Spatiotemporal Fourier transform method for the measurement of narrowband ultrasonic surface acoustic waves with TV holography

Abstract

The measurement of ultrasonic surface acoustic waves of nanometric amplitude by TV holography (TVH) was demonstrated some years ago. The spatial periodicity of the wavefield across the optical phase difference maps was exploited to yield the mechanical amplitude and phase of the propagating wave. Now we present a refinement of the technique where we also profit from the temporal periodicity, at each point of the surface, of the displacement induced by the wave. We record a series of sets of primary correlograms, which are processed to yield optical phase-difference maps. We change slightly the delay between the excitation of the wave and the measurement from one recording to the next, so that the position of the wavefield on the resultant images is shifted accordingly. Every point on the surface, which oscillates at the frequency of the wave, is thus recorded at several instants of its oscillation cycle in consecutive optical phase difference maps of the sequence. We have then spatial periodicity at a given instant across each image and temporal periodicity at a given point on the surface across the series of images. This feature is exploited to calculate a three-dimensional Fourier transform of the data. As we employ narrowband ultrasonic waves, the spatial content of the spectrum is contained in a small region of the spatial frequency plane and within a thin slice of temporal frequencies, and can be easily filtered and inverse Fourier transformed to obtain the mechanical amplitude and phase of the wave. This method intends to extend the detection capability of the TVH technique to ultrasonic waves of lower amplitude.

Characterization of defects in plates by two-dimensional ultrasonic displacement maps: comparison between pulsed TV-holography measurements and finite element method predictions

“…Our procedure 22 consists of an improved version of previous method described in reference, 21 that is based on the spatio-temporal 3D Fourier transform of a set of optical phase-change maps corresponding to successive instants delayed by a quarter of the wave period. In our case, eight optical phase-change maps delayed 250 ns were taken in each experiment and the spatio-temporal 3D Fourier transform method was applied to the whole set.…”

Numerical modeling and measurement by pulsed television holography of ultrasonic displacement maps in plates with through-thickness defects

“…Our procedure, 18 which consists of an improved version of a previous method described in Ref. 17, is based on the spatiotemporal 3-D Fourier transform of a set of optical phase-change maps corresponding to successive instants delayed by a quarter of the wave period.…”

Phase and group velocity measurement of ultrasonic guided wavetrains in plates by pulsed TV holography

“…In the procedure, to obtain ⌬⌽ i ͑x , t i ͒, a bandpass filter is applied in the frequency domain to isolate the spatio-temporal frequencies corresponding to the guided acoustic wave. 32 For this reason, the phase in Fig. 3͑c͒ shows vertical stripes with a spatial period similar to the wavelength of such acoustic wave throughout the map.…”

“…28 A second processing procedure, based on the fast Fourier transform ͑FFT͒, is applied to the optical phase-change maps to evaluate the complex amplitude of the wave. It can be applied to each individual map by utilizing the 2D FFT 31 or, as we did in the present work, to the whole set of maps by means of the spatiotemporal three-dimensional ͑3D͒ FFT, 32 rendering in both cases a set of complex optical phasechange maps ⌬⌽ i ͑x , t i ͒, with i =1,2, ... ,N. Each of these maps is proportional to the complex instantaneous out-ofplane acoustic displacement û 3 ͑x , t i ͒, i.e.,…”