Application Cases

Experiment Title: Research on Multi-Wavelength Interferometric Phase Synchronous Demodulation Method Based on Laser Phase Discrete Modulation

Research Field: Laser Measurement

Purpose of the Test:

In length measurement, Absolute Distance Measurement (ADM) enables high-precision, large-range, and instantaneous distance measurement. Unlike Relative Displacement Measurement (RDM), it doesn't require continuous counting of interference fringes for precise measurement. ADM is widely used in high-end equipment manufacturing, large mechanical component inspection, and aircraft assembly. Multi-wavelength interferometry is a fundamental and widely used ADM method, where precise demodulation of multi-wavelength interference phases is a key issue.

Test Equipment: ATA-2082 high-voltage amplifier, laser, half-wave plate, beam splitter, Michelson interferometer, measuring corner cube prism, nano-positioning linear stage, non-contact capacitive sensor, reflector, photodetector.

FDM Dual-Wavelength Interferometry Experiment Setup

Figure: FDM Dual-Wavelength Interferometry Experiment Setup

Experiment Process:

Using the FDM dual-wavelength interferometric phase synchronous demodulation method as an example, simulation analysis and experimental verification were carried out. The proposed FDM dual-wavelength interferometric measurement setup was constructed, and several experiments were conducted, including system stability, nano-displacement measurement, nano-step nonlinearity error, dual-channel displacement demodulation synchronicity, and dynamic phase demodulation experiments.

To focus on multi-wavelength interferometric phase demodulation performance, two frequency-stabilized He-Ne lasers (632.991nm, 633.429nm) in free space were used. Experiments like nano-displacement measurement were conducted to analyze phase demodulation accuracy and nonlinearity error. In the setup, two half-wave plates (HWP) set the laser beam polarization direction at 45° to the EOM (EO-PM-NR-C1, Thorlabs) optical axis. Two EOMs phase-modulated the two laser beams at different frequencies, which were combined at a beam splitter (BS). In the Michelson interferometer, the measuring corner cube prism (M2) was installed on a nano-positioning linear stage. A non-contact capacitive sensor measured displacement. The linear stage has sub-nanometer resolution, ±1nm repeatability, 15μm closed-loop travel range, and 0.03% linearity error. The FDM interferometric laser signal, reflected by a reflector (R2), was detected by a photodetector. A custom FPGA-based ADC&DAC development board processed signals, including generating phase modulation signals, acquiring FDM interferometric signals, and demodulating interference phases. The generated phase modulation signals, amplified by a dual-channel high-voltage amplifier (ATA-2082, Aigtek), drove the electro-optic modulators (EOMs). The phase modulation signals and low-pass filter settings matched the simulated signals (ω1=146kHz, ω2=195kHz, ωt=100Hz, ωL=49kHz). Adjusting the high-voltage amplifier's gain set the sine phase modulation depth of both EOMs to about 2rad.

1. Stability Experiment

To test the FDM interferometric phase synchronous demodulation system's stability when the measuring mirror M2 is stationary, a sine and triangle wave composite modulation was applied to the EOM, and the two interferometric signal demodulation phase changes were recorded. The results are shown in Figure 2.

Figure 2: Stability Experiment Results

From Figure 2, over one hour, the two phases changed by about 70°, with a per-minute change of about 1.2°. Since interferometric phase demodulation experiments generally complete within milliseconds, the target drift's impact on multi-wavelength interferometric measurement results is negligible.

2. Step Measurement Experiment

To evaluate the FDM dual-wavelength interferometric phase synchronous demodulation system's displacement measurement accuracy at the nanoscale, the optical path was first adjusted to ensure the photodetector received normal interferometric signals. The photodetector's gain knob was adjusted to set the displacement measurement signal strength to an appropriate level. The measuring mirror was installed on a P-753.1CD precision linear actuator with 15μm travel and ±1nm repeatable positioning accuracy. Starting from 0, the mirror stepped by 10nm increments to 1μm (100 points), with the stage stepping speed set at 1μm/s. The PC control software synchronously recorded the demodulated displacement and the P-753.1CD actuator position. The results are shown in Figures 3 and 4.

Figure 3: First Channel Step Experiment Results

Figure 4: Second Channel Step Experiment Results

For clarity, the displacement measurement data were shifted upward by 2μm. The maximum deviations between the system's linear displacement measurement data and the P-753.1CD actuator positioning data were 1.64nm and 1.61nm, both within ±2nm. The standard deviations were 0.81nm and 0.75nm, both within 1nm, indicating the FDM dual-wavelength interferometric phase synchronous demodulation system achieves nanoscale measurement accuracy.

