of CO2, which is particularly difficult because of its presence in the nonpolluted atmosphere outside the plume. Finally, it has been shown that the method is able to provide quantitative imaging of CO2 column density and temperature for the exhaust emissions of an engine. In summary, it can be concluded that the proposed active methodology makes it possible to use an IFTS instrument, like the Telops Hypercam, to provide quantitative imaging of column density and temperature in sources like automobile exhaust plumes, which are relatively small and cold as compared to the case of smokestack emission, commonly measured in the passive mode in the remote sensing literature. The proposed method is directly applicable to gases other than CO2 as long as their spectral signatures remain within the spectral bandwidth of the instrument. This is the case of hydrocarbons, carbon monoxide, sulfur dioxide, and many other gases that can be of interest in other industrial or environmental applications. This wide applicability suggests that IFTS, although too complex to be used as a routine inspection or detection instrument, it can be useful as a design tool for the development of novel multispectral systems and algorithms, specific for each gas of interest, that may provide practical quantitative imaging of gases. Another, more specific line of work, is related to speeding up the fitting in the hyperspectral method here described. The development of complexity reduction techniques could provide a tool for a practical approach to near real-time processing, with a great importance in field measurements. Further work along this line is already under way. The authors wish to acknowledge Fernando López and the LIR-Infrared Laboratory at Universidad Carlos III de Madrid for the continuous support and stimulus.
References 1. H. W. Prengle, C. A. Morgan, C.-S. Fang, L.-K. Huang, P. Campani, and W. W. Wu, “Infrared remote sensing and determination of pollutants in gas plumes,” Environ. Sci. Technol. 7, 417–423 (1973). 2. W. F. Herget, “Remote and cross-stack measurement of stack gas concentrations using a mobile FT-IR system,” Appl. Opt. 21, 635–641 (1982). 3. J. Wormhoudt, ed., Infrared Methods for Gaseous Measurements: Theory and Practice (Marcel Dekker, 1985). 4. K. C. Gross, K. C. Bradley, and G. P. Perram, “Remote identification and quantification of industrial smokestack effluents via maging Fourier-transform spectroscopy,” Environ. Sci. Technol. 44, 9390–9397 (2010). 5. J. L. Harley and K. C. Gross, “Remote quantification of smokestack effluent mass flow rates using imaging Fourier transform spectrometry,” Proc. SPIE 8018, 801813 (2011). 6. S. Sabbah, P. Rusch, J. H. Gerhard, C. Stöckling, J. Eichmann, and R. Harig, “Remote sensing of gases by hyperspectral imaging: results of measurements in the Hamburg port area,” Proc. SPIE 8186, 81860S (2011). 7. K. C. Bradley, S. Bowen, K. C. Gross, M. A. Marciniak, and G. P. Perram, “Imaging Fourier transform spectrometry of jet engine exhaust with the telops FIRST-MWE,” in IEEE Aerospace Conference (IEEE, 2009), pp. 1–8. 8. D. A. Burgard, G. A. Bishop, R. S. Stadtmuller, T. R. Dalton, and D. H. Stedman, “Spectroscopy applied to on-road mobile source emissions,” Appl. Spectrosc. 60, 135A–148A (2006). 9. L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Šimečková, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 110, 533–572 (2009). 10. M. Chamberland, V. Farley, A. Vallieres, A. Villemaire, L. Belhumeur, J. Giroux, and J.-F. Legault, “High-performance field-portable imaging radiometric spectrometer technology for hyperspectral imaging applications,” Proc. SPIE 5994, 59940N (2005). 11. The Harvard-Smithsonian Center for Astrophysics (CFA), Cambridge, MA, USA and V. E. Zuev Insitute of Atmosperic Optics (IAO), Tomsk, Russia, Hitran on the Web, http://hitran .iao.ru/. 12. P. R. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry, 2nd ed. (Wiley, 2007). 13. J.-P. Gagnon, Z. Habte, J. George, V. Farley, P. Tremblay, M. Chamberland, J. Romano, and D. Rosario, “Hyper-cam automated calibration method for continuous hyperspectral imaging measurements,” Proc. SPIE 7687, 76870E (2010). 14. K. C. Gross, P. Tremblay, K. C. Bradley, M. Chamberland, V. Farley, and G. P. Perram, “Instrument calibration and lineshape modeling for ultraspectral imagery measurements of industrial smokestack emissions,” Proc. SPIE 7695, 769516 (2010). 15. “Survey of global average CO2 concentration measurements,” http://www.esrl.noaa.gov/gmd/ccgg/trends/index.html. 16. P. M. McClintock, “Enhanced remote sensing performance based pilot program. Final report,” http://www.nctcog.org/ trans/air/hevp/20110730_ERSPBPP_final_report_08‑12‑2011_ jpl.pdf.
