Cristina Trillo

Measurement of the complex amplitude of transient surface acoustic waves using double-pulsed TV holography and a two-stage spatial Fourier transform method

We present a technique to measure the mechanical complex amplitude, i.e. the mechanical amplitude and phase of vibration, of an ultrasonic plane wavefield of nanometric amplitude that propagates on a surface. Our aim is to detect perturbations of the initially smooth wavefronts that indicate the presence of flaws in the material. We use bursts of surface acoustic waves (SAWs) and a double-pulsed TV holography system that records two correlograms with time separations down to 1.5 µs. The phases of the correlograms are calculated separately using the spatial Fourier transform method (SFTM) and operated on to obtain the phase change between exposures. In the resultant optical phase map, the field of instantaneous displacements of the surface (that comprises several periods of the SAW) acts as a modulated spatial carrier, now related to the mechanical phase and amplitude, that are extracted by applying the SFTM again.

Determination of thickness and elastic constants of aluminum plates from full-field wavelength measurements of single-mode narrowband Lamb waves

A method based on fitting the theoretical dispersion curves of Lamb waves to experimental data is presented to determine the thickness and two independent elastic constants of aluminum plates a few millimeters thick. The waves are generated by means of the wedge method using a narrowband source, selecting the wedge angle and the acoustic frequency f so that mainly one mode is excited. A self-developed pulsed electronic speckle pattern interferometry system renders a two dimensional map of the out-of-plane acoustic displacement field at the plate surface, which allows an accurate measurement of the acoustic wavelength lambda(1). For any mode, the relation between lambda(1) and f depends on the three unknown parameters, so at least three experimental measurements (lambda(1i),f(i)) with different frequencies and/or different modes are required to calculate them. The suitability of different Lamb modes to determine each parameter when the others are known is studied, as well as the conditions that the experimental set of values must fulfill to calculate all three parameters. Numerous Lamb modes at different frequencies are generated in each plate, and a fitting is made based on the minimization of the error function, resulting in an accuracy better than 1%.

Detection of transient surface acoustic waves of nanometric amplitude with double-pulsed TV holography.

We describe the detection of bursts of surface acoustic waves by a double-pulsed TV holography technique. We describe mathematically the long- and short-wave bursts in the output correlograms and validate theoretical results with experimental images. The use of short-wave bursts permits us to scan the surface and makes it easier to distinguish, for purposes of nondestructive testing, the disturbances produced by flaws.

Non-destructive testing with surface acoustic waves using double-pulse TV holography

In this paper we present the visualization of the out-of-plane displacement fields produced by Rayleigh and Lamb waves on aluminium surfaces, using a double-pulse TV holography technique. This method presents several interesting characteristics, as a possible way of making whole-field remote measurements of instantaneous acoustic displacements, with good immunity from environmental perturbations. We also show examples where different surface and subsurface flaws have been detected, demonstrating the great potential of this technique for non-destructive testing in industrial applications.

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

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.

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

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.

Dimensionless formulation of the convolution and angular spectrum reconstruction methods in digital holography

The evaluation of the Rayleigh-Sommerfeld diffraction formula by means of numerical convolution and angular spectrum filtering are two of the most usual reconstruction methods in digital holography. Both of them are normally implemented by using a discrete Fourier transform and a sample of, respectively, the free space impulse response function and the corresponding transfer function. In this communication we propose a modified formulation of the sampled free space impulse response and transfer functions in terms of five dimensionless parameters: the wavelength to horizontal pixel size ratio, the reconstruction distance to horizontal field size ratio, the field and pixel aspect ratios and the number of pixels in the horizontal direction. This formulation simplifies the task of comparing and finding equivalences between holographic reconstruction situations with different distance, wavelength, field and pixel sizes. The reconstruction range for each of the methods is expressed in terms of the aforementioned dimensionless parameters by analyzing the resolution limits for the impulse response and the transfer function, respectively. This notation makes very simple to decide which of the two methods should be used for given conditions as well as to tailor range extension strategies based on the effects of hologram manipulations such as zero padding or pixel splitting. The details of the implementation of the convolution and angular spectrum algorithms with the proposed formulation are disclosed paying particular attention to the consequences of the sacrificial zero-padding required to avoid aliasing in Fourier-transform based cyclic convolution.

Measuring Amplitude and Phase of Vibration With Double-Exposure Stroboscopic TV Holography

We present a technique for the measurement of both amplitude and phase of sinusoidal vibrations with double-exposure stroboscopic TV holography combining optical and mechanical phase shifting. Using double-exposure stroboscopic illumination, there is no need of recording a reference state of the object and, consequently, the measurements can be made “in flight”, with a sensitivity to environmental noise much lower and with a more efficient use of the available laser power than with the former single-exposure techniques developed for the same purpose.

Pulsed TV holography measurement and digital reconstruction of compression acoustic wave fields: application to nondestructive testing of thick metallic samples

This paper describes a technique that numerically reconstructs the complex acoustic amplitude (i.e. the acoustic amplitude and phase) of a compression acoustic wave in the interior volume of a specimen from a set of full-field optical measurements of the instantaneous displacement of the surface. The volume of a thick specimen is probed in transmission mode by short bursts of narrowband compression acoustic waves generated at one of its faces. The temporal evolution of the displacement field induced by the bursts emerging at the opposite surface is measured by pulsed digital holographic interferometry (pulsed TV holography). A spatio-temporal 3D Fourier transform processing of the measured data yields the complex acoustic amplitude at the plane of the surface as a sequence of 2D complex-valued maps. Finally, a numerical implementation of the Rayleigh–Sommerfeld diffraction formula is employed to reconstruct the complex acoustic amplitude at other planes in the interior volume of the specimen. The whole procedure can be regarded as a combination of optical digital holography and acoustical holography methods. The technique was successfully tested on aluminium specimens with and without an internal artificial defect and sample results are presented. In particular, information about the shape and position of the defect was retrieved in the experiment performed on the flawed specimen, which indicates the potential applicability of the technique for the nondestructive testing of materials.

Enhancing the sensitivity to small phase changes in double-exposure stroboscopic television holography

We present a new technique for enhancing the sensitivity of double-exposure stroboscopic television holography (TVH) to detect and measure vibrations of small amplitude. The technique is based in the modulation of the phase of the reference beam in synchronism with the vibration of the measurand and derives from a former technique that we originally contrived for phase evaluation. We propose two variants, characterized by the demodulation process used to generate the secondary correlograms, with different behaviors in terms of the sensitivity to the sign of the measurand and of the ease in detecting the presence and shape of the vibration. We have implemented this new technique in an electronic speckle-pattern interferometer and compared its performance with standard TVH techniques; vibrations with amplitudes as small as 8 nm have been observed with this setup.