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As nanotechnology have been developed rapidly, it is strongly needed to measure a displacement accurately and precisely. A sinusoidal frequency modulation (SFM) and a sinusoidal phase modulation (SPM) applied interferometers could be good candidates. In the SFM, a frequency of a light source is modulated sinusoidal way. In the SPM, a phase is modulated. Characteristics of these interferometers are defined by a modulation index. The modulation index is a function of both a frequency excursion and an initial optical path difference in the SFM, and is an amplitude of phase in the SPM. For displacement measurement, the displacement is obtained by a phase of an interference signal. A phase determination method using a phase-locked loop (PLL) is reported and a few pico-meters resolution is achieved for displacement measurement with a restriction of a specific modulation index. For precise and high resolution interferometer, a stabilizing the frequency of the light source is necessary. Because the modulation index is an essential parameter in the frequency stabilization, performing phase determination with the PLL in the arbitral modulation index must be developed. The nonlinear relationship between the phase and the displacement is a problem in arbitral modulation index. We have proposed a PLL for arbitral modulation index which successively changes the relationship from the nonlinear to the linear. PC-based calculations with a theoretical and an actual interference signals have been conducted to check the feasibility of proposed PLL. In this report, displacement measurements using PC-based calculation with actual interference signals are described.
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