Interference of white light analyzed at the output of a birefringent crystal by a fibre-optic spectrometer

Spectral interference of white-light beams propagating through a dispersive birefringent crystal alone or in a tandem configuration with a Michelson interferometer is analyzed theoretically and experimentally, including the effect of a fibre-optic spectrometer. First, the spectral interference laws are expressed analytically under the condition of a Gaussian response function of a fibre-optic spectrometer and the effect of the limiting factors is specified. Second, the theoretical analysis is accompanied by two experiments employing a Michelson interferometer, a birefringent calcite crystal of two suitable thicknesses and a fibre-optic spectrometer. Within both experiments the interference fringes are resolved only in a narrow spectral range around the so-called equalization wavelength at which the overall group optical path difference between interfering beams is zero. Knowing dispersion and thicknesses of the calcite crystal along with the bandpass of the spectrometer, the theoretical spectral interferograms and equalization wavelengths are determined and good agreement with experiment is confirmed.