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

Abstract 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. Highlights • The functional derivative of the scattered electric field with respect to the permittivity-contrast function is formulated for any order n , in harmonic regime and for a bounded three-dimensional object. • This result is an extension of an approach proposed in the past, for the computation of the first order functional derivative (Fréchet derivative). • Based on these derivatives, a limited functional expansion of the data with respect to the model parameter is proposed. A benchmark forward model is then used to test numerically on a scalar scattering problem validity and convergence of this new expansion. • As a perspective, these derivatives can be used to propose efficient inverse methods, in research areas involving a permittivity-contrast reconstruction. [ABSTRACT FROM AUTHOR]