The basis for developing projection tomographic reconstruction algorithms has been the assumption of straight-line ray-path propagation. But in the case in which propagation occurs within discretely inhomogeneous media at wavelengths of the order of the size of the scatterer, phenomena such as refraction, reflection and diffraction can no longer be neglected and a straight-line projection tomographic approach fails. This is especially evident when a large difference in refractive index occurs, such as that encountered with dm-to-mm-wave propagation in inhomogeneous atmospheric media, representing hydrometeorite distributions, the marine ocean boundary layer, the ground surface underburden, or bone and soft layers within soft tissue. An exact solution for the general vector scattering case which strictly requires a polarimetric radiative transfer approach is not available, and in this research, the assumption is made that the media are weakly diffracting so that the Born and Rytov approximations are valid. Based on this assumption, various diffraction imaging methods were developed most recently, and we are basing our studies on Devaney's back-propagation tomographic approach which was developed upon scalar wave theory. It is the main objective of this research to extend this work to the realm of electromagnetic vector wave theory for the improved diffraction-corrected imaging of radar targets embedded in clutter within the dm-to-mm-wavelength region of the electromagnetic spectrum.