Abstract
Abstract
We present a unified theoretical and simulation study of white-light spectral interferometry for two complementary metrology tasks: thickness measurement of a thin film on a substrate, and group-refractive-index dispersion measurement of a dispersive optical element. Both rest on the channeled spectrum of a slightly dispersive Michelson interferometer recorded by a fiber-optic spectrometer, following the framework of Hlubina and co-workers. For SiO$_2$/Si samples (100--450\,nm), we model the reflectance, fringe visibility, phase change on reflection and nonlinear phase, and retrieve thickness by Levenberg--Marquardt fitting of noisy channeled spectra. Retrieved thicknesses agree with true values within $\pm$0.2\,nm, with correlation coefficients above 0.998, and a $\chi^2$ scan shows a single sharp minimum at the true thickness. For an uncompensated BK7 beam splitter, we derive the equalization condition $N_g(\lambda_\mathrm{eq})=\Delta L/t+1$ and analyze 35 interferograms for mirror displacements of 10.990--11.709\,mm, giving equalization wavelengths of 480--860\,nm and group indices from 1.558 to 1.525 in agreement with the Sellmeier model. The operating point $\Delta L=11.30$\,mm gives $\lambda_\mathrm{eq}=598.5$\,nm and $N_g=1.5401$. Integrating the group index also recovers the phase index to within $7\times10^{-9}$ in the noiseless case. Together, the results establish the method as a scan-free, single-instrument approach to thin-film and dispersion metrology.