On the physical contents of some integral equations for inverse scattering from inhomogeneous objects

The physical contents of some integral equations that have been frequently used in recent years in connection with solutions of inverse source problems and of inverse scattering problems are discussed. It is shown that the integral equations can only provide information about a filtered structure of a source or a weak scatterer. The filtering is found to remove all the Fourier components of the source distribution or of the scattering potential that represent details smaller than about a wavelength of the radiated or of the scattered field. The nature of the associated filtered field is also studied, and a comparison of the integral equation method with an older reconstruction method is made.