Radiance: the natural quantity for describing diffraction and propagation

Abstract

The true nature of most physical phenomena, including the propagation of light, becomes evident when simple elegant theories and mathematical models conform to experimental observations. Often the simple nature of some natural phenomenon is obscured by applying a complex theory to model an inappropriate physical quantity in some cumbersome coordinate system or parameter space. In this paper, we integrate sound radiometric principles with scalar diffraction theory and show that diffracted radiance (not irradiance or intensity) is the natural quantity that exhibits shift-invariance if formulated in direction cosine space. Thus simple Fourier techniques can be used to predict a variety of wide-angle diffraction phenomena. These include the redistribution of radiant energy from evanescent diffracted orders to propagating ones, and the calculation of diffraction efficiencies with accuracy usually thought to require rigorous electromagnetic theory. In addition, an empirically modified Beckmann-Kirchhoff surface scatter theory has been shown to be more accurate than the classical Beckmann-Kirchhoff theory in predicting non-intuitive scatter effects at large incident and scattered angles, without the smooth-surface limitation of the Rayleigh-Rice scattering theory.