3. Nonlinearity Error Measurement Experiment

To measure the FDM dual-wavelength interferometric phase synchronous demodulation system's nonlinearity error, the measuring mirror was installed on a P-753.1CD precision linear actuator with 15μm travel and ±1nm repeatable positioning accuracy. Starting from 0, the mirror stepped by 10nm increments to 3μm (300 points), with the stage stepping speed set at 1μm/s. At each step, the real-time stage position and demodulated displacement values were recorded until the end of the measurement. The two displacement demodulation results are shown in Figures 5 and 6. Figures 5(a) and 6(a) display the system's demodulated displacement measurement values, the precision stage's position, and the error values at each step. Figures 5(b) and 6(b) show the FFT analysis results of the error values.

Figure 5: First Channel Nonlinearity Error Measurement and FFT Analysis Results

Figure 6: Second Channel Nonlinearity Error Measurement and FFT Analysis Results

External environmental changes, such as temperature and CO2 concentration, and the angular deviation between the P-753.1CD's movement direction and the beam direction, introduce linear errors, not nonlinear errors. Figures 5 and 6 show displacement errors after linear error removal. The arctangent operation in phase demodulation algorithms may introduce nonlinear errors with a π period. If phase demodulation exhibits nonlinear errors, a peak would appear at the second harmonic component. However, in the FFT analysis of displacement deviations in Figures 5 and 6, the nonlinear errors at the second harmonic component were less than 0.3nm for both displacements. The larger nonlinear error of 0.6nm at the first-order fringe (2π period) was due to polarization leakage in the PBS in the experimental setup, not the phase demodulation system, indicating the FDM dual-wavelength interferometric phase synchronous demodulation system has low nonlinear error.

4. Two-Channel Displacement Demodulation Synchronicity Experiment

To test the consistency of the two phase demodulation channels in the FDM dual-wavelength interferometric phase synchronous demodulation system, the measuring mirror was installed on a P-753.1CD precision linear actuator with 15μm travel and ±1nm repeatable positioning accuracy. Starting from 0, the mirror stepped by 10nm increments to 500nm (50 points), with the stage stepping speed set at 1μm/s. At each step, the real-time stage position and demodulated displacement values were recorded until the end of the measurement. The two displacement demodulation results and their differences are shown in Figure 7.

Figure 7: Two-Channel Phase Demodulation Synchronicity Experiment

For clarity, the first channel's displacement measurement data were shifted upward by 200nm. The figure clearly shows that the two demodulated displacement deviations remained within ±2nm, proving the FDM dual-wavelength interferometric phase synchronous demodulation system has good synchronicity between the two displacement demodulation channels.

5. Dynamic Phase Demodulation Experiment

To evaluate the system's dynamic phase synchronous detection performance, a two-channel dynamic phase demodulation experiment was conducted. For dynamic targets, Total Harmonic Distortion (THD), the ratio of the RMS amplitude of all harmonics to the fundamental frequency amplitude, assesses phase demodulation nonlinearity. Since THD analysis requires a single-frequency input, a sine voltage was applied to move the measuring mirror M2 at 30Hz within a 7rad dynamic range. The two demodulated phases were recorded simultaneously at 10kHz, as shown in Figure 8. According to the THD analysis results in Figure 9, the detected fundamental frequencies of Phase 1 and Phase 2 were 29.91Hz and 29.99Hz, with THD values of 7.65% and 7.70%, and SINAD values of 21.64dB for both, demonstrating the feasibility of the proposed dynamic phase synchronous detection scheme.

Figure 8: Two-Channel Sine Phase Demodulation Results

Figure 9: THD Analysis Results

Experimental Results:

In the FDM dual-wavelength interferometric phase synchronous demodulation system verification experiments:

1. The system stability experiment results were satisfactory, meeting the required measurement conditions.

2. In the nano-displacement measurement experiment, the maximum step error was within ±2nm, with a standard deviation of no more than 1nm.

3. The nano-scale nonlinearity error measurement experiment demonstrated that the method has low nonlinearity error, below 0.4nm.

4. In the two-channel displacement demodulation synchronicity experiment, the real-time demodulated displacement difference between the two channels was within ±2nm, confirming high synchronicity between the two phase demodulation channels.

5. In the dynamic phase demodulation experiment, a linearly varying sine voltage was applied to move the measuring mirror at 30Hz within a 7rad dynamic range. The two demodulated phases were recorded simultaneously at 10kHz. The detected fundamental frequencies of Phase 1 and Phase 2 were 29.91Hz and 29.99Hz, with THD values of 7.65% and 7.70%, and SINAD values of 21.64dB for both.

These experiments verified that the FDM dual-wavelength interferometric phase synchronous demodulation system has excellent performance.

图：ATA-2082