Stationary phase in Spectrally Resolved White Light Interferometry (SRWLI) as a refractometry tool

A new method for real-time obtention of the dispersion behavior n=n(λ) of a transparent media is presented. The procedure stands on the analysis of the hybrid bidimensional 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 the chromatic variable wavenumber σ=λ-1. Taking profit of the dispersion behavior of the sample the phase of the signal can be forced to become stationary at certain points of this hybrid plane. The line which connects the stationary phase points can be experimentally obtained through an appropriate numerical fitting. It stores the parameters of a Cauchy approximation for the refractive index.