Modulation transfer function of layered inhomogeneous random media using the small-angle approximation

Many random media such as clouds and fog are often inhomogeneously distributed and often have a layered structure. This paper presents the effects of such inhomogeneities on the image transmission in terms of the modulation transfer function (MTF). We derive an expression of the MTF for a layered inhomogeneous medium using the small-angle approximation which is valid for size parameters of >10 and optical distances of <5. We obtain numerical results and compare them with experimental data for different particle sizes and concentrations showing good agreement. We also explain the shower curtain effect using the expression for the MTF.