F-P Interferometric Vibration Measurement And Signal Processing Based On Multiple Hilbert Transform

Fabry-Pérot Interference(FPI)technology occupies an important position in high-precision vibration measurement.The measurement accuracy can be improved by modulating and demodulating the interference signal or using the optical fiber F-P interference secondary feedback technology.Therefore,the obtained power equation of the fiber F-P interference signal is processed to achieve the above-mentioned effect,thereby realizing the measurement of the vibration displacement.According to the theoretical model of optical fiber F-P interference,the power equation of optical fiber F-P interference is studied.This power equation has a specific relationship with the micro-vibration of the object,and it is used as the theoretical basis.The number of fringes of the original optical fiber F-P interference signal is doubled by squaring.The equation of vibration micro-displacement is drawn,and the principle of square operation and the principle of vibration micro-displacement reconstruction are briefly introduced.Simulation analysis of F-P interference signal under different variables(motion amplitude of object and motion frequency of object)is done,and the influence of vibration displacement on F-P interference signal is discussed,including vibration displacement greater than laser half wavelength and vibration displacement less than laser half wavelength Case.Through simulation and experiment,the relationship between the relevant variables and the waveform of the F-P interference signal is determined.Based on the principle of multiple Hilbert transforms.Combine the squaring operation with multiple Hilbert transform technology,and use the principle of multiple Hilbert transform to reconstruct the F-P interference signal after squaring the signal.The result is compared with that based on the multiple Hilbert transform.The vibration measurement improves accuracy.Based on the square operation,the even power operation is extended,and a micro-displacement measurement method under the condition that the vibration displacement is less than half the wavelength of the laser is proposed.For the F-P interference pattern where the vibration displacement of the object to be measured is less than the half wavelength of the laser,Even power operation makes a complete F-P interference fringe appear between the reversal points.Select the complete F-P interference fringe between the two reversal points to perform multiple Hilbert transforms to reconstruct the micro-vibration of the object.