Second-order Doppler-shift corrections in free-fall absolute gravimeters

In a free-fall absolute gravimeter usually a Michelson type interferometer is employed to track the trajectory of a freely falling retroreflector. The accelerated motion of the retroreflector produces a Doppler-shift in the laser wavelength. From the interference signal (beat signal) of the Doppler-shifted and the reference electromagnetic waves the relative motion of the freely falling retroreflector with respect to an inertial reference retroreflector is reconstructed. Considerations of second-order Doppler-shift terms lead to a correction in the acceleration due to gravity of several microgals (1 µGal = 10 nm s −2 ). This correction is commonly called speed of light correction . To date different correction formulae have been proposed, which differ by several microgals. In this paper we review several previous publications and show the reasons for the different results.