The stationary phase in spectrally resolved white-light interferometry as a refractometry tool

Abstract

A new method for the analysis of the dispersion behaviour of a transparent medium is presented: the refractive index n is obtained as a function of the wavelength λ: n = n(λ). The procedure is based on the analysis of the hybrid bi-dimensional fringe pattern obtained at the exit plane of a spectrometer which performs the spectral analysis of a white-light interferogram. The phase of the signal depends both on a spatial coordinate and on the chromatic variable wavenumber σ = λ−1. Taking advantage of the dispersion behaviour of the sample, the phase of the signal can be forced to become stationary at certain points of this hybrid plane. The line which joins the stationary phase points stores the parameters of a series expansion of the refractive index as a function of wavenumber. These parameters are experimentally obtained through an appropriate numerical fitting procedure.