High-order functional derivatives of the diffracted field according to the permittivity-contrast function

TL;DR

This paper develops a method to compute high-order functional derivatives of the diffracted field with respect to permittivity contrast, enhancing data fitting in electromagnetic inverse problems.

Contribution

It introduces a systematic approach to calculate derivatives of any order, extending existing methods and demonstrating improved data fitting through numerical simulations.

Findings

Higher order derivatives significantly improve data fitting.

Numerical results confirm convergence and effectiveness of the approach.

Method applied to cylindrical objects under TE polarization.

Abstract

In this work, we propose to extend an approach to calculate at any order $(n)$, the functional derivative of the diffracted field with respect to the permittivity-contrast function. These derivatives obtained for different orders are used to perform an expansion of the data according to the studied model parameter. Its convergence is discussed throughout some numerical results, obtained in the case where the forward model used to simulate the diffracted field is built in the framework of the volume integral formulation. In particular, we show that taking into account higher order derivatives improve drastically the data-fitting. The numerical application considered consists of a cylindrical object illuminated by an incident field under a ${\rm TE}$ polarisation (electric component parallel to the invariance axis).