  In this paper we introduce an optical approximation into the theory of
impedance calculation, one valid in the limit of high frequencies. This
approximation neglects diffraction effects in the radiation process, and is
conceptually equivalent to the approximation of geometric optics in
electromagnetic theory. Using this approximation, we derive equations for the
longitudinal impedance for arbitrary offsets, with respect to a reference
orbit, of source and test particles. With the help of the Panofsky-Wenzel
theorem we also obtain expressions for the transverse impedance (also for
arbitrary offsets). We further simplify these expressions for the case of the
small offsets that are typical for practical applications. Our final
expressions for the impedance, in the general case, involve two dimensional
integrals over various cross-sections of the transition. We further
demonstrate, for several known axisymmetric examples, how our method is applied
to the calculation of impedances. Finally, we discuss the accuracy of the
optical approximation and its relation to the diffraction regime in the theory
of impedance.
