Design and optimization of dihedral angle offsets for the next generation lunar retro-reflectors

Lunar laser ranging (LLR) to the Apollo retro-reflectors, which features the most long-lasting experiment in testing General Relativity theories, has remained operational over the past four decades. To date, with significant improvement of ground observatory conditions, the bottleneck of LLR accuracy lies in the retro-reflectors. A new generation of large aperture retro-reflectors with intended dihedral angle offsets have been suggested and implemented based on NASA's recent lunar projects to reduce its ranging uncertainty to be less than 1.0 mm. The technique relies on the retro-reflector's ability to offset its relative angular velocity with regard to a ground LLR observatory (LLRO), so that the LLR accuracy can be ensured along with the larger area of beam reflection. In deployment, solid corner-cube reflectors (CCRs) based on empirical successes of the Apollo 11 and 15 arrays have been selected for the next generation lunar reflectors (NGLRs) due to their stability against heat and dust problems on the Moon. In this work, we present the optical effects in designing the new retro-reflectors given various sets of intended diheral angle offsets (DAOs), and support the design principles with the measurements of of two manufactured NGLRs.