Perturbative Reciprocal Formulation for Maxwell's Equations: a First Approach

We investigate theoretically the electromagnetic field scattered by a manufactured object having inhomogeneous perturbations of electromagnetic material properties. A well-known objet having the same geometry and homogeneous material properties is exploited as a reference. Hence only small variations from reference configuration are of interest. Starting from the Volumetric-Perturbative Reciprocal Theory (VPRT), we derive an expression of the relationship between the reference configuration (which is supposed perfectly known) and the perturbed one: in addition to the permittivity, we extend the VPRT to permeability perturbations and we derive the first order expression for axisymmetric objects having axisymmetric perturbations. The resulting formulation can be used in a direct way, for example to propagate uncertainties, as well as to solve an inverse problem for example in non-destructive testing applications.