Theoretical considerations for time‐dependent transient scattering

Transient scattering, particulary the associated pole configuration, is nowadays intensively studied for target identification purposes. At least theoretically, it is interesting to understand the effects introduced by time dependence. However, these heretofore neglected phenomena might be even of practical importance for cases where the velocities are close to the wave velocity, e.g., acoustics, or where the distances between scatterer and source are small. Although the simple Doppler effect becomes ambiguous for short pulse scattering, the velocity effects are present, manifesting themselves in virtual migration of poles and virtual creation of poles of higher multiplicity. The new ideas are explored by using the spectral approach, i.e., the wealth of studies available on Doppler effects and harmonic scattering is exploited, and by complex integration the conclusions pertinent to pulse scattering can be drawn. Inasmuch as this is a theoretical study, focusing mainly on electromagnetic waves, the exact relatlvistic formalism is used. The first‐order velocity effects, which are of more practical interest, are emphasized.