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 fibreoptic 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.
IntroductionRecent advances in spectral-domain optical interferometry [1, 2] have attracted considerable interest in using portable miniature fibre-optic spectrometers in various fields of optics and in measuring their parameters and characteristics. Among the functions and parameters characterizing spectrometers, response functions and bandpasses are the most important. Time-domain and spectral-domain interferometric techniques [2,3], including the applications of Fabry-Perot and Michelson interferometers or prism-and grating-based spectrometers, play key roles in measuring not only the temporal coherence functions and the spectra of light sources, but also the parameters and characteristics of the spectral instruments [4][5][6][7][8][9]. Thus, instrument functions [4], modulation transfer functions [5] and spectral slit widths of a grating [5] and a prism spectrometer [6] have been measured or determined for given spectrometer slit widths. More recently, time-domain and spectral-domain low-coherence interferometry has been used to measure the spectral bandpasses of a fibre-optic spectrometer with different read optical fibres [7]. Most recently, a white-light spectral interferometric technique has been used to measure the wavelength dependence of the spectral bandpass of the spectrometer [8]. Moreover, the constant-bandwidth operation of the Czerny-Turner monochromator has been reviewed [9].