A survey of the physical optics inverse scattering identity

The physical optics approximation is applied to the acoustic and electromagnetic direct scattering integral representation, yielding an inverse scattering identity which relates the characteristic function of a scatterer to the three-dimensional spatial Fourier transform of the augmented far-field scattering amplitude. This identity requires full scattering information for all frequencies and aspect angles. An integral equation for incomplete scattering information for this identity is developed. This integral equation is for the unknown characteristic function of the scatterer in terms of the known incomplete scattering information. The kernel of this integral equation is the three-dimensional spatial Fourier transform of the known characteristic function of the scattering information aperture. A regularized analytic closed-form solution to this integral equation is obtained. Synthesized numerico-experimental results verifying this solution are presented. The details of some special cases, consisting of a priori knowledge about the scatterer or the scattering information aperture, are presented.