Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer

The effect of a fibre-optic spectrometer on analysed spectral interference of two beams from a white-light source is studied theoretically and experimentally, including the effect of dispersion in an interferometer. First, the spectral interference law is expressed analytically under the condition of a Gaussian response function of a fibre-optic spectrometer, and then second, the theoretical analysis is accompanied by three experiments employing a fibre-optic spectrometer and a Michelson interferometer with different amounts of dispersion. Within one experiment the interference fringes are resolved over a wide spectral range and within two experiments the interference fringes are resolved only in a narrow spectral range around a wavelength at which the group optical path difference between interfering beams is zero. Knowing dispersion in the interferometer and the bandpass of the spectrometer, the positions of the interferometer mirror in the corresponding range are determined and good agreement between the recorded spectral interferograms and the theoretical ones is found.