Wide-angle diffuser transmission functions and far-zone speckle

Models for the transmission of light through either rough-surface or bulk diffusers are presented. Since the transmission function contains a dependence on the input angle, it is convenient to use an angular-spectrum representation for the input illumination in the general case. Computer simulations of far-zone speckle patterns and analytical calculations of the ensemble-averaged radiation patterns are made with and without the angle dependence in the transmission function. We find that this angular dependence is relatively unimportant with input illumination near normal incidence. However, the computer simulation demonstrates that the angle dependence can make a significant difference in the detail of the speckle pattern for a complex input spectrum or even for a single plane wave at large (≥30°) angles of incidence. The essential effect of the angle dependence on the averaged radiation patterns is to increase the effective roughness of the diffuser.