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.
A simple and low-budget method aiming to generate phase difference equivalent to picoscalemeasured displacements of heterodyne interferometers is proposed. By changing the length of an interference arm in an interferometer-like optical configuration, a small phase difference between the two wavelengths is generated for creating the same effect as a picoscale-measured displacement of the heterodyne interferometer. It is derived and experimentally demonstrated that the zoom factor, defined as the ratio of displacements in a heterodyne interferometer and the proposed method leading to the same phase difference, is proportional to the beat frequency and generally in a scale of 10 −9. Thus, instead of ultraprecision piezo-stages, only a commercial linear guide rail is equipped in the method, and rigorous vibrating isolation is not necessary. The method has been already used to evaluate signal-processing electronics of a heterodyne grating interferometer.
An optical configuration of double-diffracted spatially separated heterodyne grating interferometer with a mechanical fixture was designed. To further investigate its features and provide robust measurements, the alignment tolerance in double-diffracted spatially separated heterodyne grating interferometer was qualitatively and quantitatively analyzed. Except for the offset error causing no influence on the interfering signal, the effect of the other four errors, roll, yaw, pitch angles, and stand-off error were geometrically analyzed and mathematically modeled. The simulation result quantified the position mismatches of output beams in a double-diffracted configuration and found the crucial structural parameters related to the intensity of interfering signals. Experiments based on the grating interferometer with a mechanical fixture and the same optical configuration built by independent optical components were implemented, whose results agreed with the simulation. Besides, the results showed that the proposed grating interferometer structure could tolerate the ±1100 arcsec roll movement, ±440 arcsec yaw movement, ±280 arcsec pitch movement, and ±0.6 mm stand-off error when -10 dB intensity loss is afforded.
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