Effects of multiple scattering and thermal emission on targetbackground signatures sensed through obscuring atmospheres

摘要

We report on the application of a recently developed method for producing exact solutions of the thermal version of the radiative transfer equation~1. The method is demonstrated to be accurate to within five significant figures when compared with the one dimensional plane layer solutions published by van de Hulst~2; and, has the added capability for treating discrete, localized, aerosol clouds of spherical and cylindrical symmetry. The method, described in detail in a companion paper~1, is only briefly summarized here, where our main purpose is to demonstrate the utility of the method for calculating emissivity functions of finite aerosol clouds of arbitrary optical thickness and albedo, and most likely to occur on the modern "cluttered" battlefield. The emissivity functions are then used to determine apparent temperatures including effects of both internal thermal emission and in-scatter from the ambient surroundings. We apply the results to four generic scenarios including the mid and far IR and a hypothetical "full spectrum" band. In all cases, calculations show that errors on the order of several degrees in the sensed temperature can occur if cloud emissivity is not accounted for, with errors being most pronounced at the higher values of optical depth and albedo. We also demonstrate that significant discrepancies can occur when comparing results from different spectral bands, especially for the mid IR which consistently shows higher apparent temperatures than the other bands, including the full spectrum case. Results of emissivity calculations show that in almost no case can one justify the simple Beer's Law model that essentially ignores emissive/scattering effects; however, there is reason for optimism in the use of other simplyfing first and higher order approximations used in some contemporary models. The present version of the model treats only Gaussian aerosol distributions and isotropic scattering; although neither assumption necessarily represents a restriction on the method.