Dual dihedral angles for bidirectionally scattered electromagnetic waves

A spherical coordinate system is typically used to quantify the directional characteristics of doubly hemispherical scattering of bidirectional reflectance distribution function (BRDF) entailing an incident angle or cone angle from surface normal, and a heading or azimuthal angle from the incident plane. An alternate angular coordinate system is described entailing two dihedral angles. One component is a dihedral angle from the incident plane, simply out-of-plane, and the second component is a dihedral angle from the specular beam to the detector direction projected onto the incident plane, or simply degrees off specular. The suggested system is believed easier to convey scattering characteristics, and to compute the scattering from complex surfaces such as mountains with exposed rocks, or buildings. This communication presents an example of an experimental configuration to measure a doubly hemispherical BRDF, a mathematical formulation to relate the angular coordinate systems, and a computational example