Application Cases

Experiment Title: Displacement Measurement Experiments with Linear Phase-Modulated Dual Homodyne Interferometer

Testing Purpose:To test the drift of the phase difference between the two interference signals caused by environmental parameter changes during long - term measurements when the measurement mirror M2 is stationary in the dual homodyne interferometer.

Testing Equipment:Voltage amplifier, He−Ne laser, signal generator, electro - optic phase modulator, polarizer, ordinary beam splitter, corner - cube prism, etc.

Experimental Process:

Figure 1: Experimental Setup of Displacement Measurement System with Dual Homodyne Interferometer

The experimental setup of the displacement measurement system with a dual homodyne interferometer is shown in Figure 1. After the optical path is adjusted, the measurement mirror M2 remains stationary. The EOM (Electro - Optic Modulator) uses linear phase modulation, and the modulation signal is generated by the signal generator. The sawtooth wave frequency is set to 500 Hz, and the amplitude is initially set to around 7.5 V. Then, the amplitude is fine - tuned to make the interference signal a complete cosine signal. The phase difference between the interference signals detected by PD1 and PD2 is continuously measured and recorded over a long period. To ensure the stability of the experimental environment and reduce interference from other factors, the experiment is conducted at night.

Experimental Results:

Figure 2: Results of 6 - Hour Phase - Difference Stability Test

As shown in Figure 2, the results indicate that the phase difference changes by approximately 80° over 6 hours, corresponding to a change of about 0.2° per minute. For displacement measurement experiments, the typical measurement speed is at the millimeter - per - second level, and the entire experiment can be completed within a few minutes. Therefore, under good environmental conditions, the phase - difference drift during a single displacement measurement is minimal.

In the displacement measurement experiments with a linear phase - modulated dual homodyne interferometer:

1. The phase - difference measurement stability experiment shows a change of about 0.2° per minute over 6 hours, which meets the experimental measurement requirements.

2. The results of the nanometer - level displacement measurement experiment are as follows: the mean and standard deviation of the displacement error do not exceed 1 nm.

3. The results of the micrometer - level displacement measurement experiment are as follows: the mean displacement error is within 1 nm, and the standard deviation of the displacement error ranges from 1.42 nm to 3.21 nm.

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