The correct location of the optical centre of corner reflectors

Abstract

I reiterate the derivation of the optical centre position of corner reflectors given by Peck (1948). However, my derivation in the paper uses the absolute optical path lengths instead of the relative optical path lengths presented by Peck. I also show that the optical centre of the corner-cube retroreflector depends on the refractive index of the surrounding medium, and thus the surrounding medium affects its position by more than 3 µm for a typical solid glass retroreflector. The effect of the surrounding medium that is acting by means of the relative index of refraction was later reinterpreted as the absolute index of refraction, and therefore lost in the calculations. The error from such a reinterpretation exceeds the optical centre adjustment error, which is typically realized to be as low as 1 µm. In the future, the correction of such an offset in the optical centre position can improve the precision of interferometric measurements, especially those of absolute gravimeters. The corresponding effect on the measurement of gravitational acceleration can be in tenths of μGal.