  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.
