Simplification for Fraunhofer diffracting pattern of various randomly oriented ice crystals in cirrus

Abstract

This paper deals with Fraunhofer diffraction by an ensemble of independent randomly oriented ice crystals of assorted shapes, like those of cirrus clouds. There is no restriction on the shape of each crystal. It is shown that light flux density in the Fourier plane is azimuth-invariant and varies as 1/sin(4)θ, θ being the angle of diffraction. The analytical formula proposed is exact. The key point of this study is conservation of electromagnetic energy.