  Recent advances in experimental techniques now permit to measure the Casimir
force with unprecedented precision. In order to achieve a comparable precision
in the theoretical prediction of the force, it is necessary to accurately
determine the electric permittivity of the materials constituting the plates
along the imaginary frequency axis. The latter quantity is not directly
accessible to experiments, but it can be determined via dispersion relations
from experimental optical data. In the experimentally important case of
conductors, however, a serious drawback of the standard dispersion relations
commonly used for this purpose, is their strong dependence on the chosen
low-frequency extrapolation of the experimental optical data, which introduces
a significant and not easily controllable uncertainty in the result. In this
paper we show that a simple modification of the standard dispersion relations,
involving suitable analytic window functions, resolves this difficulty, making
it possible to reliably determine the electric permittivity at imaginary
frequencies solely using experimental optical data in the frequency interval
where they are available, without any need of uncontrolled data extrapolations.
