Demonstration of the nontrivial boundary dependence of the Casimir force

The Casimir force between an aluminum-coated plate with small sinusoidal corrugations and a large sphere was measured for surface separations between 0.1 and 0.9 mu m using an atomic force microscope. The measured force shows significant deviation from the perturbative theory. The measured Casimir force between the same sphere and flat plate shows good agreement with the same theory in the limit of zero amplitude of corrugation. These together demonstrate the nontrivial boundary dependence of the Casimir force. [S0031-9007(99)09229-7].