Inverse Scattering Under the Born Approximation Using an Object T-Matrix and Full Bistatic Spherical Sampling Geometry

Equations are derived for rapid generation of the electromagnetic inverse scattering solution of a dielectric object with known T-matrix under the Born approximation in a full bistatic spherical sampling geometry. Given an object T-matrix and no other information, the dielectric inversion can be computed without simulating forward scattering data under the conditions of quad-pol bistatic measurements over the sphere. Using the normal equation solution, the dielectric contrast is computed by deconvolving the T-matrix backprojected image with the vector bistatic point target response. The normal matrix is given analytically and has Toeplitz structure that facilitates fast Fourier transform (FFT)-accelerated conjugate gradient solutions of the matrix inverse. This is validated numerically using the T-matrix scattering solution for electrically large collections of dielectric objects. The formulation provides a semi-analytical expression for 3-D electromagnetic Born reconstruction.