Identification versus imaging

Summary form only given, as follows. The singularity expansion method (SEM) represents the Laplace transform of a transient electromagnetic signal scattered by a target in terms of the superposition of a complex pole series and entire functions. Since the pole pattern in the Laplace domain is representative for a particular target, identification schemes have been built upon this observation, yet they suffered from the very noise sensitivity of pole extraction algorithms and from the long-time misunderstanding of the role of the entire functions. The clarifying contributions by Dudley and his students are recognized, in particular for the application of SEM to ultrasonic elastic wave scattering for nondestructive testing purposes. It turned our that in this case, the entire function contributions become overwhelmingly dominant, and therefore, it seemed much more appropriate to concentrate on these "first arrivals" employing imaging instead of identification schemes. The development and evaluation of such imaging algorithms is reviewed as being approximate linearized solutions of inverse scattering, and applications with regard to scalar acoustic, vector electromagnetic and tensor elastic waves are presented, which range from ultrasonic testing to ground probing radar. In cases where resonant-complex pole-contributions contaminate the-entire function-first arrivals, nonlinear inverse scattering schemes have to be applied, and some results referring to the Ipswich data are presented.