High-frequency diffraction can be described by iterations based on an approximate formulation of the boundary conditions. The method formulated is analogous to the Born series of scattering theory. It is used to study the interaction of short bunches with the beam environment in terms of the impedances. The impedances of typical elements of an accelerator structure are obtained. The crosstalk between elements, the impedance of a periodic array, and the effect of a taper are discussed. The method can be applied to a cavity of an arbitrary shape.