Application Cases

Experiment Name: Displacement Measurement Experiment with Improved PGC Demodulation Algorithm

Experiment Purpose: To verify the effectiveness of the improved PGC demodulation algorithm in suppressing nonlinear errors introduced by phase delay and modulation depth in practical applications.

Testing Equipment: Voltage amplifier, function generator, frequency-stabilized laser, electro-optic phase modulator, detector, etc.

Experiment Process:

Figure 1: Schematic and experimental setup of the sine phase-modulated interferometer based on EOM modulation

A sine phase-modulated interferometer based on EOM modulation was set up as shown in Figure 1. The He-Ne frequency-stabilized laser used in the light source section, model XL-80, has an output wavelength of 632.990577 nm. The optical path structure includes a quarter-wave plate (QWP), a beam splitter cube (BS), corner cube prisms (M1 and M2), an electro-optic phase modulator (EOM), and a photodetector (PD). The measurement mirror M2 is mounted on a rail with a total travel range of 15 μm, a unidirectional repeatability of 1 nm, and a displacement resolution of 0.05 nm.

In the experiment, the sine modulation signal is generated by an FPGA development board and output through a DAC module. After being amplified by a single-stage operational amplifier and then a high-voltage amplifier (amplified 20 times), the signal is connected to the EOM for driving. By adjusting the initial phase and amplitude of the sine modulation signal, the phase delay and modulation depth in the experimental system can be controlled. The function generator outputs a sine signal to the Analogin input of the P-753.1CD rail, controlling the rail to perform sinusoidal motion within a range of 1000 nm at a frequency of 350 Hz. Phase demodulation is performed under three different conditions of phase delay and modulation depth (1. Modulation depth of 2.63 rad, phase delay of 0°; 2. Modulation depth of 2.63 rad, phase delay of 80°; 3. Modulation depth of 2.23 rad, phase delay of 0°). For comparison, the PGC-Arctan algorithm is used for phase demodulation under the same phase delay and modulation depth conditions. The measurement results of the improved PGC phase demodulation algorithm and the PGC-Arctan demodulation algorithm are recorded simultaneously.

Experimental Results:

Figure 2 and Table 1 show the results of the sinusoidal displacement experiment under different phase delays and modulation depths. Figures 2(a), 2(c), and 2(e) illustrate how the shape of the demodulated displacement is affected by phase delay and modulation depth for the two algorithms. Figures 2(b), 2(d), and 2(f) present the FFT analysis of the demodulated displacement for the two algorithms, with the FFT using a Hanning window function. The 2nd to 8th harmonic components at 700 Hz, 1050 Hz, etc., in the figure indicate the magnitude of nonlinear errors in the demodulation results. The THD and SINAD for the two algorithms are summarized in Table 4.1. The experimental results show that when the modulation depth is 2.63 rad and the phase delay is 0°, the nonlinear errors for both algorithms are below 1 nm, and the demodulated displacement shape is an ideal sine wave. When the phase delay is 0° and the modulation depth is reduced to 2.23 rad, the shape of the demodulated displacement using the PGC-Arctan algorithm is affected, with nonlinear errors exceeding 5 nm. The THD increases to 1.171%, and SINAD decreases to 38.54 dB. When the modulation depth is 2.63 rad and the phase delay is increased to 80°, the shape of the demodulated displacement using the PGC-Arctan algorithm is significantly affected, with nonlinear errors exceeding 10 nm. The THD increases to 4.618%, and SINAD decreases to 26.71 dB. In all three cases, the improved PGC demodulation algorithm consistently produces an ideal sine wave for the demodulated displacement, with THD below 0.12% and SINAD above 58 dB, indicating that the demodulation results of the improved PGC algorithm are unaffected by phase delay and modulation depth.

Figure 2: Experimental results of sinusoidal displacement under different phase delays and modulation depths

Table 1: FFT analysis results of the demodulated displacement

Voltage Amplifier Recommendation: ATA-2082

Figure: Specification Parameters of the ATA-2082 High-Voltage Amplifier

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