Linking Rayleigh-Rice theory with near linear shift invariance in light scattering phenomena

Understanding topographic scatter has been the subject of many publications. For optically smooth surfaces that scatter only from roughness (and not from contamination, films or bulk defects) the Rayleigh-Rice relationship resulting from a rigorous electromagnetic treatment has been successfully used for over three decades and experimentally proven at wavelengths ranging from the X-Ray to the far infrared (even to radar waves). The “holy grail” of roughness-induced scatter would be a relationship that is not limited to just optically smooth surfaces, but could be used for any surface where the material optical constants and the surface power spectral density function (PSD) are known. Just input these quantities and calculate the BRDF associated with any source incident angle, wavelength and polarization. This is an extremely challenging problem, but that has not stopped a number of attempts. An intuitive requirement on such general relationships is that they must reduce to the simple Rayleigh-Rice formula for sufficiently smooth surfaces. Unfortunately that does not always happen. Because most optically smooth surfaces also scatter from non-topographic features, doubt creeps in about the accuracy of Rayleigh-Rice. This paper investigates these issues and explains some of the confusion generated in recent years. The authors believe there are measurement issues, scatter source issues and rough surface derivation issues, but that Rayleigh- Rice is accurate as formulated and should not be “corrected.” Moreover, it will be shown that the empirically observed near shift invariance of surface scatter phenomena is a direct consequence of the Rayleigh-Rice theory.