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Extraction of Incident Irradiance from LWIR Hyperspectral Imagery Pierre Lahaie, DRDC Valcartier 2459 De La Bravoure Road, Quebec, Qc, Canada

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Extraction of Incident Irradiance from LWIR Hyperspectral Imagery Pierre Lahaie, DRDC Valcartier 2459 De La Bravoure Road, Quebec, Qc, Canada DRDC-RDDC-2015-P140 Extraction of incident irradiance from LWIR hyperspectral imagery Pierre Lahaie, DRDC Valcartier 2459 De la Bravoure Road, Quebec, Qc, Canada ABSTRACT The atmospheric correction of thermal hyperspectral imagery can be separated in two distinct processes: Atmospheric Compensation (AC) and Temperature and Emissivity separation (TES). TES requires for input at each pixel, the ground leaving radiance and the atmospheric downwelling irradiance, which are the outputs of the AC process. The extraction from imagery of the downwelling irradiance requires assumptions about some of the pixels’ nature, the sensor and the atmosphere. Another difficulty is that, often the sensor’s spectral response is not well characterized. To deal with this unknown, we defined a spectral mean operator that is used to filter the ground leaving radiance and a computation of the downwelling irradiance from MODTRAN. A user will select a number of pixels in the image for which the emissivity is assumed to be known. The emissivity of these pixels is assumed to be smooth and that the only spectrally fast varying variable in the downwelling irradiance. Using these assumptions we built an algorithm to estimate the downwelling irradiance. The algorithm is used on all the selected pixels. The estimated irradiance is the average on the spectral channels of the resulting computation. The algorithm performs well in simulation and results are shown for errors in the assumed emissivity and for errors in the atmospheric profiles. The sensor noise influences mainly the required number of pixels. Keywords: Hyperspectral imagery, atmospheric correction, temperature emissivity separation 1. INTRODUCTION The atmospheric correction of thermal hyperspectral imagery aims at extracting the temperature and the emissivity of the material imaged by a sensor in the long wave infrared (LWIR) spectral band. It can be divided in two parts: atmospheric compensation (AC) and temperature emissivity separation (TES). TES algorithms such as ARTEMISS [1, 2] and DEFILTE [3] require for input the ground leaving radiance and the atmospheric downwelling irradiance. These inputs are produced by atmospheric compensation of sensor measured radiance. An important difficulty is the estimation from imagery of the atmospheric downwelling irradiance. This paper proposes an approach to perform that task. The downwelling irradiance is difficult to estimate because, very often the spectral radiance emanating from materials that are smooth spectrally is very high and therefore the content of reflected radiance is small. Using spectrally smooth pixel is useful to reduce the impact of spectral features in the corrected spectra. The algorithm makes use of a known or at least an assumed spectral emissivity for a number of pixels and of an assumed atmospheric profile. The atmospheric profile is useful to provide a basis for the estimated downwelling irradiance. The impact on the TES application will be to reduce the error of the estimated temperature. The paper is organized as follow: We first describe the algorithm; then the simulation used to assess the sensitivity of the algorithm to noise and to the error on atmospheric profile. The results of the simulations are provided and described, finally we conclude. Equation (1) shows the sensor measured radiance and equation (2) is the ground leaving radiance. (1) (2) Where is the radiance measured by the sensor, is the ground leaving radiance (The radiance emitted by the pixel’s material, composed partly of self-radiation and of the reflection of incident light), is the transmittance, is the path radiance, is the emissivity of the pixel’s material, is the blackbody radiation at the temperature T and finally L is the incident downwelling irradiance on the pixel transformed in radiance using the assumption that the material is Lambertian. In the remainder of the document we refer to the downwelling irradiance as the radiance reflected by the material. There are often many problems in the way for extracting the downwelling irradiance. The first is that since we do not know the characteristics of the image, we have to use assumptions about the nature of some pixels’ material and temperatures. We also need some prior data about the atmospheric profiles. One other difficulty is that very often the spectral response of each sensor’s pixel is not well characterized. 