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An imaging Fourier transform spectrometer operating in the medium infrared (1800–5000 cm−1 ) has been used to image two gas sources: a controlled CO2 leak at room temperature and the exhaust of a combustion engine. Spectra have been acquired at a resolution of 0.5 cm−1 using an extended blackbody as the background. By fitting them with theoretical spectra generated with parameters from the High-Resolution Transmission Molecular Absorption database, quantitative maps of temperature and gas column density (concentration·path product) for the gas plumes have been obtained. Spectra are related to gas plume parameters by means of a radiometric model that takes into account not only gas absorption, but also its emission and the atmospheric absorption, as well as the instrument lineshape function. Measurements for the gas leak show very good agreement between retrieved and nominal values of temperature and CO2 column density. This result has direct application to obtain quantitative imaging of exhaust emissions from automobiles and other mobile sources, as shown here with measurements of exhaust gases in a diesel engine. © 2015 Optical Society of America OCIS codes: (110.3080) Infrared imaging; (110.4234) Multispectral and hyperspectral imaging; (010.1120) Air pollution monitoring; (120.0280) Remote sensing and sensors; (300.6300) Spectroscopy, Fourier transforms; (120.1740) Combustion diagnostics. http://dx.doi.org/10.1364/AO.54.000141
1. Introduction
The recent development of commercially available imaging Fourier transform spectrometers (IFTS) has opened a new range of possibilities in the field of remote sensing of pollutants. While the use of Fourier transform spectrometry to measure gas effluents from smokestacks and other industrial sources already has a long history [1–3], the spatial resolution provided by imaging instruments adds a new dimension to this technique, making it much more powerful [4]. Not only column densities of pollutants and plume temperature can be mapped, but also, since the small instantaneous field of view (IFOV) of each pixel minimizes spatial averaging of inhomogeneous regions, simpler models can be used for data analysis and quantification is much more accurate. 1559-128X/15/020141-09$15.00/0 © 2015 Optical Society of America
The study of the time evolution of images even makes it possible to track the gas flow and estimate effluent mass flow rates [5]. Previous IFTS studies of pollutant sources have focused on emission from smokestacks of power plant facilities. Although some mobile sources like ships [6] or aircraft engines [7] have been measured, remote measurement of automobile exhaust emissions has been limited to nonimaging methods, that, furthermore, provide only ratios of pollutants rather than absolute values [8]. In this work, we explore the ability of IFTS to provide quantitative images of temperature and gas column density of this kind of gas sources. This problem poses some specific difficulties since the amount of gases involved is much smaller and the temperatures are typically lower, whereas measurement distances will be usually shorter. In order to obtain the temperature and column density values from experimental spectra, an accurate modelization must be made from both the scene 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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and the instrument. Therefore, a radiometric model has been developed, which is described in detail in Section 2. This model dictates the relationship between the ideal radiance spectra at the sensor’s location and the temperature and composition of the gas plume. These ideal spectra have been obtained with a line-by-line method using the High-Resolution Transmission Molecular Absorption (HITRAN) spectroscopic database [9]. In order to compare them with the measured spectra, however, instrumental effects must be taken into account. They are summarized in an instrument lineshape function that is convolved with the ideal spectra. The widened spectra are compared then with the measured spectra for each pixel, by a fitting algorithm that explores temperature (T) and column density (Q) values until it finds the optimal agreement, thus providing the measured (T, Q) couple. Computation of the simulated spectra, instrumental widening, and the fitting procedure are explained in Section 3. The method developed in Sections 2 and 3 is applied to experimental measurements in Section 4. A Telops Hypercam IFTS instrument [10] operating in the medium infrared has been used in two measurement campaigns; first in the laboratory with a controlled CO2 leak and then measuring emissions from the diesel engine of an automobile. Finally, conclusions and guidelines for future work are drawn in Section 5. 2. Radiative Model
In a typical experimental setup for IFTS gas measurement (Fig. 1), the instrument images a gas plume against a background and provides a measurement of the spectral radiance incoming to each pixel. In order to relate this radiance with the plume parameters, a radiative model of the measurement configuration is needed. We will make the following simplifying assumptions: 1. For each pixel, the exhaust plume is modeled by a single temperature and a single value of concentration for each gas; i.e., the plume is assumed to be homogeneous in the IFOV and these values are considered as line-of-sight averages. With this approximation we can ignore internal absorption of radiation emitted by the plume, and characterize it by a single transmittance τpl and emittance εpl 1 − τpl at each pixel.
