A diagonal-based heterodyne grating interferometer (HGI) for two-dimensional displacement measurement is presented. It can simultaneously realize the high signal contrast and signal-to-noise ratio (SNR) with the specially designed cross grating. Meanwhile, an eightfold optical subdivision can be acquired with the proposed phase decoupling method. The signal contrast of 96.55% and SNR of 50 dB are obtained with laser power of 0.45 mW. Several tests including linear displacement, planar displacement, and stability are conducted in the experiments. The theoretical resolution of 0.125 nm, the short-range repeatability of 2.35 and 3.24 nm under round-trip movement of 10 μm, and the system stability better than ± 4 and ± 6 nm over 10 min are achieved for the X- and Y-directions, respectively. In addition, the measurement errors including geometric, nonlinear, and noncommon-path errors are analyzed. The results demonstrate that the proposed diagonal-based configuration combined with cross gratings is extremely suitable for HGIs, which has the potential to simultaneously improve the performance and practicability of HGIs.
We present a compact displacement measurement system based on single grating and 3×3 coupler, possessing the capability of large range and nanometer precision. With the introduction of 3×3 coupler for phase shift in interference signal, the present scheme has the advantages of simple structure, convenient alignment, and insensitivity to air turbulence, resulting in high robustness. We accordingly developed an efficient and precision signal processing method for phase demodulation on a digital signal processing, adapting to characteristics of outputs in 3×3 coupler, achieving a high-powered subdivision of the interference phase. It was validated that the phase precision was about 1<sup>°</sup> even when phase and amplitude errors were added to interference signals in the simulation, which corresponded to a displacement precision of about 3nm.
A novel low-noise front-end electronics was proposed for detection of light signals with intensity about 10 μW and frequency above 2.7 MHz. The direct current (DC) power supply, pre-amplifier and main-amplifier were first designed, simulated and then realized. Small-size components were used to make the power supply small, and the pre-amplifier and main-amplifier were the least capacitors to avoid the phase shift of the signals. The performance of the developed front-end electronics was verified in cross-grating diffraction experiments. The results indicated that the output peak-topeak noise of the ±5 V DC power supply was about 2 mV, and the total output current was 1.25 A. The signal-to-noise ratio (SNR) of the output signal of the pre-amplifier was about 50 dB, and it increased to nearly 60 dB after the mainamplifier, which means this front-end electronics was especially suitable for using in the phase-sensitive and integrated precision measurement systems.
Based on the detailed derivation of the displacement measurement principle with Jones matrix method, the optical system of the heterodyne grating interferometry that we previously proposed was modified. A reflection phase grating with smaller grating pitch was designed with rigorous coupled-wave analysis (RCWA) to improve the measurement performance. The first order diffraction efficiency of 47.35% and 56.24% were obtained for TE and TM polarization, respectively. Therefore the TM polarization was chose to enhance the signal-to-noise ratio (SNR) of the beat signal. Meanwhile, the errors of the optical system resulting from grating non-uniformity, frequency mixing, polarization mixing and polarization-frequency mixing were discussed as well. It was shown that the frequency mixing was the main source of the errors, and the modified heterodyne grating interferometry had the potential to realize nanometer resolution for displacement measurement.