Reciprocity and the formulation of inverse profiling problems

The reciprocity theorem for scalar wave functions in its global form is used to formulate inverse profiling problems in a systematic way in terms of domain integral equations in the time-Laplace domain (s domain) as well as in the time domain. The resulting equations relate the field in an “actual” configuration, containing the medium to be probed, and the field in an auxiliary background configuration. Four typical transmitter-receiver situations, important in inverse profiling experiments, are considered. In addition, the formulation of the Porter-Bojarski integral equation for “exact” inversion is discussed.