The Influence of Dihedral Angle Error Stability on Beam Deviation for Hollow Retro-Reflectors

Retro-reflectors consist of three reflective optical surfaces, which are oriented to reflect the input beam by 180 ◦. For retro-reflector components, it is common to specify an angular beam deviation tolerance, or rather the deviation from the exact 180 def return direction. Precision-aligned retro-reflectors provide 180 deg beam deviation with tolerances on the order of an arcsecond. It is well known that the performance of the retro-reflector depends on the ability to precisely orient the reflective surfaces at mutually perpendicular angles. Precision assembly is therefore critical to ensure highly accurate beam deviation. The dihedral angle errors, and hence the reflected beam deviation, can be measured for the retro-reflector after fabrication, typically by using interferometric techniques. Yet, what is not commonly reported for a fabricated retro-reflector is the stability of the angular beam deviation. For instance, thermo-mechanical effects of the components will contribute to variations in the return beam direction. While the actual stability is design-specific one can develop a mathematical representation for the expected change in the reflected beam direction as a function of the variation in the dihedral angle errors. Presented here is a mathematical formulation for a hollow retro-reflector's beam deviation as a function of the dihedral angle error stability.