Bidirectional reflectance spectroscopy 7: The single particle phase function hockey stick relation

The measured volume-average single particle angular scattering functions of a large number of types of particle of interest for planetary regoliths in the visible-near-IR wavelength region can be represented to a reasonable approximation by two-parameter, double Henyey–Greenstein functions. When the two parameters of this function are plotted against one another they are found to be inversely correlated and lie within a restricted zone shaped like a hockey stick within the parameter space. The centroid of the zone is a curve that can be represented by a simple empirical equation. The wide variety of types of particles used to construct the plot implies that this equation may represent most of the particles found in regoliths. This means that when modeling the bidirectional reflectance of a regolith it may be possible to reduce the number of parameters necessary to specify the reflectance, and also to characterize the entire single particle phase function from observations at phase angles less than 90°. Even if the hockey stick relation has a finite width, rather than being a line, it restricts the parameter space that must be searched when fitting data. The curve should also be useful for forward modeling particle phase functions.