Fig. 1. Schematics of the radiative model. 142
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2. The emission of the atmosphere is negligible. This approximation is justified as long as the atmospheric temperature is much lower than those of the plume and/or the background. 3. The background emissivity εb is large, so that the reflection of ambient radiation in the background is negligible. 4. The plume is in local thermal equilibrium (so that Boltzmann distribution holds), and the effects of absorption and scattering by particulate matter are negligible. These assumptions, usually made for smokestacks effluents [4], are even more justified for combustion engine emissions, usually cleaner (with less particles) and at lower temperatures. With these approximations, the incoming radiance at the radiometer is Lin LBB T b · εb · τa1 τpl τa2 LBB T pl · 1 − τpl τa2 ; (1) where τpl , τa1 , and τa2 are, respectively, the transmittances of the plume and the first and second atmospheric paths (atm1 and atm2 in Fig. 1), LBB stands for Planck’s blackbody radiance, and T b , T pl are, respectively, the temperatures of the background and the plume. For each wavenumber, transmittance depends on temperature, optical path, and concentrations of each chemical species. It will be assumed also that Lambert–Beer’s law holds, i.e., that for a single chemical absorbing species, with an optical path L, τ is given by τν; C; T e−kν;TL e−αν;TCL ;
(2)
where the absorption coefficient k has been written in terms of the absorptivity α and the concentration C, k αC, and the dependence of k and α on wavenumber and temperature has been shown explicitly. Absorptivities are generally well known and can be extracted from spectroscopic databases like HITRAN [9]. If there is more than one absorbing species, τν is just a product of terms like Eq. (2), one for each species. Our aim is to obtain values of plume concentration Cpl and temperature T pl from experimental measurements of Lin ν. In fact, since only the product Cpl L appears in the equations, our result will be the column density Qpl ≡ Cpl L rather than the concentration Cpl , and we will measure the amount of gas, as usual in spectroscopic remote sensing methods, in units of ppm · m (parts per million per meter). The final products of our measurement method will be a “column density image” and a “temperature image” with values of, respectively, Qpl ≡ Cpl L and T pl at each point in the field of view. To solve Eq. (1) for the plume column density and temperature is not possible because both parameters are coupled in the Lambert–Beer expression of transmittance [Eq. (2)], where the absorptivity α depends on T pl in a nontrivial way. Instead, they will be
determined by a fitting process: we will calculate theoretical spectra and assign to each pixel the concentration and temperature values which provide the best fit to the experimental spectra. This process can be somewhat simplified for the extreme cases of very hot or very cold backgrounds. A.
Solving the Model: Absorption Mode
When the background is much hotter than the plume, the second term in Eq. (1), accounting for the plume emission, can be neglected. This is the so-called absorption (or active) mode. Equation (1) becomes BB a1 pl a2 Lin on;abs ≈ L T b · εb · τ τ τ :
(3)
The subindex on, abs has been added to indicate that the plume is “on” and measurement is in absorption mode. The plume transmittance is then (showing explicitly the dependencies on wavenumber, temperature, and column densities) τpl ν; Qpl ; T pl ≈
Lin on;abs ν LBB ν; T b · εb · τa ν; Qa ; T a
;
(4)
where τa stands for the total atmospheric transmittance, and τa τa1 · τa2 (it will be assumed that temperature is the same for the atmospheric paths 1 and 2). If the background temperature and atmospheric transmittance are known [so that the denominator in Eq. (4) is known], values of plume column density Qpl and temperature T pl can be determined by fitting the theoretical τ [Eq. (2)] to this experimental value. All the terms in Eq. (4) can be measured experimentally if it is possible to turn off the plume, in order to have a reference spectrum BB Lin ν; T b · εb · τa ν; Qa ; T a off ;abs ν ≈ L
·τ
pl0
ν; Qa ; T a :
(5)
where τpl0 stands for the transmittance of the region of atmosphere that was occupied by the plume when it was “on”. Since it will be assumed that τpl0 ≈ 1 (thin plume), the plume transmittance is simply τpl ν; Qpl ; T pl ≈ B.
