  The measurement of the lateral Casimir force between two aligned sinusoidally
corrugated Au-coated surfaces has been performed in the nonadditive regime. The
use of deeper corrugations also allowed to demonstrate an asymmetry in the
phase dependences of the lateral Casimir force, as predicted earlier. The
measurement data are found to be in excellent agreement with the exact
theoretical results computed at T=300 K including effect of real material
properties. The deviations between the exact theory and the proximity force
approximation are quantified. The obtained results are topical for applications
in nanomachines.
