Fig. 1. System schematic of a PGC demodulation model and method with high-speed and high-precision performance.

Fig. 2. Block diagram of the FMI demodulation system based on the PGC algorithm. FMI: fiber-optic micro-probe laser interferometer; RO: reference oscillator; LPF: low-pass filter; Arctan: inverse tangent algorithm. The left side of the Arctan algorithm represents the actual interference setup, while the right side shows the equivalent diagram. The green and yellow wireframes on both sides correspond to the equivalent ADC1* and ADC2*, respectively.

Fig. 3. (a) Relationship of displacement measuring resolution with equivalent acquisition bits and SINAD. (b), (c) Displacement measurement results around point A and point B, respectively, within 1 s.

Fig. 4. Block diagram of resolution equivalent model including each error term.

Fig. 5. Effect of CPD of the system on equivalent acquisition bits and SINAD. (a), (b) First and second harmonic demodulation signals, respectively.

Fig. 6. Influence of modulation frequency and initial delay angle on equivalent acquisition bits and SINAD for work distance in the 2 m range. (a), (b) Variation curves of equivalent acquisition bits and SINAD for the first and second harmonic demodulation signals with the work distance when the modulation frequency is 3 MHz, 7 MHz, and 10 MHz. (c), (d) Variation curves of equivalent acquisition bits and SINAD for the first and second harmonic demodulation signals with the work distance when the initial delay angle is 0 deg, 45 deg, 90 deg, and 135 deg.

Fig. 7. High-speed and large-range PGC modulation and demodulation experimental device with dynamic CPD compensation. DDS unit: direct digital synthesis unit; DAC: digital-to-analog converter; DFB laser: distributed feedback laser; OC: optical fiber circulator; SMF: single-mode fiber; GRIN: gradient index lens; BS: beam splitting prism; M1: first reflector; M2: second reflector; APD: photodetector; PVD: peak value detection unit; ±Δ: variation of static CPD.

Fig. 8. Static test of equivalent acquisition accuracy of the phase-generated carrier lock-in amplifiers. (a), (b) Equivalent test results for the primary and secondary channels, respectively.

Fig. 9. Phase static noise test of the signal demodulation system.

Fig. 10. Comparison of CPD compensation effects of different demodulation methods. (a) Comparison of the influence of the phase to be measured φ0 on the carrier phase delay φτ′ calculated by the former research method and the proposed method. (b) Comparison of the calculated carrier phase delay φτ′ with the true value of carrier phase delay φτ using the former research method and the proposed method.

Fig. 11. Electrical test results of the displacement measuring resolution of the demodulating system. (a) 0.36 nm, (b) 0.20 nm, (c) 0.15 nm, and (d) 0.10 nm.

Fig. 12. Fitting results at speeds of 383.2 mm/s, 766.4 mm/s, 1149.6 mm/s, and 1532.8 mm/s.

Fig. 13. Results of measurement velocity residual of the demodulating system at speeds of (a) 383.2 mm/s, (b) 766.4 mm/s, (c) 1149.6 mm/s, and (d) 1532.8 mm/s.

Fig. 14. Relationship between standard deviation of measurement and motion frequency.