Far field in transient two-dimensional scattering

A heuristic definition of far field is given for time-domain two-dimensional scattering that simplifies the expression of the scattered far field as an integral over the sources. The meaning of this definition and of the ensuing simplifications is clarified by Fourier transforming the approximate time-domain result to compare it with well-known frequency-domain expressions in the Fresnel and Fraunhofer approximations.