Anomalous diffraction of light with geometrical path statistics of rays and a Gaussian ray approximation

The anomalous-diffraction theory (ADT) of extinction of light by soft particles is shown to be determined by a statistical distribution of the geometrical paths of individual rays inside the particles. Light extinction depends on the mean and the mean-squared geometrical paths of the rays. Analytical formulas for optical efficiencies from a Gaussian distribution of the geometrical paths of rays are derived. This Gaussian ray approximation reduces to the exact ADT in the intermediate case of light scattering for an arbitrary soft particle and describes well the extinction of light from a system of randomly oriented and (or) polydisperse particles. The implications for probing of the sizes and shapes of particles by light extinction are discussed.