  Layers with gradient refractive-index profile are an attractive alternative
to conventional homogeneous stack coatings. However, the optical
characterization and monitoring of the graded refractive-index profile is a
complex issue, which has been typically solved by using a simplified model of
mixed materials. Although this approach provides a solution to the problem, the
precision, which can be expected from optical characterization of the
refractive index gradient, remains unclear. In this work, we study optical
characterization of SiO_xN_y layers deposited via reactive dual ion beam
sputtering. To characterize the deposited layers, we use several methods
including reflectance, and transmittance spectra at a broad range of incident
angles, together with spectral ellipsometry. All the data were simultaneously
fitted with a general profile of refractive index. The expected profile used in
our fit was based on characterization of SiO_xN_y layers with a varying
stoichiometry. By altering of the profile, we discussed sensitivity of such
alternation on fit quality and we studied ambiguity of merit-function
minimization. We demonstrate that while the scanning of particular parameters
of the profile can be seemingly very precise, we obtain a very good agreement
between the experimental data and model for a broad range of gradient shapes,
where the refractive-index value on major part of the profile can differ as
much as 0.02 from the mean value.
