Sinusoidal phase modulating absolute distance measurement interferometer combining frequency-sweeping and multi-wavelength interferometry.

A sinusoidal phase modulating absolute distance measurement (ADM) interferometer combining frequency-sweeping interferometry (FSI) and multi-wavelength interferometry (MWI) is proposed in this paper. The swept frequency in FSI and the wavelengths for MWI are calibrated by an optical frequency comb, so the distance measurement can be directly traced back to the SI definition of a meter. With a simple optical structure, an ADM interferometer consisting of a measurement interferometer and a monitor interferometer is constructed without polarization optics. A near-infrared external cavity diode laser (ECDL) calibrated by an optical frequency comb is used as a work source of the measurement interferometer for frequency sweeping and hopping. The monitor interferometer using a He-Ne laser runs parallel to the measurement interferometer to monitor the fluctuation of the measured distance during the measurement. Experiments for absolute distance measurements in a range of 8.25 m were carried out to verify the feasibility of the proposed ADM interferometer. The experimental results show that the maximum measurement error is less than 1 µm compared with an incremental-type laser interferometer.

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

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.

Real-time phase delay compensation of PGC demodulation in sinusoidal phase-modulation interferometer for nanometer displacement measurement.

As the phase delay between the carrier component of the detected interference signal and the carrier has adverse effect for phase generated carrier (PGC) demodulation, it is essential to compensate the phase delay to improve the accuracy of precision displacement measurement in sinusoidal phase-modulation interferometer (SPMI). In this paper, a real-time phase delay compensation method is proposed by regulating a compensating phase introduced to the carrier to maximize the output of the low pass filter so as to make the carrier synchronize with the interference signal. The influence of phase delay for PGC demodulation is analyzed and the method for real-time phase delay compensation is described in detail. The simulation of the method was performed to verify the validity of the phase delay compensation algorithm. A SPMI using an EOM was constructed and several comparative experiments were carried out to demonstrate the feasibility of the proposed method. The experimental results show that the phase delay can be compensated accurately in real time, and nanometer accuracy is achieved for precision displacement measurement.