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.

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.

Grating interferometers that measure in-plane and out-of-plane displacements are not only effective two-degree-of-freedom (DOF) sensors, but are also basic units of six-DOF measurement systems. Besides resolution and accuracy, periodic nonlinear errors, misalignment tolerance, and size of reading heads are more crucial than ever. In this work, a spatially separated heterodyne grating interferometer that measures in- and out-of-plane displacements is proposed. A prototype with 3 mm diameter beams with a size of 69 mm × 51 mm × 41 mm was built and tested. The experiment results show that the 30 s stability is 2.5 nm; the periodic nonlinear errors of the two measuring directions are less than the resolutions (0.25 nm for in-plane motions and 0.15 nm for out-of-plane motions). Double-diffracted configuration ensures that the misalignment tolerances are three axes larger than ±2 mrad.

Representation of orientation is important in a six-degree-of-freedom grating interferometer but only a few studies have focused on this topic. Roll-pitch-