Speckle noise detection and correction for frequency-scanning interferometry in vibration measurement.

• A comprehensive set of speckle noise suppression and vibration demodulation algorithms tailored for dynamic non-cooperative target measurement in frequency-scanning interferometry. • Analyzed the characteristics of speckle noise at instantaneous frequency, and provided the numerical solution for instantaneous frequency based on complex shifted Morlet wavelets. • Proposed a parameter-adjustable smoothing weight function for bidirectional prediction and correction base on the ARI model, coupled with smoothing through bidirectional filtering. • The surface vibration of black alumina was extracted through Kalman filtering, with an amplitude error of ± 17 nm and a frequency error of ± 0.021 Hz. • Restore the axial end face runout of the DC motor. Speckle noise significantly impairs the accuracy of vibration measurements for non-cooperative targets in frequency-scanning interferometry (FSI). To restore the real vibration, this paper proposes a comprehensive vibration demodulation algorithm based on the FSI. We established an FSI vibration model accounting for speckle noise. The extraction of instantaneous frequency from the interference signal is performed using a complex-shifted Morlet wavelet. An autoregressive differential model, incorporating a smooth weight function, is applied for bidirectional prediction to correct speckle noise. Finally, the true vibration of the target is restored through Kalman filtering. We validated the algorithm's accuracy using a Monte Carlo strategy. The experimental results show that the surface vibration of black aluminum oxide alloy and the axial runout of the DC motor during operation was successfully captured, and the time–frequency analysis results showed that this method has strong robustness against dense speckle noise. [ABSTRACT FROM AUTHOR]