  Hapke proposed a convenient and widely used analytical model to describe the
spectro-photometry of granular materials. Using a compilation of the published
data, Hapke (2012, Icarus, 221, 1079-1083) recently studied the relationship of
b and c for natural examples and proposed the hockey stick relation (excluding
b>0.5 and c>0.5). For the moment, there is no theoretical explanation for this
relationship. One goal of this article is to study a possible bias due to the
retrieval method. We expand here an innovative Bayesian inversion method in
order to study into detail the uncertainties of retrieved parameters. On
Emission Phase Function (EPF) data, we demonstrate that the uncertainties of
the retrieved parameters follow the same hockey stick relation, suggesting that
this relation is due to the fact that b and c are coupled parameters in the
Hapke model instead of a natural phenomena. Nevertheless, the data used in the
Hapke (2012) compilation generally are full Bidirectional Reflectance Diffusion
Function (BRDF) that are shown not to be subject to this artifact. Moreover,
the Bayesian method is a good tool to test if the sampling geometry is
sufficient to constrain the parameters (single scattering albedo, surface
roughness, b, c, opposition effect). We performed sensitivity tests by
mimicking various surface scattering properties and various single
image-like/disk resolved image, EPF-like and BRDF-like geometric sampling
conditions. The second goal of this article is to estimate the favorable
geometric conditions for an accurate estimation of photometric parameters in
order to provide new constraints for future observation campaigns and
instrumentations.
