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.

Abstract. We present a novel numerical modeling of ultrasonic Lamb and Rayleigh wave propagation and scattering by through-thickness defects like holes and slots in homogeneous plates, and its experimental verification in both near and far field by a self-developed pulsed TV holography system. In contrast to rigorous vectorial formulation of elasticity theory, our model is based on the 2-D scalar wave equation over the plate surface, with specific boundary conditions in the defects and plate edges. The experimental data include complex amplitude maps of the out-of-plane displacements of the plate surface, obtained by a two-step spatiotemporal Fourier transform method. We find a fair match between the numerical and experimental results, which allows for quantitative characterization of the defects.

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Abstract. The derivation of expressions to evaluate the local standard uncertainty of the complex amplitude of the numerically reconstructed field as well as of the phase-change measurements resulting from Fourier-and quasi-Fourier transform digital holographic interferometry is presented. Applying the law of propagation of uncertainty, as defined in the "Guide to the expression of uncertainty in measurement," to the digital reconstruction of holograms by Fourier transformation and to the subsequent calculation of the phase change between two such reconstructions results in a set of expressions, which allow the evaluation of the uncertainties of the complex amplitude and of the phase change at every pixel of the reconstruction in terms of the measured values and their standard uncertainty in the pixels of the original digital holograms. These expressions are increasingly simplified by first assuming a linear dependence between the squared uncertainty and the local value of the original holograms, and then considering that the object beam is a speckle pattern. We assess the behavior of the method by comparing the predicted standard uncertainty with the sample variance obtained from experiments conducted under repeatability conditions, and find a good agreement between both quantities.

Pulsed TV-holography (PTVH) can be used for obtaining two-dimensional maps of instantaneous out-of-plane displacements in plates. In particular, scattering patterns generated by the interaction of elastic waves with defects can be measured with PTVH and employed for non-destructive inspection and damage detection in plate structures. For quantitative characterization of damage (position, dimensions, orientation, etc.) on this basis, modeling of elastic wave scattering is usually performed in terms of full-vector three-dimensional formulations based on elasticity theory. In this work, a finite element method (FEM) applied to a two-dimensional scalar model based on Helmholtz equation is employed for obtaining a quantitative description of the scattering patterns, avoiding the aforementioned more complex and rigorous standard approach. Simulated scattering patterns are obtained with the scalar FEM assuming harmonic regime and free-stress boundary conditions. The corresponding experimental interaction of narrowband Rayleigh-Lamb waves with artificial defects in plates are measured using our specifically developed PTVH system. In our case, the raw optical phase-difference values are processed by employing a specially developed procedure, based on a two step spatial Fourier transform method, to derive a high quality two-dimensional acoustic field map from which an important part of the noise component has been filtered out. A comparison between filtered experimental maps and FEM simulated maps is developed, considering defects with different sizes in relation to the acoustic wavelength.