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Vibration measurement is significant and widely used in the fields of spacecraft performance evaluation, material damage detection, machinery diagnostics, and acoustic sensing. Specifically, the vibration measurement based on a sinusoidal phase modulation laser interferometer has become a lasting research focus because of the advantages of strong anti-electromagnetic interference, high sensitivity, and large dynamic range. Sinusoidal phase modulation interferometers based on external modulation use adding piezoelectric ceramics or electro-optic modulators to the reference arm of the optical path. Introducing additional components will increase the hardware cost of the measurement system and result in a longer reference arm, which may introduce drift errors. Differently, sinusoidal phase modulation interferometers based on internal modulation directly modulate the laser current sinusoidally. The advantage is that no additional modulation devices need to be introduced. Besides, the collimator, spectroscope, and reference mirror in the measurement optical path can be integrated into a single fiber microprobe, improving practicality. However, it inevitably has periodic nonlinear errors caused by the phase modulation depth, carrier phase delay, and additional intensity modulation, which limits the accuracy of vibration measurement.
In this paper, a fiber microprobe vibration measurement system based on internal modulation has been developed to solve the problems mentioned above. A sinusoidal phase modulation laser source is generated by modulating the current of a distributed feedback laser (DFB) with a sinusoidal signal. After passing through a fiber circulator and a microprobe, the output laser beam is used to measure the displacement of the vibration source. The returned laser beam interferes with the reference laser reflected by the microprobe to generate a phase generated carrier (PGC) interference signal. A real-time interference signal processing algorithm is designed based on a programmable logic gate array (FPGA) digital computing platform. The error items introduced by additional intensity modulation and other factors are extracted through five-parameter ellipse fitting to compensate for the phase nonlinear error, and achieve high-precision measurement of vibration displacement. The fast Fourier transform (FFT) algorithm is used to analyze the vibration displacement. Theoretical analysis was conducted and a vibration measurement verification system was built. Interference signal demodulation experiments, step displacement measurement experiments, and vibration measurement experiments were carried out. The experimental results show that the vibration frequency range of the system covers 1142 Hz. In the 10-µm step displacement experiment, the average deviation measured is 0.173 µm. The resolution of vibration measurement is 1.221 Hz, and the harmonic distortion is less than 1.36%. The measurement system is expected to be applied in the field of precision vibration measurement.
Schematics of vibration measurement by a fiber microprobe with internal modulation. (a) Optical part; (b) Signal processing
Results of nonlinear errors from simulation. (a) Lissajous figures; (b) Phase demodulation error
Schematic diagram of signal processing based on ellipse fitting
Microprobe vibration measurement system based on internal modulation
Measurement results of semi-simulation. (a) Vibration measurement results of 0.5 kHz; (b) Vibration spectrum of 0.5 kHz; (c) Vibration measurement results of 0.8 kHz; (d) Vibration spectrum of 0.8 kHz; (e) Vibration measurement results of 1.0 kHz; (f) Vibration spectrum of 1.0 kHz
Lissajous figures in phase demodulation. (a) Initial Lissajous figure; (b) Lissajous figures after compensation of each step
Phase demodulation results after each step. (a) Initial phase demodulation results; (b) First compensation; (c) Second compensation; (d) Third compensation
Results of static displacement measurement
Comparison results of linear displacement
Results of vibration test. (a) Vibration measurement results of 25 Hz; (b) Vibration spectrum of 25 Hz; (c) Vibration measurement results of 50 Hz; (d) Vibration spectrum of 50 Hz; (e) Vibration measurement results of 600 Hz; (f) Vibration spectrum of 600 Hz
Results of amplitude and THD at different vibration frequencies