Dispersion curve measurement using Talbot bands

Abstract

Talbot bands, looking like a channelled spectrum, are produced when a phase plate is partly inserted in the field of a spectroscope. The position and the spacing of the bands in the spectrum of the source directly depends on the optical thickness and therefore the refractive index of the phase plate. In the case of a transmission grating spectroscope, the bands appear only in spectral orders on the same side as the phase plate. The bands can be observed also in case of a two stepped plate, their position being related to the difference of the two refractive indices of the plate, they appear in spectrum orders on the side where the higher index half plate have been inserted in. Using this early known phenomenon in conjunction with modern technology, we propose a method based upon an accurate determination of the positions of these dark bands for computing the dispersion curve of any transparent liquid or solid material, the curve being built up from only one experiment whereas several are required usually. In this paper, after the method have been described, experimental results obtained with known glasses are reported proving the efficiency and the reliability of the technique. Also this method is extended to birefringent materials, it is shown that the extraordinary and ordinary dispersion curve can be obtained simultaneously. Experimental results on liquid crystals materials are reported Proposition d'une nouvelle methode pour obtenir la courbe de dispersion de materiaux transparents. Methode basee sur une determination precise de la position des bandes dans le spectre, associee a une manipulation numerique des donnees conduisant a l'obtention de la courbe de dispersion et ce en une seule experience