A numerical method to invert the dielectric permittivity profile from the R
iccati equation using the Newton-Kantorovich iterative scheme is described.
Instead of handling the equations in terms of usual geometrical depth, we
determine the profile as a function of the electromagnetic path length sinc
e the convergence and the stability of the solution are found to be signifi
cantly better in this case. The initial profile used as a starting, point f
or the inversion is obtained by another method employing successive reconst
ruction of dielectric interfaces and homogeneous layers in a step-like form
. This method, though not always accurate, is fast and well suited for the
approximate reconstruction of the profile, thus creating ideal starting con
ditions for the previous approach. As a result, the computation time is con
siderably reduced without using any a priori information. The approach is a
pplicable to both continuous and discontinuous profiles of high contrast an
d exhibits a good stability of the solution with respect to noisy input dat
a. A lossy medium profile can also be inverted provided the overall thickne
ss of the inhomogeneous slab and the background permittivity are known.