A grating interferometer, called the “optical encoder,” is a commonly used tool for precise displacement measurements. In contrast to a laser interferometer, a grating interferometer is insensitive...

Periodic nonlinear errors caused by frequency mixing are serious obstacles for increasing the resolution of heterodyne grating interferometers. To eliminate the periodic nonlinear errors, a spatially separated heterodyne grating interferometer is proposed in this study. Two modulated beams with different frequencies are transferred respectively by two fibers, which form a spatially separated construction. A couple of comparison experiments in both time domain and frequency domain are designed and conducted. The results of the frequency-spectrum analysis experiment showed that the periodic nonlinear errors were no larger than 0.086 nm, which proved that the proposed system was effectual in eliminating periodic nonlinear errors.

This paper presents a real-time method to compensate for the variable cyclic error in a homodyne laser interferometer. The parameters describing the quadrature signals of the interferometer are estimated using simple peak value detectors. The cyclic error in the homodyne laser interferometer was then corrected through simple arithmetic calculations of the quadrature signals. A field programmable gate array was utilized for the real-time compensation of the cyclic error in a homodyne laser interferometer. The simulation and experimental results indicated that the proposed method could provide a cyclic error that was fixed without compensation down to a value under 0.6 nm in a homodyne laser interferometer. The proposed method could also reduce the time-varying cyclic error to a value under 0.6 nm in a homodyne laser interferometer, in contrast to the equivalent value of 13.3 nm for a conventional elliptical fitting method.

This study presents an analysis of the cyclic nonlinearity in the homodyne interferometer starting from the interference principle. We present the design for an enhanced homodyne interferometer without DC offset, for which the nonlinearity model will not be influenced by the intensity of the measurement beam. Our experimental results show that the enhanced interferometer can suppress the nonlinearity to less than 0.5 nm with a system calibration involving gain adjustment and phase-correction methods.

Residual periodic errors detected in picometer-level heterodyne interferometers cannot be explained by the model based on double-frequency mixing. A new model is established and proposed in this paper for analysis of these errors. The multi-order Doppler frequency shift ghost beams from measurement beam itself are involved in final interference leading to multi-order periodic errors, whether or not frequency-mixing originating from the two incident beams occurs. For model validation, a novel setup free from double-frequency mixing is constructed. The analyzed measurement signal shows that phase mixing of measurement beam itself can lead to multi-order periodic errors ranging from tens of picometers to one nanometer.

Even after the Heydemann correction, residual nonlinear errors, ranging from hundreds of picometers to several nanometers, are still found in heterodyne laser interferometers. This is a crucial factor impeding the realization of picometer level metrology, but its source and mechanism have barely been investigated. To study this problem, a novel nonlinear model based on optical mixing and coupling with ghost reflection is proposed and then verified by experiments. After intense investigation of this new model’s influence, results indicate that new additional high-order and negative-order nonlinear harmonics, arising from ghost reflection and its coupling with optical mixing, have only a negligible contribution to the overall nonlinear error. In real applications, any effect on the Lissajous trajectory might be invisible due to the small ghost reflectance. However, even a tiny ghost reflection can significantly worsen the effectiveness of the Heydemann correction, or even make this correction completely ineffective, i.e., compensation makes the error larger rather than smaller. Moreover, the residual nonlinear error after correction is dominated only by ghost reflectance.