Precision absolute gravity measurements are growing in importance, especially
in the context of the new definition of the kilogram. For the case of free-fall
absolute gravimeters with a Michelson-type interferometer tracking the position
of a free falling body, one of the effects that needs to be taken into account
is the speed of light perturbation due to the finite speed of propagation of
light. This effect has been extensively discussed in the past, and there is at
present a disagreement between different studies. In this work, we present the
analysis of new data and confirm the result expected from the theoretical
analysis applied nowadays in free-fall gravimeters. We also review the standard
derivations of this effect (by using phase shift or Doppler effect arguments)
and show their equivalence
