Inverse Scattering

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Abstract
A three-dimensional electromagnetic Inverse Scattering Identity, based on the Physical Optics approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse scattering identity is proven. This identity requires complete scattering information for all frequencies and aspect angles. A non-singular integral equation is developed for the arbitrary case of incomplete frequency and/or aspect angle scattering information. A general closed form solution to this integral equation is developed, which yields the shape of a scatterer from such incomplete information. A specific practical radar solution is presented. The resolution of this solution is developed, yielding short-pulse target resolution radar system parameter equations. The general inverse scattering and radiation problem associated with the three-dimensional inhomogeneous scalar field Helmholtz wave equation is formulated as a Fredholm integro-differential equation of the second kind. The far-field inverse integro-differential equation is solved in closed form with the aid of a single resolvent integral operator, which can be readily evaluated numerically with the aid of the fast Fourier transform algorithm. The inverse integro-differential equation and its solution are then generalized to the reduced vector wave equation resulting from Maxwell's equations. A formal statement of the inverse problem is presented. It is shown that the first order Neumann series solution of the inverse integro- differential equation as well as the first order term of its exact solution represent the physical optics approximation and the equations governing synthetic microwave holography.

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