Deviation from reciprocity in bidirectional reflectance

Abstract

Abstract. The subject of the paper is to discuss and quantify deviations from reciprocity of the bidirectional reflectance distribution function (BRDF), i.e., the difference of BRDF obtained when inverting illumination and viewing directions. Directional reciprocity is not valid in general, because when the illumination beam has a spatial extension larger than the viewed area (as is most often the case for BRDF measurements), some of the scatterers building up the observed radiance are located at different places in reciprocal measurements. The physical systems under consideration in the two experiments are different, hence the breakdown of reciprocity. The paper develops a theory aiming at a quantitative estimation of deviations from directional reciprocity due to this factor. The theory is based on integral forms of the radiative transfer equation in a horizontal slab of heterogeneous absorbing and scattering media. The observed scene radiance is expanded in a series of scattering orders. Integral expressions of the single-and multiple-scattering radiance are derived and put in a form suitable for the analysis of the reciprocity problem. IntroductionThe principle of reciprocity, also referred to as Helmoltz reciprocity, is widely accepted in various branches of physics. Its modern and most general form [Van der Hulst, 1980] states that "in any linear physical system, the channels which lead from a cause at one point to an effect at another point can be equally well traversed in the opposite direction. Let the cause be first placed at P and the effect measured at Q; and in a second experiment, carried out in the same physical system, let the cause be at Q and the effect at P. The reciprocity principle is then expressed by the proportionality: effect at Q/cause at P = effect at P/cause at Q.

A Generalized Linear Transport Model for Spatially Correlated Stochastic Media

“…It is indeed consistent with realworld satellite observations of reciprocity violation uncovered by DiGirolamo et al [61] in spatially variable cloud scenes inside a relatively broad field of view, and readily replicated with numerical Monte Carlo simulations. These findings were soon explained theoretically by Leroy [62]. This provides an element of validation of the new model and, by the same token, invalidates for atmospheric applications all models for RT in stochastic media based on either homogenization or linear mixing.…”

Image-based acquisition and modeling of polarimetric reflectance

“…While Helmoltz reciprocity approximately holds in our dataset, we found that large discrepancies occur when assuming bilateral symmetry during polarized measurements. Similar observations were made in prior studies of polarized reflectance [Clarke and Parry 1985;Leroy 2001] and diffuse-specular pBRDFs [Baek et al 2018]. For this reason, our pBRDF parameterization uses ∈ [− , ] in contrast to previous BRDF datasets.…”

Atmospheric Shortwave Radiative Transfer Modeling

“…Note that both Minnaert and Lommel-Seeliger functions are also reciprocal. However, several studies question the reciprocity of the surface BRDF (Kriebel 1996, Li et al 1999, Leroy 2001, Snyder 2002.…”