Lin on;abs ν : in Loff ;abs ν
(6)
Solving the Model: Emission Mode
If, on the other hand, the background is much cooler than the plume, its contribution to the measured radiance will be negligible. This is the emission (or passive) mode. In this case, Eq. (1) becomes BB Lin T pl · 1 − τpl · τa on;emi ν ≈ L
(7)
and the experimental transmittance spectrum is τpl ν; Qpl ; T pl ≈ 1 −
Lin on;emi ν LBB ν; T pl · τa ν; Qa2 ; T a2
: (8)
This is formally similar to Eq. (4), but there is a crucial difference. While the denominator in Eq. (4) can be measured with a reference spectrum, or, in any case, can be estimated if the background temperature and atmospheric data are known, the denominator in Eq. (8) contains the plume temperature, which is precisely what has to be determined. So, transmittance cannot be measured experimentally, and it is the measured radiance which must be fitted by the calculated right-hand side of Eq. (7). This means that the radiometer must be accurately calibrated in radiance, and values of Qa2 and T a2 must be known. The only simplification, as compared to the general case, is that the parameters of the background (T b ) and the atmospheric path between the background and the plume (Qa1 , T a1 ) do not appear in the equations. C.
Approach of This Work
In our case, the temperature of the exhaust gases was expected to be relatively low, about 140°C. In the spectral region of the CO2 emission/absorption band, at 4.2 μm, even for a very thick flame with ε 1 the emitted radiance at 140°C is more that 15 times smaller than the radiation of a 350°C background. This fact, together with the complications just described for the emission mode, suggested to focus on measurements in the absorption mode. Two radiance spectra are measured against the hot background: Lmeas on;abs ν with the plume “on” and Lmeas off ;abs ν with the plume “off.” According to Eq. (6), an experimental plume transmittance spectrum, τpl exp , has been defined as τpl exp ν ≡
Lmeas on;abs ν : meas Loff ;abs ν
(9)
This spectrum must be fitted by theoretical transmittance spectra τpl th ν; Qpl ; T pl , calculated with Eq. (2), to obtain Qpl and T pl as the parameters which provide the best fit. 3. Theoretical Spectra and Fitting Procedure A. Ideal, High-Resolution Transmittance Spectra
In order to generate theoretical spectra, the starting point is to know the fundamental spectroscopic parameters of the molecules. There exist several databases with this information. We have used HITRAN [9], which catalogs the line center positions and intensities of a great variety of gas molecules in the IR region. A very convenient web implementation, HITRAN on the Web [11], computes, by summing up the standard lineshapes of single absorption lines (“line-by-line method”), the spectra of absorption coefficient (k αC, [cm−1 ]), and transmittance (τ). However, in order to fit the experimental spectra, many iterations have to be performed, and therefore theoretical spectra must be generated in a fast way, without having to recourse to the web application each time the concentration or temperature is varied. The main difficulty lies in the temperature 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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Absorptivivity as a function of temperature for different wavenumbers 20
B.
Instrumental Widening
The spectra constructed thus far are high-resolution, ideal spectra, with absorption features of intrinsic width. In order to be compared to the measured spectra, they need to be previously processed to take into account instrumental effects. Specifically, they must be convolved with the instrumental lineshape function (ILS) to account for finite instrument resolution. In our case, a triangular apodization was used, and therefore the ILS is a squared sinc function [12]. However, when calculating the theoretical transmittance spectrum τpl th ν, it is not correct to simply convolve the ideal spectrum with the ILS. The reason is that τpl th ν is going to be compared to the experimental transmittance spectrum τpl exp ν, and this is not measured directly, but rather as a ratio [Eq. (9)] of two radiance spectra measured by our inmeas strument, Lmeas on;abs and Loff ;abs . While in Eq. (6) the atmospheric transmittance and blackbody radiance terms cancel out for ideal spectra, this is no longer true for the experimental spectra, because they are affected by the instrumental resolution. Therefore, the correct spectrum τpl th ν must be calculated as a ratio of widened radiances R τpl th ν
144
−1
2310 cm
−1
2320 cm
16
2330 cm−1 −1
14
−1
2340 cm
−1
2350 cm
12 10 8 6 4 2
αT; ν p3 ν · T 3p p2 ν · T 2p p1 ν · T p p0 ν: (10) The dependence of absorptivities on temperature for each gas has been thus parametrized in the region from 2000 to 2400 cm−1 , with a spectral resolution of 0.01 cm−1. Althoug this step is not enough to reproduce accurately the shape of some individual lines, that can be as narrow as 0.05 cm−1 for CO2, the effect is very small on the widened spectra used for fitting. An example of the dependence of the absorptivity on temperature for CO2 at some specific wavenumbers is shown in Fig. 2. With this parametrization it is easy to construct transmittance spectra for arbitrary values of T and CL, using Eq. (2).
