The Casimir force between rough metallic plates

The Casimir force between two metallic plates is affected by their roughness state. This effect is usually calculated through the so-called "proximity force approximation" which is only valid for small enough wave vectors in the spectrum of the roughness pro. le. We introduce here a more general description with a wave-vector-dependent roughness sensitivity of the Casimir effect. Since the proximity force approximation underestimates the effect, a measurement of the roughness spectrum is needed to achieve the desired level of accuracy in the theory-experiment comparison.