A laser homodyne straightness interferometer with simultaneous measurement of six degrees of freedom motion errors is proposed for precision linear stage metrology. In this interferometer, the vertical straightness error and its position are measured by interference fringe counting, the yaw and pitch errors are obtained by measuring the spacing changes of interference fringe and the horizontal straightness and roll errors are determined by laser collimation. The merit of this interferometer is that four degrees of freedom motion errors are obtained by using laser interferometry with high accuracy. The optical configuration of the proposed interferometer is designed. The principle of the simultaneous measurement of six degrees of freedom errors including yaw, pitch, roll, two straightness errors and straightness error's position of measured linear stage is depicted in detail, and the compensation of crosstalk effects on straightness error and its position measurements is presented. At last, an experimental setup is constructed and several experiments are performed to demonstrate the feasibility of the proposed interferometer and the compensation method.

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.

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The laser beam drift seriously influences the accuracy of straightness or displacement measurement in laser interferometers, especially for the long travel measurement. To solve this problem, a heterodyne straightness and displacement measuring interferometer with laser beam drift compensation is proposed. In this interferometer, the simultaneous measurement of straightness error and displacement is realized by using heterodyne interferometry, and the laser beam drift is determined to compensate the measurement results of straightness error and displacement in real time. The optical configuration of the interferometer is designed. The principle of the simultaneous measurement of straightness, displacement, and laser beam drift is depicted and analyzed in detail. And the compensation of the laser beam drift for the straightness error and displacement is presented. Several experiments were performed to verify the feasibility of the interferometer and the effectiveness of the laser beam drift compensation. The experiments of laser beam stability show that the position stability of the laser beam spot can be improved by more than 50% after compensation. The measurement and compensation experiments of straightness error and displacement by testing a linear stage at different distances show that the straightness and displacement obtained from the interferometer are in agreement with those obtained from a compared interferometer and the measured stage. These demonstrate that the merits of this interferometer are not only eliminating the influence of laser beam drift on the measurement accuracy but also having the abilities of simultaneous measurement of straightness error and displacement as well as being suitable for long-travel linear stage metrology.

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Frequency sweeping interferometry with reference interferometer based on sinusoidal phase modulating technique is proposed in this paper for absolute distance measurement. With the frequency of the external cavity diode laser (ECDL) swept continuously in sinusoidal, a HeNe laser was employed to monitor the drifts of the target and the reference length, and influences caused by drifts during the measurement were compensated in real time. Sinusoidal phase modulation with non-overlapping frequencies were applied to the two laser lights individually by two electro-optic modulators (EOM), and the interference phases corresponding to the two laser lights were extracted simultaneously using the phase generated carrier (PGC) demodulation based on frequency-division multiplex technique. Performance of the phase detection method has been verified by nanometer displacement measurements. Experimental results show that the measurement uncertainty can be considerably reduced by compensating the influences of drifts and by applying linear regression to get the ratio of interference phase changes between the measurement interferometer and the reference interferometer. Comparison of the absolute distance measurement with an incremental interferometer yields a measurement uncertainty of 10−5, which is in good agreement with the estimation of the measurement uncertainty.