−1
2300 cm 18
Absorptivity (cm )
dependence of the absorptivity. The strategy that we have followed consists in approximating that temperature dependence with a known function. In order to do that, many simulations of k, at different temperatures and at the highest resolution available, have been calculated for each gas of interest with HITRAN on the Web. Pressure was fixed at 1 atm and gas abundance at 100%, so that, since k αC, the k thus calculated is numerically equal to α if concentrations are measured in % at atmospheric pressure. These values of α have been fitted by third-order polynomial functions. In this way, all the information needed to generate spectra is reduced to four parameters per wavenumber
0 300
325
350
375
400
450
Fig. 2. Temperature dependence of the absorptivity of CO2 at several wavenumbers. Dependence on ν is extremely strong, so for wavenumbers very close to these exact values results can be very different. Continuous lines are fittings by third-order polynomials.
R τpl th ν
LBB ν0 ; T b · εb · τa ν0 · τpl ν0 · ILSν − ν0 dν0 R BB 0 ; L ν ; T b · εb · τa ν0 · ILSν − ν0 dν0 (11)
where τpl ν and τa ν stand for the ideal transmittance spectra of the plume and the atmosphere, respectively, as provided by HITRAN. They are functions (not explicitly displayed) of the temperatures (T pl , T a ) and column densities (Qpl , Qa ). Since the blackbody has a relatively flat spectral profile, and the same can be expected for εb, they can be simplified out with very good approximation R τpl th ν
≈
τa ν0 · τpl ν0 · ILSν − ν0 dν0 R a 0 : τ ν · ILSν − ν0 dν0
(12)
In contrast, the effect of the atmospheric term τa ν0 cannot be simplified. Therefore, through instrumental widening, values of T a and Qa affect somewhat the measured spectra. The effect is small for the usual values of concentrations and distances, although not generally negligible (in particular when measuring CO2 concentrations in the plume, since CO2 is a component of the unpolluted atmosphere). C.
Effects of Plume Emission
If the emission of the plume is not negligible, the approximations used in the absorption mode will be no longer valid, and the full radiometric model must be considered. Equation (12) should be changed to
LBB ν0 ; T b · εb · τa ν0 · τpl ν0 LBB ν0 ; T pl · 1 − τpl ν0 · τa ν0 · ILSν − ν0 dν0 R BB 0 : L ν ; T b · εb · τa ν0 · ILSν − ν0 dν0
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Temperature (K)
(13)
The emitted plume radiance becomes relevant when two conditions hold: gas plume temperatures are comparable to those of the background and transmittance in the spectral band used for fitting is small (i.e., emissivity is high). Thus, the importance of emission can be minimized by a proper selection of the spectral region. In any case, taking into account the emission factor simply makes calculations longer, but has no significant effects on the convergence of the fitting algorithm. D.
Experimental Spectra and Fitting Procedure
For clarity of exposition, we describe here the procedure assuming that there is a single gas with absorption lines in the measured spectral region. The generalization to several gases is straightforward: simply, there is an additional unknown value of column density to be determined for each additional gas. As already explained, our aim is to find for each pixel the couple of values (Qpl , T pl ) for which the theoretical spectrum τpl th ν; Qpl ; T pl provides the best fit to the experimental spectrum τpl exp ν; i.e., one that minimizes the sum of squared errors (SSE) between pl τpl th and τ exp . Experimental spectra have been acquired with a Telops Hypercam IFTS system. In this instrument, the incoming radiance is modulated by a Michelson interferometer, and then is detected by an InSb 320 × 256 focal plane array (IFOV 0.35 mrad), sensitive in the medium infrared (1800 to 5000 cm−1 ). An interferogram is acquired at each pixel, which, after processing, provides spectra with a maximum resolution of 0.25 cm−1, although in this work all spectra have been measured at 0.5 cm−1 in order to reduce acquisition time. Technical details on the instrument can be found in the literature [10,13]. In order to compare two spectra, both must have the same number of points and they must correspond to the same wavenumbers. For the 0.5 cm−1 nominal resolution of experimental spectra, separation between consecutive wavenumbers is 0.417 cm−1. However, this resolution is poor for theoretical spectra, and therefore the interferograms have been padded with zeros to a length seven times larger, so that the step in the wavenumber axis of τpl exp ν was reduced to 0.0595 cm−1 . The wavenumber axis of the experimental spectra must be corrected also because in the Michelson interferometer the angular deviation from the optical axis affects by a multiplicative factor the wavenumber values [14]. The correction factor for each pixel can be estimated using as a wavenumber reference a well-defined absorption line at a known spectral position; in our case, the 1918 cm−1 water line was employed. This means that the experimental spectra take values at slightly different wavenumbers for different pixels. In order to have a common wavenumber axis for the whole image, interpolated spectra with values at the wavenumbers of the optical axis have been used in the fitting process.
