Topographic Mapping and Photometric Retrieval at Pixel Precision for the Máni Lunar Mission

TOPOGRAPHIC MAPPING AND PHOTOMETRIC RETRIEVAL AT PIXEL PRECISION FOR THE MÁNI LUNAR MISSION. Iris Fernandes1 Klaus Mosegaard1. Frederic Schmidt2,3, Jens Frydenvang4, 1Niels Bohr Insitute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen N, Denmark, 2Université Paris-Saclay, CNRS, GEOPS, 91405, Orsay, France, 3Institut Universitaire de France, 4Globe Institute, Øster Voldgade 7, 1350 København, Denmark. Corresponding email: ir[email protected]k Introduction: High-resolution lunar topography and precise reflectance mapping are key tools for understanding the Moon’s surface, mission planning, and de-risking Lunar landings. Building on our previous work [1,2], we have developed an improved methodology integrating DEM estimation with an advanced RTLS reflectance model [3]. This enables creation of pixel-resolution topographic and reflectance maps from existing datasets. Exemplified by mapping of the Apollo 15 site, our method significantly enhances surface characterization, aiding uncertainty quantification and surface roughness analysis. This research serves as the foundation for the scientific rationale of the Máni mission [6] which is an European Space Agency (ESA) lunar mission, currently in pre-Phase A. Unlike LRO [3], which emphasized spatial coverage, Máni (old Norse for the Moon) will deploy a satellite with a high-resolution imager optimized for acquiring high-fidelity overlapping datasets covering a wide range of observation geometries. This will refine reflectance models and improve topographic accuracy, benefiting landing site selection, mission planning, rover navigation, and scientific studies. We present a computationally efficient method that is able to simultaneously capture fine-scale topographic and reflectance variations, and at the same time produces uncertainty maps, providing pixel-wise confidence estimates. The methodology is applicable to Lunar surface characterization in general based on available images, and it forms the backbone of the ESA Máni mission data products. Methodology: Our improved approach integrates high-resolution Apollo 15 imagery with laser altimetry data [4], applying an advanced photo-clinometric (also referred to “shape-from-shading”) model that accounts for complex illumination and observation geometry. This enables pixel-level detail in both digital elevation models (DEMs) and reflectance maps, significantly improving accuracy in uncertainty quantification and surface roughness characterization. First, we carefully reproject and align the images of the target. Then, we used the quantitative radiance I calibrated from all images using photo-clinometry to estimate the slopes and height. In our mathematical framework, we solve the non-linear inverse problem: 𝐼 = 𝑔(𝑇, 𝑘𝐿,𝑘𝑉,𝑘𝐺) where 𝐼 is the observed light intensity, 𝑇 is the unknown terrain height, 𝑘𝐿,𝑘𝑉,𝑘𝐺 are the unknown RTLS reflectance coefficients [2], and 𝑔 is the forward function mapping the surface parameters into the observations. We used the LOLA DEM as a prior in order to refine pre-existing laser ranging topography. The solution is obtained in two steps where the first includes determination of terrain gradients and reflectance coefficients, and the second is estimation of the DEM based on the computed gradients. Our formulation allows us to derive pixel-wise confidence estimates, incorporating illumination variations, observational noise, and modeling uncertainties, advancing lunar terrain analysis for future missions. Figure 1 - Results from the Apollo 15 landing site. (a) and (b) Selected NAC images (c) LOLA DEM (d) Computed High-resolution DEM revealing small-scale features such as small crater ejecta and boulder fields. Figure 2 – Results of the kG map. The increased resolution allows for the identification of fine details, not only in surface topography, but also in surface properties. Results: Using the Apollo 15 landing site as a test case, we processed 6 images with Solar North azimuths between 116° and 254° , view angles close to 0° , and incidence angles between 27° and 59° . Figure 1 shows the computed DEMs compared to the LOLA data from the area [5]. Figure 2 shows the reflectance coefficients 𝑘! , indicating a significant variability of the surface roughness over the area. Figure 3 is a map of the posterior uncertainty (standard deviation) of topographic heights, estimated by the method. Data uncertainties and a priori uncertainty about the difference between the laser ranging DEM and the unknown high-resolution DEM, is carefully tracked through the equations to produce reliable uncertainties on the estimated high-resolution DEM. Figure 3 - Spatial representation of the confidence level in the derived topography, enabling a more robust assessment of terrain reliability for mission planning applications. Uncertainties are low (4 cm) compared to the terrain height variation (15 m), where the highest uncertainty is at the Lunar module. Discussion: This work is based on probabilistic inverse problem theory, as presented in [1], and on the reflectance estimation methodology put forward in [2]. A key advantage of the probabilistic formulation is its ability to systematically trace all sources of noise in both observational data and the mathematical model, eliminating the need for arbitrary tuning parameters or ad-hoc assumptions. The combined method reconstructs high-resolution topography and reflectance maps purely from available data and reasonable a priori bounds on the solution, ensuring physically meaningful results. In our inverse problem framework, we use a constrained optimization approach where observational constraints (imagery and altimetry) and well-defined physical bounds on the solution are combined rigorously. The Sylvester equation ensures consistency across datasets, reinforcing reconstruction reliability at a high computational speed. Additionally, the integration of an advanced RTLS model refines surface albedo estimation, linking observed radiance to terrain features without empirical corrections. The uncertainty quantification maps are the first of its kind in lunar topographic modeling, giving confidence estimates that identify regions of lower reliability and linking uncertainty to physical causes, such as insufficient illumination in images. This insight enhances the understanding of data limitations and provides a diagnostic tool for future lunar imaging missions. This capability directly impacts the Máni ESA lunar mission, which is designed to optimize data acquisition for high-resolution reflectance modeling. Unlike LRO, which prioritizes broad spatial coverage, this mission will systematically acquire multi-angular overlapping images, reducing shadowed region uncertainties and improving photometric inversion reliability. This refined observational strategy will enhance topographic and reflectance models. Beyond theoretical advancements, these results have operational significance. The uncertainty maps serve as a critical tool for mission planning and risk assessment, guiding landing site selection and rover path planning by highlighting areas where additional data is needed. By associating uncertainty with illumination conditions, we provide a physically interpretable metric for decision-making in future lunar and planetary missions. Ultimately, this work establishes a path to rigorous mathematical foundation for high-resolution lunar mapping. The combination of inverse problem theory, photometric modeling, and uncertainty quantification offers a self-consistent methodology applicable to other celestial bodies. With the ESA Máni mission providing unprecedented datasets, this research is a crucial step toward next-generation planetary cartography that is both scientifically robust and operationally relevant. References: [1] Fernandes I. and Mosegaard K. (2022) Planetary and Space Science, 218, 105514. [2] Ceamanos X., et al.. (2012) J. Geophys. Res., 118, 1323-1346. [3] Lucht, W.; et al. (2000) IEEE TGRS, 38, 977998 [4] Robinson M. S. et al. (2010) Space Sci. Rev., 150, 81-124. [5] Smith D. E. et al. (2010) Geophys. Res. Lett., 37, L18204. [6] https://activities.esa.int/4000146824