A critical assessment of the Hapke photometric model

Abstract

The photometric model developed by Hapke is commonly used to study surface structure and composition of atmosphereless celestial bodies using photometric measurements. However, this model has shortcomings that weaken its applications. For instance, some of the model parameters are empirical and mutually dependent. Moreover, the photometric model is eclectic and approximate; e.g., (1) the model simultaneously considers the single-scattering phase-function as backscattering and isotropic when describing, respectively, incoherent and coherent multiple scattering, which is physically impossible; (2) the approximation of the incoherent multiple scattering function takes into account the function anisotropy for the incident and emergent angles, but ignores the anisotropy for the azimuth angle that is of equal importance; (3) the model also ignores the dependence of the shadow-hiding effect of particles and coherent-backscattering enhancement on illuminating/viewing geometry, accounting only for the phase-angle component; (4) the azimuthal dependence of the shadow-hiding effect on random topographies is introduced ad hoc and is not verified; moreover, the shadow phase function may produce a non-physical maximum at large angles of viewing. We test the Hapke model using a computer simulation of ray-tracing in particulate surfaces, showing significant differences between the Hapke model and the ray-tracing results. We also apply the Hapke model to the interpretation of laboratory photometry of several well-characterized powdered samples measured in two wavelengths. The samples were measured in three states: as particles in air, as a particulate surface formed by freely spilled particles, and after compressing the particulate surface. The Hapke model parameters were completely inconsistent in the interpretation of these laboratory data. Our attempt to map the Hapke parameters using a series of telescopic calibrated images of the Moon acquired at different phase angles demonstrates that the model does not provide a physically meaningful distribution of its parameters. We also suggest that the small increase of the circular polarization ratio μC at decreasing phase angle (<10°), which is observed for lunar samples, is not evidence of the coherent-backscattering effect of the Moon. We suggest that Clementine observations carried out with the UV–Vis and NIR cameras demonstrate that the coherent-backscattering effect exists only for bright lunar surface areas with albedo higher than 30%.