Relationship between and measurement of differential scattering coefficient (σ0) and bidirectional reflectance distribution function (BRDF)

The microwave and optical scattering formulations are reviewed, a relationship between them at the same wavelength is presented, and the measurement conditions for obtaining range-independent and equipment-independent values are discussed. It is shown that the physical mechanism of scattering of electromagnetic beams from a surface can be quantified by either a differential scattering coefficient (σ⁰) or a bidirectional reflectance distribution function (BRDF). For a diffuse surface, σ⁰=4π BRDF cos θ_i cos θ_r, where θ_i and θ_r are the incident and reflected angles, respectively, from the surface normal. The geometrical constraints inferred in the measurement of coherent electromagnetic wave scattering from relatively small objects are easily satisfied to obtain range- and equipment-independent values, but care in experimental design is required when dealing with large surfaces. More care is also required when dealing with surfaces entailing specular features in addition to diffuse features