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

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 presicion hollow SiC CCRs for next-generation LLR operations.

高精度角锥反射棱镜（corner-cube retroreflectors, CCRs）是先进月球激光测距（lunar laser ranging, LLR）的关键核心器件，其可实现亚毫米级的地月距离测量——这一精度水平是开展严格相对论引力检验、深化月球地球物理学研究认知的必要前提。在本研究中，我们针对孔径覆盖80~110 mm的单个CCR开发了一套完整的二维傅里叶光学模型。该模型纳入了真实的热机械波前误差、精细的衍射效应以及速度像差偏移量。我们的分析揭示了孔径尺寸与像差角偏移之间存在显著耦合效应：在近理想工况下，更大尺寸的CCR可获得较高的轴上光通量，但其窄衍射主瓣在中等像差偏移条件下会出现显著光通量损失，因此更适配主瓣更宽的小尺寸孔径方案。此外，对比熔融石英实心结构与空心碳化硅（silicon-carbide, SiC）CCR可知，空心设计不仅可实现具有竞争力乃至更优的光子返回率——尤其在相位误差相对更低的1064 nm波段——且在相同孔径尺寸下可实现近一个数量级的质量减重。上述研究结果为优化CCR设计以在真实月球环境下达成亚毫米级性能构建了鲁棒的定量分析框架，并凸显了高精度空心SiC CCR在下一代LLR任务中的显著优势。

搜集汇总

背景与挑战

背景概述

该数据集聚焦于高精度月球角立方体后向反射器（CCRs），通过二维傅里叶光学模型分析孔径大小、热机械波前误差和速度像差偏移对月球激光测距性能的影响，发现较小孔径在适度像差偏移下表现更优。同时，比较实心熔融石英和空心碳化硅设计，指出空心设计在1064 nm波长下具有更高的光子返回和显著的重量减轻优势，为下一代亚毫米级精度月球测距提供了优化框架。