At each pixel, the fitting procedure is as follows. We start by assuming a value for the couples Qpl ; T pl and Qa ; T a . The ideal transmittance spectra τpl , τa are calculated with Eqs. (10) and (2) at the points of the wavenumber axis of the experimental spectra. Then the theoretical spectrum τpl th is calculated with Eq. (12) [or with Eq. (13) if plume emission is not negligible]. The differences with τpl exp for each wavenumber are summed up in quadrature to get the SSE. The Nelder–Mead minimization algorithm, as implemented in MATLAB software, is used then to find the value of Qpl ; T pl for the next iteration, until convergence is reached [recalculation of Qa ; T a is usually not necessary, but is also possible]. The process is repeated for each pixel to obtain the images of column density and temperature. E. Spectral Region for Fitting and Error Estimation
The full spectra provided by the Telops Hypercam range approximately from 1800 to 5000 cm−1 . With a spectral step of 0.0595 cm−1, as described in the previous section, this means ≈ 53; 800 points for each pixel. Even using a subwindow instead of the whole image, the fitting process requires a lot of computing resources, in particular because of the convolutions of the ideal spectra with the ILS performed at each iteration. In addition, for each gas there may be regions with very strong or very weak absorption features, that are scarcely sensitive to gas concentrations. Therefore, it is advisable to select an optimal spectral subregion for the fitting process. For the particular case of CO2, the region with strongest absorption lines in the medium IR ranges from 2280 to 2400 cm−1 . However, this strong absorption means that for long optical paths, the response can be saturated even with the atmospheric CO2 . This can be appreciated in Fig. 3, which is the spectrum of a blackbody at T 350°C seen through 2.75 m of nominally clean atmosphere (no plume), at a 0.5 cm−1 resolution. Even for a relatively short path, the region of the strong absorption peak at ∼2350 cm−1 has low signal and should be avoided,
Fig. 3. Typical reference spectrum (no gas plume), measured for a 350°C blackbody with 0.5 cm−1 resolution, at a distance of 2.75 m. The inset shows the region of the CO2 medium infrared absorption band. 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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4. Experimental Results
In order to test the results of the measurement method in a controlled laboratory environment, a series of validation experiments was performed . A.
Laboratory Setup and Measurements
B. Analysis of Results
The column density results of the iterative fitting procedure, performed in the 2240 to 2280 cm−1 spectral region, are shown in Fig. 5, for the first horizontal line of pixels above the exhaust pipe. Results have been obtained assuming a 400 ppm concentration [15] for ambient CO2 and the measured T a 25°C. Two column density profiles are shown: circles have been obtained using the absorption approach, whereas for squares the full radiometric model, including plume emission effects, has been employed. Both profiles are compared with the optical path for each pixel (plotted with a different vertical axis), estimated from the tube diameter through a simple geometrical calculation. Since a CO2 concentration of 100% is being used, it is easy to compare magnitudes: the column density should be Q 15700 ppm · m at the tube center (where the path is 15.7 mm) and should follow elsewhere the optical path profile.
