  The Hapke model has been widely used to describe the photometrical behavior
of planetary surface through the Bi-directional Reflectance Distribution
Function (BRDF), but the uncertainties about retrieved parameters has been
difficult to handle so far. A recent study proposed to estimate the
uncertainties using a Bayesian approach (Schmidt et al., Icarus 2015). In the
present article, we first propose an improved numerical implementation to speed
up the uncertainties estimation. Then, we conduct two synthetic studies about
photometric measurements in order to analyze the influence of observation
geometry:
  First, we introduce the concept of "efficiency" of a set of geometries to
sample the photometric behavior. A set of angular sampling elements (noted as
geometry) is efficient if the retrieved Hapke parameters are close to the
expected ones. We compared different geometries and found that the principal
plane with high incidence is the most efficient geometry among the tested ones.
In particular, such geometries are better than poorly sampled full BRDF.
  Second, we test the analysis scheme of a collection of photometric data
acquired from various locations in order to answer the question: are these
locations photometrically homogeneous or not? For instance, this question
arises when combining data from an entire planetary body, where each spatial
position is sampled at a single geometry. We tested the ability of the Bayesian
method to decipher two situations, in the presence of noise: (i) a
photometrically homogeneous surface (all observations with the same photometric
behavior), or (ii) an heterogeneous surface with two distinct photometrical
properties (half observations with photometric behavior 1, other half with
photometric behavior 2). We show that the naive interpretation of the results
provided by Bayesian method is not able to solve this problem.
