T-Matrix Backprojection Imaging for Scalar and Vector Electromagnetic Waves

Expressions for the ideal free-space backprojected image of an object with known transition matrix (T-matrix) are derived for scalar and vector electromagnetic waves in bistatic and monostatic geometries. Discrete backprojection sums are extended to continuous integrals over source/receiver spheres. Images are formed without the need to generate or process scattered field data. The final expressions only depend on regular wave functions in the frame of the object and the object T-matrix. The formulation is validated numerically using the aggregate T-matrix solution for a collection of acoustic and dielectric spheres. Applications include assessment and validation of free-space focusing and T-matrix scattering solutions.