Asymmetric dihedral angle offsets for large-size lunar laser ranging retroreflectors

The distribution of two-dimensional velocity aberration is off-centered by 5 to 6 microradians in lunar laser ranging, due to the stable measurement geometry in the motion of the Earth and the Moon. The optical responses of hollow-type retroreflectors are investigated through numerical simulations, especially focusing on large-size, single-reflector targets that can ultimately minimize the systematic error in future lunar laser ranging. An asymmetric dihedral angle offset, i.e. setting unequal angles between the three back faces, is found to be effective for retroreflectors that are larger than 100 mm in diameter. Our numerical simulation results reveal that the optimized return energy increases approximately 3.5 times more than symmetric dihedral angle cases, and the optimized dihedral angle offsets are 0.65-0.8 arcseconds for one angle, and zeroes for the other two angles.