Claire Prada

Application of the DORT method to the detection and characterization of two targets in a shallow water wave-guide

The decomposition of the time-reversal operator (DORT in French) is an active array detection technique. It requires the measurement of the array response matrix K(/spl omega/) and consists in the analysis of the eigenvalues and the eigenvectors of the time-reversal operator K*K which provides information on the presence and localization of scatterers in the medium. It was shown that the DORT method allows to separate and localize pointlike scatterers in a shallow water wave-guide [J. Acoust. Soc. Am. Mordant et al. (1998) and Fotegot et al. (2003)]. Here, we extend the study to the detection and frequency characterization of two spherical targets. Small scale ultrasonic experiments are performed with a 3.9 MHz 24 elements transducer array and two spheres of 2 and 3 mm diameter in a 31 mm deep wave-guide. These scatterers correspond to 15 < ka < 25 leading to a non-isotropic scattered field. We have developed a theoretical model taking into account the wave-guide and the acoustic properties of the spheres and using the partial waves decomposition of the scattered field. We calculate the singular values of the array response matrix. This theoretical approach is in good agreement with the experimental results. This 1/325/sup th/ scale ultrasonic experiment corresponds to a shallow water experiment with a 12 kHz Vertical Linear Array (VLA).

Decomposition of the time-reversal operator applied to quantitative characterization of small elastic cylinders

Recent experiments showed how the DORT method can be used for the characterization of elastic cylinders imbedded in water (Minonzio et al., J. Acoust. Soc. Am. 117 (2), pp 789-798, 2005). Here, the small cylinder limit (k0a < 0.5) is considered. The singular values of the array response matrix are studied. It is show that the first singular value is proportional to k0(α + β)a 2 and the second one is proportional to k0βa 2 where a is the radius, α is the compressibility contrast, β is the density contrast between the cylinder and the fluid. Thus, the linear frequency dependence of the two singular values provides two equations with three unknowns, α, β and a. If one of these three parameters is known (for example, α is about 1 for metals), the other two can be determined. Measurements carried out for materials of α ranging from 0.6 to 0.99 and β between 0.1 and 1.6 are presented. A good agreement between calculated and experimental singular values was observed. Generalized expressions of the two first singular values are also given for k0a < 10. The analysis of acoustic scattering is an important tool for object identification. It has applications among non-destructive evaluation, medical imaging or underwater acoustics. The decomposition of the time-reversal operator (DORT method in French) is a new approach to scattering analysis that was developed since 1994 and is applied to detection and selective focusing through non-homogeneous media with array of transducers (1). The principle is the analysis of the complete set of pulse echo responses of the array. The eigenvalues and the eigenvectors of the time-reversal operator (i.e., singular values and singular vectors of the array response matrix) provide information on the scatterers in the insonified medium. Recent experiments showed how the DORT method can also be used for the characterization of sub-wavelength scatterers (2),(3), as elastic cylinders (4), imbedded in water. It has been shown that a single elastic scatterer is generally associated to several singular values and that the singular vectors are combinations of the projection on the array of the normal modes of vibrations (monopolar, dipolar, quadripolar...). After a brief presentation of these recent results, we focus on the case of small cylinder (k0a < 0.5), for which the two first normal modes are preponderant. The singular values and the singular vectors of the array response matrix are calculated and experimentally observed. We show that there are two preponderant singular values and study their dependence on the geometrical parameters, the cylinder radius a, the compressibility contrast α, and the density contrast β between the cylinder and the fluid. We present experimental results obtained in the MHz range for cylinders of different material and diameters using 96 transducers array. We also propose generalized expressions of the two first singular values, valid for k0a < 10.

Design of a time reversal mirror for medium scale experiments

A rigid 24-element acoustic source-receiver array has been jointly developed by ATLANTIDE, LOA and ECA. The array, based on COTS equipment, is specified to be easily deployed from a pier and to allow simple and low cost at sea experiments with water depths up to 20 meters. Dedicated to underwater detection and focusing applications in very shallow water, the instrumentation can be deployed in various acoustic time reversal configurations: detection of drifting objects, acoustic barrier, communication with AUV, etc. The system performance based on the time reversal concept and more particularly on the Time Reversal Operator Decomposition method (D.O.R.T.) is currently being estimated by experiments in a pool and in the bay of Brest.

First tests of the DORT method at 12 kHz in a shallow water waveguide

The Decomposition of the Time Reversal Operator (DORT method) has been introduced by Prada et al. (1996) as a generalization of the iterative time-reversal process. The effectiveness of this method for ultrasonic detection and selective focusing on different scatterers in an inhomogeneous media has been shown. The robustness of the method in an ultrasonic wave guide has been demonstrated by Mordant et al. (1999). Whereas the performance of classical detection methods usually decreases due to multiple reflections at the waveguide interfaces, the DORT method takes advantage of the wave guide boundaries and multi-path propagation in order to improve spatial resolution. In this work, we present the first experiment in a realistic shallow water waveguide with a 24 elements source receiver array at 12 kHz central frequency. The DORT method is applied in order to detect two targets at 27 m distance. Numerical and experimental backpropagation of the dominant singular vectors of the array response matrix enable the localization of the individual targets.

Dispersion curve measurements of a fluid filled femoral neck mimicking phantom

Quantitative ultrasonic measurements at the hip are supposed to improve fracture risk prediction. The cortical shell of the femoral neck is now known to behave as a waveguide, supporting the propagation of circumferential waves. Measurement of circumferential waves dispersion curves using the DORT method (Decomposition of the time reversal operator [1]) on an empty tube of bone mimicking material was recently reported. In the present study, the method is adapted to the measurement of the dispersion curves of a tube of bone-mimicking material filled with a marrow-mimicking fluid. Difficulty compared with the empty tube arises from interferences of reflections on cavity walls with circumferential waves. Mixing of these two contributions makes the identification of guided waves focal spots in the backpropagation plane difficult. Based on comparison of results of two simulated experiments, involving separately the two contributions, a criterion of selection of relevant focal spots was proposed. Filtering of the backpropagation plane using this criterion was added to the DORT process and then applied to experimental and simulated signals. Several branches of dispersion curves were experimentally obtained.

Local and noncontact measurements of corrosion and adhesive disbond using zero-group velocity lamb modes

A non-contact laser based ultrasonic technique is proposed for detecting plate thickness variations due to corrosion and adhesive disbonds between two plates. The method exploited the resonance at the minimum frequency of the S1 Lamb mode dispersion curve. At this minimum frequency the group velocity vanishes, whereas the phase velocity remains finite. The energy deposited by the laser pulse, generates a local vibration of the plate. This vibration is detected at the same point by an optical interferometer. Due the finite wavelength of the S1-ZGV mode, the spatial resolution is approximately limited to twice the plate thickness. First experiments show the ability to image a 1.5-mum deep corroded area on the back side of a 0.5-mm thick Duralumin plate. With the same technique we investigate the state of adhesive bonds between Duralumin and glass plates. The S1-mode resonance is strongly attenuated when plates are rigidly bond. In the case of small adhesive layers, we observed others resonances, associated with ZGV modes of the multi-layer structure, whose frequencies and amplitudes vary with adhesive thickness.