Efficiency of BRDF sampling and bias on the average photometric behavior

TL;DR

This paper improves the efficiency of Bayesian uncertainty estimation for Hapke BRDF models and analyzes how observation geometry affects parameter retrieval and surface homogeneity detection.

Contribution

It introduces a faster numerical implementation for Bayesian uncertainty estimation and evaluates the impact of observation geometry on parameter accuracy and surface heterogeneity detection.

Findings

Principal plane with high incidence is the most efficient sampling geometry.

Efficient geometries yield more accurate Hapke parameter retrieval.

Bayesian analysis can distinguish between homogeneous and heterogeneous surfaces with noise.

Abstract

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.