Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces

The bidirectional reflectance distribution function (BRDF) is one of the most important surface properties for terrestrial remote sensing, but its definition for structured surfaces is not fully understood. The BRDF of flat surfaces has a straightforward definition and is usually considered to be reciprocal, which means the value is the same when the source and detector angles are switched. Structured surfaces, such as forest canopies and grasslands, require an extension of the definition of BRDF and some additional measurement conditions. In this paper, a definition for the BRDF of structured surfaces is proposed, and it is shown that with this definition, the BRDF is reciprocal. In addition some of the related geometrical measurement requirements are discussed. It is concluded that reciprocity should apply for both measurements and models of structured surfaces and that field measurements violate reciprocity not because the BRDF itself is nonreciprocal, but because of uncorrected geometric and radiometric factors