Adjoint fields for inverse profiling with intensity-type measurements

In some practical applications, the phase measurement of the scattered fields are too corrupted by noise to be useful or even there is no phase measurement at all (e.g. optical measurement setup). Even if there is some effort nowadays to provide experimental setups which measure all components of the scattered fields, our purpose herein is to investigate an inversion scheme based on modulus information only. Instead of trying to extract some phase information from the measurement, we directly propose an iterative approach, where the parameter of interest, namely the contrast of permittivity, is gradually adjusted by minimizing a cost functional properly defined