Beam divergence errors in unbalanced laser interferometers – Case study with a free-fall absolute gravimeter FG5X

Laser interferometers play a key role in high-precision length measurements. One source of error in such a measurement is the relative length error induced by the divergence angle due to laser collimation. Often the error is calculated by the formula of Dorenwendt and Bönsch, which, however, is strictly valid only for balanced interferometers and negligible travel ranges. Free-fall absolute gravimeters, such as FG5(X), contain a highly unbalanced interferometer. This requires a further correction, which has a non-negligible contribution for large beam divergence angles, or equivalently, small beam waists.

Here we present a high-accuracy method for the determination of the beam divergence error in unbalanced laser interferometers. First, we determine the beam parameters of a beam exiting a collimator, by means of a Shack-Hartmann sensor. Then, we calculate the relative length error with a revised correction formula. Finally, we perform absolute gravity measurements with an FG5X, and compare our results to our theoretical predictions. As a result, we get a relative length error in the order of ${-2.8·10}^{-9}$ for a commercial Thorlabs TC25APC-633 triplet collimator, which is comparable with the built-in collimators of FG5(X) gravimeters. The outcome is also applicable to other interferometer setups. In special, the findings are important for the realization of the SI unit kilogram via the Kibble balance method.