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

In this work, we propose to extend an approach to calculate at any order (n), the functional derivative of the scattered field with respect to the permittivity-contrast function of a three-dimensional object. These derivatives obtained for different orders are used to perform an expansion of the data according to the studied model parameter. Its validity and convergence are tested throughout some numerical results obtained for a scalar scattering problem. In particular, we show that taking into account higher order derivatives improve drastically, the fitting of benchmark data generated by a well-known forward model.