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A graded refractive index silicon oxynitride (SiOxNy) thin film was prepared on a silicon substrate by ion assisted deposition. Spectroscopic ellipsometry (SE) was used to optically analyze the film. The measured SE spectra (2500-8200 Å) were analyzed with several fitting models, whose construction was based on an Auger depth profile of the film. In each model, the optical response of SiOxNy was described using the Bruggeman effective medium approximation, by modeling it as a physical mixture of two distinct phases: silicon dioxide and silicon nitride. Grading was modeled by varying the silicon nitride volume fraction with depth below the surface, according to an assumed profile. Fitting results were very sensitive to the profile chosen, which was different for each model. Experimentation with the profile led to a model which produced a remarkably good fit, over the entire spectral range. As a result, the film thickness and its refractive index profile were determined. The index profile determined by SE analysis was found to be consistent with the Auger profile.