Real-time normalization and nonlinearity evaluation methods of the PGC-arctan demodulation in an EOM-based sinusoidal phase modulating interferometer

Abstract

In order to reduce the nonlinearity caused by an error of phase modulation depth, carrier phase delay and non-ideal performance of the low pass filters in the sinusoidal phase modulating interferometer (SPMI), a modified EOM-based SPMI is proposed in this paper to realize real-time normalization of the quadrature components for the arctangent approach of phase generated carrier (PGC-Arctan) demodulation. To verify the effectiveness of the real-time normalization technique, a fixed-phase-difference detection method is presented to evaluate the periodic nonlinearity in real time. The modified EOM-based SPMI is consisted of a monitor interferometer and a probe interferometer. The two interferometers share a reference corner cube, which is mounted on a slowly moving stage, thus periodic interference signals are generated for real-time normalization of the quadrature components in PGC demodulation. Subtracting the demodulated phase of the monitor interferometer from the phase of the probe interferometer, the phase to be measured can be obtained. The fixed-phase-difference detection method is realized by detecting an interference signal with two photodetectors, which are placed at an interval of quarter fringe, and the variation of the fixed-phase-difference can reflect the nonlinear error in PGC demodulation. Experiments of real-time normalization, nonlinear error evaluation of PGC demodulation, and displacement measurement were implemented to demonstrate the effectiveness of the proposed method. Experimental results show that the nonlinear error of phase demodulation reduced to less than ± 1° with real-time normalization, and nanometer displacement measurement is realized.

Precision measurement of the refractive index of air using a phase modulated homodyne interferometer with a variable length vacuum cavity

“…Usually, PGC-Arctan approach is adopted to demodulate the phase ϕ(t), in which a pair of quadrature components is obtained by mixing I(t) with cos(ω c t) and cos(2ω c t), respectively, as shown in figure 2. As previous works mentioned, due to the disturbance of light intensity, the drift of modulation depth, and the phase delay of carrier phase, the quadrature components are often deteriorated to a time-varying ellipse [21][22][23]:…”