A precision PGC demodulation for homodyne interferometer modulated with a combined sinusoidal and triangular signal is proposed. Using a triangular signal as additional modulation, a continuous phase-shifted interference signal for ellipse fitting is generated whether the measured object is in static or moving state. The real-time ellipse fitting and correction of the AC amplitudes and DC offsets of the quadrature components in PGC demodulation can be realized. The merit of this modulation is that it can eliminate thoroughly the periodic nonlinearity resulting from the influences of light intensity disturbance, the drift of modulation depth, the carrier phase delay, and non-ideal performance of the low pass filters in the conversional PGC demodulation. The principle and realization of the signal processing with the combined modulation signal are described in detail. The experiments of accuracy and rate evaluations of ellipse fitting, nanometer, and millimeter displacement measurements were performed to verify the feasibility of the proposed demodulation. The experimental results show that the elliptical parameters of the quadrature components can be achieved precisely in real time and nanometer accuracy was realized in displacement measurements.
In order to compensate the nonlinear error of a heterodyne interferometer caused by both frequency mixing and phase demodulating electronics in real time, a novel iterative algorithm with a digital lock-in phase demodulator is proposed in this paper. By using iterative translating and scaling transforms, the phase diagram of the two output signals from phase demodulator is corrected from an ellipse with center offset to a circle at origin. As a result, the correct phase can be obtained and the nonlinear error is compensated. The nonlinear error in heterodyne interferometer is analyzed, the digital lock-in phase demodulator is designed and the iterative compensation algorithm is presented. Simulation and displacement measurement experiments were performed to verify the effectiveness of the proposed method. The experimental results demonstrated that proposed method is able to reduce the nonlinear error obviously and realize nanometer displacement measurement.
A novel dual-homodyne interferometer, in which one interferometer acts as the reference interferometer and the other as the measurement one, is proposed to eliminate periodic nonlinearity for nanometer displacement measurement. By using one electro-optic phase modulator to modulate the common reference arm of the two interferometers, the DC interference signals of homodyne interferometers are modulated to AC signals. The measured displacement is carried on the phase difference change of the two AC interference signals. To address the influence of unequal fluctuations of the DC offsets of interference signals on the zero-crossing phase detection, a new phase difference detection method is proposed by counting the sample numbers in positive and negative half periods of interference signals. The merits of this interferometer are not only eliminating the nonlinear errors inherent to heterodyne and homodyne interferometers but also having the abilities of strong anti-interference, insensitivity to laser power drift and the unequal gain of detectors, as well as not demanding quadrature signals. An experiment of nanometer displacement measurement was performed to verify the feasibility of the interferometer, and the results show that sub-nanometer accuracy can be realized without periodic nonlinearity. The large displacement experiment shows that the results obtained with the proposed interferometer are in good accordance with those obtained from a comparison interferometer. These results show that the proposed interferometer can realize large displacement measurement with nanometer accuracy.
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