LDV-guided sub-Nyquist fringe projection for high-precision full-field non-single-frequency vibration measurements

This paper presents a high-precision full-field vibration measurement method that integrates low-frame-rate Fourier transform profilometry (FTP) with laser Doppler vibrometry (LDV) to capture bandwidth-limited vibration signals at frequencies exceeding the camera Nyquist limit. By exploiting bandpass sampling, the proposed approach enables non-contact measurement of non-single-frequency vibrations, including swept-sine and multi-frequency excitations, without the need for high-speed cameras. High-precision single-point LDV measurements are used to guide temporal noise decoupling via short-time Fourier transform ridge extraction, while spatial noise is further suppressed by two-dimensional Chebyshev polynomial fitting, forming a dual-domain denoising strategy that significantly enhances FTP precision. Experimental validation on acrylic and aluminum plates, as well as on a real laptop touchpad, demonstrates that the reconstructed operational deflection shapes (ODSs) achieve modal assurance criterion (MAC) values above 0.9 with respect to continuous-scanning LDV references, with a measurement precision of approximately 10 -4 of the fringe spacing. Furthermore, compared with conventional temporal and spatial filtering methods, the proposed method consistently yields lower spectral reconstruction error and better full-field ODS agreement, as reflected by lower mean absolute percentage error and mean squared error values, together with higher MAC values. Validation on a real laptop touchpad further demonstrates the practical utility and application potential of the proposed method for cost-effective high-accuracy vibration monitoring.