Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method

Abstract

The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation.

Digital Stroboscopic Holography Setup for Deformation Measurement at Both Quasi-Static and Acoustic Frequencies

“…[3] More recently, stroboscopic holography was truly digitized when phase-shifted double-exposure holograms were recorded on a digital CCD camera for subsequent reconstruction. [4,5] In other approaches, the laser pulses were not only timed at two opposite phases within the vibration period, but spread out to different vibration phases, [6][7][8] such as in Figure 1 from this article. The approaches chosen in [6] and [7] are based on a high-power continuous laser ($10 W) and high frame rate recordings (within-period acquisition) and are both aimed for industrial applications at <1 kHz frequencies.…”

“…The current setup has advantages over earlier published methods. [6,7] A wider frequency range (measured and presented: 5 Hz -16.7 kHz; theoretically: 0 Hz -250 kHz), a shorter acquisition time and a better spatial resolution than in similar setups can be achieved, as will be covered in detail in the discussion of this article. Since both amplitude and phase of the excitation signal are precisely measured relative to the ultra-short high-energy laser pulses, the complex transfer function (i.e., magnitude and phase) of the studied surface relative to the input is available after the experiment.…”

“…As discussed in Section 4.1 even higher frequencies are achievable when using further optimized electronics, which is not expensive at all in comparison to ultra-high frame rate cameras. Furthermore, as the camera frame rate is no limiting factor in our setup, the CCD target resolution can be allowed to be much higher (2452 Â 2054), compared to 256 Â 256 [6] and 856 Â 848 [7] in the mentioned papers. The advantages of more available pixels include a better spatial resolution and a lower limit on the allowed distance between the camera and the object.…”

“…[3][4][5] In recent years, a new concept of stroboscopic holography has been implemented, based on multiple very short phase-locked pulses cycling through the vibration period so that the entire time-dependent motion of the studied surface can be visualized. [5][6][7][8][9][10] The setup for stroboscopic holography that is presented in this article allows imaging of dynamic out-of-plane displacements over the entire surface of an object as a function of time over a very wide frequency range. The current setup has advantages over earlier published methods.…”

Evaluation of surface acoustic waves on the human skin using quasi-time-averaged digital Fresnel holograms

“…Hybrid techniques combining heterodyne holography with time-averaging or frequency shifting were also proposed recently [51][52][53]. Lastly, the use of high speed recordings was reported [54][55][56][57][58][59][60]. The setup is thus considerably simplified because it does not require a pulsed (or double pulsed) laser or the stroboscopic generation of light pulses.…”