Column density (ppm·m)
A hollow copper pipe, with an internal diameter of 15.7 mm, was disposed vertically, as is shown in Fig. 4, and connected to a calibrated gas bottle with a 100% CO2 concentration. A radiant heater, with a high emissivity surface of 29.5 × 29.5 cm at T 600°C (not shown in Fig. 4), was placed close to the bottom of the tube in order to heat the copper
pipeline and, consequently, the gas flow. This heating procedure has been preferred to a combustion device (as a blow torch or similar) since CO2 and H2 O produced in combustion could interfere with the experiment. An extended area (6 × 6 in.) blackbody, with nominal emissivity ε 0.94 and temperature T 350°C, was placed as a background behind the pipe outlet. A thermocouple was also positioned at the mouth of the tube. The Telops Hypercam was placed at a distance of 3.10 m and collected four interferograms for both reference (in the absence of flow) and CO2 gas flow. The spectral resolution was 0.5 cm−1 and the spatial subwindowing 120 × 100 pixels. Each set of four acquired interferograms was preprocessed by calculating its median, and then Fourier-transformed to meas obtain the Lmeas on;abs ν and Loff ;abs ν spectra necessary to calculate the experimental transmittance spectrum.
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since transmittances obtained with Eq. (9) will be very noisy. On the contrary, it has been found that transmittances in the interval from 2240 to 2280 cm−1 (corresponding to the fundamental transition of 16 O13 C16 O) show a good sensitivity to the concentration variations of CO2 in the whole range studied. At the same time, the relative weakness of absorption lines in that region implies that results are less sensitive to atmospheric CO2 concentration and temperature. For these reasons, this region has been selected to apply the fitting procedure. An estimation of the uncertainties in T pl and Qpl associated with the fitting method has been made by performing radiometric simulations of τpl ν, calculated with Eq. (13). A range of noise levels was added to the ideal radiance spectra, from the value measured in a reference spectrum (∼1 mW∕m2 sr in the 2280 to 2400 cm−1 region) to a value ten times higher. For each noise step, τ was calculated for 100 random values of temperature and column density. The mean relative error of the retrieved values ranged from 1.6% to 1.8% for T pl (measured in K), and from 0.2% to 0.5% for Qpl. Therefore, for the noise levels expected in our measurements, expected errors are small and the method is quite robust.
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Fig. 4. Experimental setup employed in the validation measurements, as viewed from the IFTS. CO2 comes out of the copper pipe placed vertically at the center, and is observed against the background of the extended blackbody. A horizontal thermocouple is seen at the right-hand side, with its tip at the mouth of the tube. 146
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Fig. 5. Two retrieved column density profiles at the pipe outlet, both compared with the optical path estimated for each pixel. One of the profiles (squares) is retrieved by employing the full radiometric model, taking into account the emission term. The second profile (circles) is based on the absorption approach, neglecting self-emission effects.
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The figure shows clearly that the emission term has a small but appreciable contribution, and if it is taken into account, retrieved column densities agree very well with their nominal values in a wide region around the center of the tube, with errors smaller than 1%. Discrepancies appear at tube edges, where the optical path abruptly falls down to zero, while the retrieved concentration suffers a smooth variation. This effect can be explained by the nonideal modulation transfer function of the optical system, since defocusing, lens aberrations, and other effects attenuate high spatial frequencies. The results of the measurement method are shown in Fig. 6, where both column density [Fig. 6(a)] and temperature [Fig. 6(c)] images are displayed. In order to speed up calculations, a preclassification has been made, excluding pixels with very high transmittance (therefore, with negligible CO2 concentration) from the fiting process. In Figures 6(b) and 6(d) there have been also plotted, respectively, several column density and temperature profiles, taken at the same rows, marked in the respective images (the line named as “Row 86” corresponds to the profiles in Fig. 5). Results for density column agree with the expected gas dilution, as peak values
fall down as the plume moves away from the tube outlet. It is difficult to estimate properly the accuracy of the retrieved temperature values, since thermocouple measurements in gas flows are affected by important uncertainties and, in any case, provide only a point measurement. Despite this fact, the horizontal temperature profiles at different heights shown in Fig. 6(d) are very plausible, since they depict a thermal structure that agrees with the heating procedure employed, where the walls of the pipeline are responsible for heating the gas flow, and the absolute values also agree with those given by the thermocouple, of about T 100°C. The quality of the fit can be appreciated also by looking directly to the spectra. Figure 7 shows experimental and theoretical transmittance for a pixel above the tube center, in the middle of the gas plume. It is clear that there is a very good agreement between both data sets, especially in the fitted region, from 2240 to 2280 cm−1 . The relative error between empirical and theoretical fitted transmittance, depl pl fined as jτpl th − τexp j∕τexp , is also represented; the graph shows how it becomes larger for those wavenumbers outside the fitted bandwidth. 10 January 2015 / Vol. 54, No. 2 / APPLIED OPTICS
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C.
