The Bidirectional Reflectance Distribution Function (BRDF) is defined as the quotient between the spectral radiance Ir(θr,φr) reflected by a sample in a particular direction (θr,φr) and the spectral irradiance F(θi,φi) from the source that illuminates it under a direction (θi,φi) . It depends on both the incidence and viewing angles. From this point of view it represents an absolute definition of reflectance whose value, as is known, depends on the geometry of the illumination and observations directions. This function well describes variability in surface anisotropy, its shape and magnitude is determined by the structure of the sample element and its optical attributes.
The BRDF is given by
BRDF(θi,φi; θr,φr; λ)=(Ir(θr,φr))/(F(θi,φi))
where Ir is the surface leaving spectral radiance and F is the spectral irradiance , θ and φ are zenithal and azimuthal angles respectively of the direction (view angles) of reflected radiance Ir(θr,φr) and of incident irradiance F(θi,φi), λ is the wavelength.