Passive Remote Sensing by Infrared Spectrometry
Passive remote sensing of toxic vapor clouds is based on the analysis of the ambient infrared radiation in the range 650 – 1500 cm -1. Figure 1 illustrates the measurement setup of the method. The radiation measured by the spectrometer contains the spectral signatures of the background of the field of view, the vapor cloud, and the atmosphere. The propagation of radiation through the atmosphere is described by the theory of radiative transfer14. Computer programs such as MODTRAN15 and FASCODE16 use models for the atmosphere and perform calculations of radiative transfer.
FIG. 1. Measurement setup of passive remote sensing of vapor clouds.
In order to describe the basic characteristics of spectra measured
by a passive infrared spectrometer a simple model with three layers can be used
(Figure 1). The layers are considered homogeneous with regard to all physical
and chemical properties. Radiation from the background, for example, the sky or
a surface (Layer 3) propagates through the vapor cloud (Layer 2) and the atmosphere
between the cloud and the spectrometer (Layer 1). The radiation containing the
signatures of all layers is measured by the spectrometer.
IIn this model the radiance measured by the spectrometer L1 is
where ti is the transmittance of
layer i, Bi is the spectral radiance of a blackbody at
the temperature of layer i, Ti. L3 is
the radiance that enters the layer of the cloud from the background. All
quantities in Equation (1) are frequency dependent. The contribution of scattering
is neglected. If the temperatures of the layers 1 and 2 are equal, Equation (1)
can be simplified:
The radiance difference between the total radiance L1 and the radiance of the background L3 is
where . It follows from Equation (3) that the radiance difference caused by a cloud is proportional to . It is also limited by because . This also limits the spectral range that can be used for remote sensing of gases at ambient temperature because the maximum signal to noise ratio (obtained if t2 = 0) is given by the ratio of and the noise equivalent spectral radiance of the measurement. If the radiance of the background and the temperature of the vapor cloud are known, it is possible to simplify one of the Equations (2) or (3) to calculate the transmittance and absorbance, which can be used to identify and quantify the compounds of the vapor cloud. However, in many cases it is not possible to measure a background spectrum. Thus, the data processing algorithm should not require a background spectrum. The radiance spectrum generally does not have a constant baseline. The upper and lower envelopes of the spectrum of the radiance are given by the gas (cloud and atmosphere) temperatures and the temperature of the background. The emittance (: wavenumber) of many surfaces is high and almost constant in the range 650 – 1500 cm-1. Thus, the emission spectrum of these materials has a high degree of similarity to the spectrum of a blackbody and the spectrum of the brightness temperature TBr() of these surfaces is almost constant. The brightness temperature is defined by the Planck function:
[: spectral radiance]. It is calculated by solving Eq. (4) for TBr
[h: Planck’s constant, c: speed of light, k: Boltzmann’s constant]. In the case of an ideal blackbody () the spectrum of the brightness temperature is constant (the temperature of the blackbody). Therefore, in the case of a background surface with high and constant emittance, the spectral signatures of the atmosphere and the signature of the vapor cloud appear on a constant baseline in the brightness temperature spectrum. Thus, the brightness temperature spectrum is better suited for direct analysis than the radiance spectrum. In order to calculate the radiance spectrum and the brightness temperature spectrum from a measured spectrum, the responsivity and the instrument emission of the spectrometer have to be determined by a radiometric calibration17. Figures 2 and 3 illustrate the steps for the calculation of a brightness temperature spectrum.
FIG. 2. Uncalibrated spectrum (a) and radiance spectrum (b) of methanol vapor in front of a painted wall with an atmospheric optical path (clMethanol = 600 ppm m, TMethanol = 298 K).
FIG. 3. Brightness temperature spectrum of methanol vapor in front of a painted wall with an atmospheric optical path. The absorption signature of methanol is observed on a constant baseline. The spectrum contains the absorption signature of a polyethylene (PE) foil, which was used as the window of the gas cell.
For long optical pathlengths (d > 100 m)
the atmosphere is almost opaque in the range 650 - 690 cm
» 0) because of the presence of CO2. Thus, in this
spectral range the temperature spectrum yields the temperature of the ambient
air (Figure 3). In the range 800 – 1250 cm-1, the
transmittance of the atmosphere is high and the temperature spectrum yields the
brightness temperature of the background. This spectral range is used for the
identification of vapor clouds. The range above 1250 cm-1 contains
absorption lines of the trace gases methane, nitrous oxide, and water.
Here, a is the maximum absorption coefficient of the compound and NESR is the noise equivalent spectral radiance. Because the calculation is based on the assumption of thermal equilibrium, the NECL calculated by this method should only be used to estimate the order of magnitude of the limit of detection. Figure 4 shows a temperature spectrum of a brick wall with an atmospheric optical path. The distance of the wall from the spectrometer is d » 200 m. The surface of bricks has a high emittance, but in the range 1000 – 1100 cm -1 a decrease in the value of the emittance is observed18,19. This results in a dip in the baseline in that region. Because the signatures of background materials are generally a slow varying function of the frequency, they are treated as baseline shifts in this work. The spectrum also contains the signatures of the gases of the atmosphere. In the range 1000 - 1080 cm-1 the emission signature of ozone is observed. The region between 1100 cm-1 and 1200 cm-1 contains emission lines of water, whereas in the range above 1200 cm-1 absorption lines of water (and other trace gases) are observed. The emission lines of ozone and water are caused by radiation from the sky, which is reflected by the wall. The absorption signatures are caused by stronger lines of water. In this region the absorption by water molecules in the path between the spectrometer and the background dominates.
FIG. 4. Brightness temperature spectrum of a brick wall with an atmospheric optical path.
FIG. 5. Brightness temperature spectrum of methanol vapor (clMethanol = 400 ppm m, TMethanol = 294 K) in front of a brick wall with an atmospheric optical path. The emission signature of methanol (centered at 1033 cm-1) is superimposed by the signature of ozone.
Although for many natural and man made surfaces there is only a weak dependence of the emittance on the frequency, the brightness temperature difference caused by the non-constant emittance is often greater than the signal of the vapor cloud. As an example, Figure 5 shows a spectrum of methanol vapor with an atmospheric optical path and a brick wall as the background of the field of view. The signature of methanol in the range 980 - 1080 cm -1 is superimposed by the emission signature of ozone and the baseline is not constant in that region. Moreover, the sky as the background of the field of view does not yield a constant baseline in the brightness temperature spectrum (Figure 6). Thus, an appropriate baseline correction algorithm is a prerequisite for the analysis of the spectra.
FIG. 6. Brightness temperature spectrum of methanol vapor (clMethanol = 800 ppm m, TMethanol = 297 K). The background of the measurement is the sky at a low angle of elevation. The signature of methanol is superimposed by the emission signature of ozone.