Measuring distances and displacements by an interferometric technique using a low-resolution miniature fiber optic spectrometer

The feasibility of the technique utilizing the spectral-domain two-beam interference resolved by a low-resolution miniature fiber optic spectrometer is demonstrated in measuring distances and displacements when two different light sources are used. First, when a low-coherence source, namely a multimode laser diode TOLD 9 140 is used in the configuration of a dispersive Michelson interferometer, a cross-correlation procedure between the measured and the theoretical spectral interferograms is applied to estimate the group optical path differences (OPDs) between beams corresponding to different positions of one of the mirrors of the interferometer and needed in the displacement evaluations. Second, when a white-light source, namely a halogen lamp is used in the configuration of a non-dispersive Michelson interferometer, the measured spectral interferograms are processed by a phase locked loop (PLL) method, which is a special simplified version of the general recurrence non-linear data processing method previously presented, to obtain the corresponding group OPDs between beams in the interferometer or the displacements. The PLL method is realized in iterative mode which provides the unwrapped spectral fringe phase recovery. The accuracy of the iterative PLL method is investigated via processing the measured spectral interferograms.