Unveiling the characteristics of the lunar surface by massive inversion of the Hapke model
Authors: Nguyen Dung Tri , Jacquemoud Stéphane , Lucas Antoine , Douté Sylvain , Ferrari Cécile , Coustance Sophie , Marcq Sébastien , Meygret Aimé 
Published: March 2024

Understanding the physical characteristics of terrestrial and planetary surfaces is imperative for unraveling the complexity of landscape formation and evolution, and to develop strategies for future planetary rover missions. Photometry is one of the most widely used methods for studying these characteristics. The light scattered by a surface is quantified by the bidirectional reflectance distribution function (BRDF), providing a uniquely detailed optical measurement for each target observed. Hapke model inversion, an approach widely used over the past decades, reveals complex surface attributes, including roughness, porosity, grain size and shape, micro-texture, mineral composition, and more.
Although the challenges of restrictive data conditions and limited computational capabilities impeded the inversion of the Hapke model for large-scale surface analysis, we&#8217;ve addressed these issues with appropriate data and a comprehensive framework. Extracting multiangular surface data requires optical sensors with pointing capabilities and, by extension, images captured from different illumination directions. Earth observation satellites such as the Pleiades constellation managed by the Centre National d&#8217;&#201;tudes Spatiales (CNES), have demonstrated their agility in extracting large-scale BRDF data on the Moon for optical sensor calibration. The processing chain involves geometric correction using digital elevation models supplied by NASA, and inversion of the Hapke model on each pixel, which is facilitated by a fast Bayesian inversion framework (Kugler et al., 2022). Inversion of the Hapke model on the BRDF extracted from each pixel generates maps of the six model parameters for the areas studied on the near side of the lunar surface, primarily the Apollo landing sites.
The BRDFs extracted from Pleiades images over the Apollo 17 landing site are consistent with prior knowledge of the photometric behavior of the Moon's surface. The quality of these BRDFs prompted us to extend our analysis to a 10&#176; x 10&#176; region around the mentioned site. Given the 1.5 km ground sampling distance of Pleiades images, the map size is 200 x 200 pixels (approximately 300 x 300 km). The distribution of the parameter values reflects the topography of the region, with a notable contrast between flat and steeply sloping areas. Optimal fits with an acceptable level of error are obtained on flat terrain, while the algorithm encounters difficulties in steeply sloping areas due to the complexity of the terrain within the large ground sampling distance.&#160; In the current state, the application of the framework is extending to cover the near side of the Moon. The parameters obtained for each terrain unit will be compared with previous works (Souchon et al., 2013; Sato et al., 2014; Gimar et al., 2022; Marshal et al., 2023; Nagori et al., 2023) and correlated with a geological map (Fortezzo et al., 2020).
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