2. ALGORITHM DESCRIPTION We assume in the algorithm that the atmospheric compensation (AC) has been performed correctly. The AC process is the removal of the atmospheric path radiance accumulated in the air on the path from the target to the sensor and of the transmittance of the atmosphere on the same path. It usually requires the estimation of these two parameters from either use of a modelling approach, MODTRAN [4] for example or by the use of an in scene technique such as ISAC [5]. The ground leaving radiance (2) is obtained from the sensor measured radiance (1) when the path radiance and the transmittance are removed. The emissivity is the first unknown related to the pixels that are used to estimate the downwelling irradiance. Often the emissivity of the suitable pixels in the image is not known exactly. Assumptions have to be used and emissivities contained in spectral libraries can be used when the material is known or assumed. The emissivities contained in spectral libraries are generally averages valid for a specific material. Any error in the used spectral emissivity compared to the effective emissivity of the material in the pixel will map in the whole image when TES will be performed. This is the main reason why spectrally smooth emissivities shall be used. Materials having spectrally smooth characteristics generally have a high emissivity. This will have an impact on the number of pixels that shall be used since the reflected radiance, the signal of interest here, will show a smaller signal to noise ratio. A second problem is the fact that, the whole spectral response of each pixel of the sensor is not well known and in fact is very difficult to measure accurately and for all variations of the sensor. Assumptions about the response can be used, but, they generally give worst results. This is due in the thermal infrared to the large number of spectral absorption lines. To alleviate this, a spectral average of the sensor spectrum is computed over a window that is large enough to reduce the impact of wrong registration of the spectral bands; therefore if some lines are introduced or ignored in the computation their impact will be reduced due to the large number of lines. The same window width is used to compute the downwelling irradiance from a model like MODTRAN, this considered as being the mean of the downwelling irradiance. We define a spectral mean operator having the following general form: (3) Where, is the quantity that is averaged and is the spectral index (wavelength, wavenumber or frequency). Starting with the ground emitted radiance we obtain: (4) For many materials the emissivity can be assumed to have a slow variation with wavelength, so, inside the window, it can be considered as constant. If the variation is linear, the mean will be the same as the median value and therefore a linear variation is suitable. In the case of the blackbody function, it also has a slow variation and therefore as long as the window is small enough, it can be considered constant. The spectral unit or spectral domain (wavelength, frequency or wavenumber) also has an influence for the blackbody consideration since the variation is linear for a wide range of temperatures in the thermal band. The following approximation to (4) can be used: (5) Subtracting (5) from (2) and isolating the downwelling irradiance yield: (6) In (6), the sensor measurement and its spectral average are taken directly from the image. The emissivity has to be assumed or measured or obtained from another source and the spectral average of the downwelling irradiance has to be obtained from either a direct ground measurement or an atmospheric model such as MODTRAN. There are therefore many unknowns and uncontrolled parameters for which it is required to perform a sensitivity analysis. Sensor noise is another component of the problem that needs to be assessed. The following section on simulation describes how this sensitivity analysis has been performed. 3. SIMULATION In this section we study the impact of the variation of three parameters of the system and of the sensor, the emissivity, the error on atmospheric profiles and the sensor noise. There could be very important other difficulties that are not studied example of which are the sensor calibration and the spectral registration. We assume that a good estimation of the emissivity mean has been performed and that therefore only the variation of it around the mean have impacts. If the emissivity average used in the computation is wrong, equation (6) becomes: (7) Where and are respectively the real average emissivity of the material and the assumed emissivity while , and are respectively the estimated, the real and the modeled downwelling irradiance. The estimated downwelling irradiance will contain in some way the difference in spectral features between the real emissivity and the assumed emissivity. If the emissivity is spectrally smooth the spectral features will not have a high importance in the result. Independently, if there is a difference between the spectral average of the real and the modeled downwelling irradiance, it will map in the offset of the estimated downwelling irradiance. In many cases however, the atmospheric profiles provided by weather authorities will be close enough to the real profiles and MODTRAN is thought to be close to about 5% from measured atmospheric optical parameters. All the simulations have been performed in the wavenumber domain with a sensor having 128 bands extending from 744 to 1232 cm-1 with steps of 4 cm-1.
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