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Contrast transmittance is an important quantity used in the analysis of electro-optical sensors. It depends upon the geometry of the sensor relative to the target and background as well as the optical properties of the obscuring medium. Earlier models of contrast transmittance treated either broadband systems or uniform sky conditions. The models dealt with in this paper are concerned with contrast transmittance for finite clouds, overcast skies, and precipitation conditions for any wavelength in the visible and infrared spectral regions where scattering processes are dominant. Solutions to the problem are presented for single scattering, multiple scattering, and thermal emission for various positions of the observer and target. The models are applicable to nighttime as well as daytime conditions and are useful for the analysis of the performance of electro-optical systems in adverse situations such as dust clouds, smoke clouds, heavy overcast skies, and rainfall. In addition to the contrast transmittance, the models also allow one to calculate the transmittance and path radiance for the same geometry and values of the optical parameters. The basic input parameters for these models consist of the volume scattering and volume extinction coefficients for specific wavelengths, the scattering phase functions, the surface albedo, the coordinates of the observer relative to the target and the source of radiation, and the background spectral radiance. Three spectral regions were examined in detail; the visible at a wavelength of 0.55 pm, the mid infrared at 4.0 μm, and the thermal infrared at 10.0 μm. In the visible region scattering processes are dominant; in the mid infrared, scattering and thermal emission are equally important; and at a wavelength of 10.0 μm only the thermal emission is of significance.
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