High-Precision Lunar Corner-Cube Retroreflectors: A Wave-Optics Perspective

Abstract: High-precision corner-cube retroreflectors (CCRs) are critical for advanced lunar laser ranging (LLR) because they enable sub-millimeter-scale measurements of the Earth-Moon distance -- a level of precision essential for rigorous tests of relativistic gravitation and for advancing our understanding of lunar geophysics. In this work, we develop a comprehensive two-dimensional Fourier-optics model for single CCRs with apertures ranging from 80-110 mm. Our model incorporates realistic thermal-mechanical wavefront errors, detailed diffraction effects, and velocity aberration offsets. Our analysis reveals a strong coupling between aperture size and aberration angular offset: while larger CCRs deliver high on-axis flux under near-ideal conditions, their narrow diffraction lobes suffer significant flux loss at moderate aberration offsets, thereby favoring smaller apertures with broader main lobes. Furthermore, comparisons between solid fused-silica and hollow silicon-carbide (SiC) CCRs show that hollow designs not only achieve competitive or superior photon return -- particularly at 1064 nm, where phase errors are relatively reduced -- but also offer nearly an order-of-magnitude mass reduction for the same aperture sizes. These results establish a robust quantitative framework for optimizing CCR designs to perform at the sub-millimeter level under realistic lunar conditions and underscore the advantages of precision hollow SiC CCRs for next-generation LLR operations.