Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. the full Maxwell equations

We consider solutions to the time-harmonic Maxwell Equations. For such solutions we provide a rigorous derivation of the the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. These formulas generalize those by Vogelius and Volkov, where only solutions with "transverse electric" and "transverse magnetic" symmetries were considered. Our formulas may be expected to lead to very effective computational identification algorithms, aimed at determining specific internal features of an object based on electromagnetic boundary measurements.