Contrast Transmittance in Spatial Frequency Space Modulation Transfer Function

In a derivation similar to the contrast transmittance derivation, it can be shown that the transmittance of equivalent contrast through the atmosphere in the presence of aerosols is given by and Ceq r and Ceq 0 are the equivalent contrast at distance r and 0, respectively, while Mt{ a is the atmospheric modulation transfer function. The parameter the average scene radiance, is the zero-order term in a two-dimensional Fourier decomposition of the scene radiance field.

Comparison of Eqs. (18) and (23) shows that if hN0 = then contrast transmittance in real and spatial frequency space is identical. In most cases, the feature within the image of interest is small compared with its surroundings, and average radiance, flM, is very nearly the same as background radiance hNn. This is a very satisfying result. Whether one is interested in using modern psychophysical spatial frequency models to examine how much aerosol can be introduced into the atmosphere before it is noticed or how image contrast is changed as a function of aerosol load, the calculation is reduced to understanding the dependence of the atmospheric

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