Extension of Scalar to Vector Propagation Tomography — A Computer Numerical Approach

Microwave imaging by three‐dimensional Born linearization of electromagnetic scattering

“…To prove this statement, let us consider an incident electric field vector polarized in a coordinate direction, for instance, As can be noticed, the present formulation allows us to take into account the vectorial nature of the scattered electric field, in that the terms containing the second derivatives make it possible to partially take into account the depolarization effects due to a scatterer, which, in general, can be inhomogeneous in all three spatial directions. Though within the Born approximation, such a formulation is then more complete and contains more information than the scalar formulation commonly used for imaging models that disregard depolarization effects [Slaney et al, 1984;James et al, 1985], and according to which the scattered field can be defined by the where On is equal to 0 outside the nth subdomain. Furthermore, we note that if we choose a suitable incident electric field vector, the computation of (24) can be considerably simplified.…”

“…It is worth noting that the moment method is not the only possible one, as other techniques could be used to invert the Fredholm equation of electromagnetic scattering (for a detailed reference see for example James et al [1985]). In particular, filtered backpropagation [Devaney, 1985[Devaney, , 1986] could be employed directly, after some modifications, to generate a pseudoinverse.…”