  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).
