Reconciling and validating the Ashworth-Davies Doppler shifts of an arbitrarily translating mirror.

We simplify, to first order in , the generalized, special relativistic treatment of a Doppler shift from an arbitrarily translating mirror originally derived by Ashworth and Davies [Proc. IEEE64, 280 (1976)IEEPAD0018-921910.1109/PROC.1976.10098]. We show that it is in good agreement with a somewhat modified, but more intuitive, derivation that only considers the constancy of the speed of light. We experimentally demonstrate the theoretical predictions using phase-insensitive frequency measurements in a liquid crystal light valve with mirror translations of only a few tens of nanometers per second.