Equivalence relations and symmetries for laboratory, LIDAR, and planetary Müeller matrix scattering geometries

Symmetry relationships for optical observations of matter generally fall into several common scattering geometries. The "planetary" configuration is preferred by observers of extraterrestrial planets, "laboratory" observations are performed in the biomedical research field, and the LIDAR configuration is preferred by those using lasers to probe optical properties of horizontal surfaces with mirror or axial symmetry. This paper begins with the Stokes matrix formalism and uses symmetries of Müller matrix scattering to establish links among the mathematical symmetries of each geometric configuration. We finish the paper by identifying and correcting an influential misapplication of rotational scattering matrices in the literature. The corrected equation should find wide application in models of the LIDAR scattering process.