  The impact of imperfections, which are always present on surfaces of lenses
with centimeter-size curvature radii, on the Casimir force in the lens-plate
geometry is investigated. It is shown that the commonly used formulation of the
proximity force approximation is inapplicable for spherical lenses with surface
imperfections, such as bubbles and pits. More general expressions for the
Casimir force are derived that take surface imperfections into account. Using
these expressions we show that surface imperfections can both increase and
decrease the magnitude of the Casimir force up to a few tens of percent when
compared with the case of a perfectly spherical lens. We demonstrate that the
Casimir force between a perfectly spherical lens and a plate described by the
Drude model can be made approximately equal to the force between a sphere with
some surface imperfection and a plate described by the plasma model, and vice
versa. In the case of a metallic sphere and semiconductor plate, approximately
the same Casimir forces are obtained for four different descriptions of charge
carriers in the semiconductor if appropriate surface imperfections on the lens
surface are present. The conclusion is made that there is a fundamental problem
in the interpretation of measurement data for the Casimir force, obtained by
using spherical lenses of centimeter-size radii, and their comparison with
theory.