Engine Measurements
After the proposed method was checked through the validation tests just described, it was applied to measurements of the exhaust duct of an automobile diesel engine. Four interferograms were averaged for each measurement, with a total acquisition time of nearly five minutes. Given the turbulent nature of the plume it would have been advisable to average more interferograms, but stabilization of the engine was imperfect and appreciable drifts appeared for longer times. Figures 8 and 9 show the obtained maps of CO2 column density and temperature. Fitting was performed, as previously, in the 2240 to 2280 cm−1 region. Errors in this case are bound to be larger than in the controlled CO2 leak since spectra are noisier noise due to turbulence. However, although we have no independent measurements of Q and T to estimate errors, we can be reasonably sure that these errors are small, since simulation of noisy spectra has shown that the fitting algorithm is quite
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robust: a tenfold increase in the noise of radiance spectra (measured in the fitting region) only increased the average error from 1.6% to 1.8% for T (measured in K) and from 0.2% to 0.5% for Q. Since variability of the exhaust plume during the acquisition time is larger than this, we conclude that errors should not be significant for our measurement conditions. In addition to carbon dioxide, several gases are expected in the exhaust emission of an internal combustion engine. Water, carbon monoxide, and hydrocarbons could be observed in the medium infrared, and even (if present in large concentrations) nitrogen oxides or sulfur dioxide. However, although pixels in the exhaust plume were analyzed in the full spectral range, only CO2 and H2 O were identified during this measurement campaign. In fact, this is to be expected in our case, since typical concentration values in the exhaust of a state-of-the-art diesel engine are quite small, with mean values for CO, total hydrocarbons, NOx , and SO2 below the detection limits estimated from the experimental spectra [16]. Nevertheless, the proposed methodology is suitable for all the mentioned species if present in high enough concentrations (as in gross pollutant vehicles), and its application might be even simpler than in the CO2 case, since they are absent in a typical atmosphere. 5. Conclusions and Future Work
A method to remotely quantify pollutant effluents, using an imaging Fourier transform spectrometer (IFTS) to provide “maps” of column density and temperature of the gas plumes, has been developed, tested in the laboratory for a controlled CO2 leak, and applied to the exhaust emissions of a diesel engine. Using as single input the raw data provided by the Telops Hypercam IFTS (interferograms at each pixel), the full FTIR spectral processing has been worked out. Radiative propagation, from the IR source to the sensor, has been modeled including
instrument effects, and a routine to create synthetic spectra from the HITRAN database parameters and to fit experimental spectra to them has been created. These procedures have been integrated into a methodology that is based on the calculation of ratios of spectra in the absorption mode (i.e., an active method that uses a hot background). These ratios are equivalent to transmittances in the simple case of negligible emission (low plume temperature), but plume emission is also taken into account if necessary. The use of ratios implies that a strict radiometric calibration is not required. This leads to a robust measurement method, with a low sensitivity to many influence factors, such as detector spectral responsivity or atmospheric transmittance. Validation measurements have been carried out with highly successful results in terms of both temperature and gas concentration retrieval in the case of CO2, which is particularly difficult because of its presence in the nonpolluted atmosphere outside the plume. Finally, it has been shown that the method is able to provide quantitative imaging of CO2 column density and temperature for the exhaust emissions of an engine. In summary, it can be concluded that the proposed active methodology makes it possible to use an IFTS instrument, like the Telops Hypercam, to provide quantitative imaging of column density and temperature in sources like automobile exhaust plumes, which are relatively small and cold as compared to the case of smokestack emission, commonly measured in the passive mode in the remote sensing literature. The proposed method is directly applicable to gases other than CO2 as long as their spectral signatures remain within the spectral bandwidth of the instrument. This is the case of hydrocarbons, carbon monoxide, sulfur dioxide, and many other gases that can be of interest in other industrial or environmental applications. This wide applicability suggests that IFTS, although too complex to be used as a routine inspection or detection instrument, it can be useful as a design tool for the development of novel multispectral systems and algorithms, specific for each gas of interest, that may provide practical quantitative imaging of gases. Another, more specific line of work, is related to speeding up the fitting in the hyperspectral method here described. The development of complexity reduction techniques could provide a tool for a practical approach to near real-time processing, with a great importance in field measurements. Further work along this line is already under way. The authors wish to acknowledge Fernando López and the LIR-Infrared Laboratory at Universidad Carlos III de Madrid for the continuous support and stimulus.
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