Samuel Rodriguez

Fast topological imaging

Mathematical optimization methods based on the topological sensitivity analysis have been used to develop innovative ultrasonic imaging methods. With a single illumination of the medium, they have proved experimentally to yield a lateral resolution comparable to classical multiple-illumination techniques. As these methods are based on the numerical simulations of two wave fields, they require extensive computation. A time-domain finite-difference scheme is usually used for that purpose. This paper presents the development of an experimental imaging method based on the topological sensitivity. The numerical cost is reduced by replacing the numerical simulations by simple mathematical operations between the radiation patterns of the arrays transducers and the frequency-domain signals to be emitted. These radiation patterns are preliminary computed once and for all. They were obtained with a finite element model for the anisotropic elastodynamic case and with semi-analytical integrations for the acoustic case. Experimental results are presented for a composite material sample and for a prefractal network immersed in water. A lateral resolution below 2.5 times the wavelength is obtained with a single plane wave illumination. The method is also applied with multiple illuminations, so that objects hidden in complex media can be investigated.

Plane wave echo particle image velocimetry

The present work deals with the application of Topological Imaging to Ultrasonic Echo-Particle Image Velocimetry (Echo-PIV). Echo-PIV is a recent alternative to optical PIV for measuring the instantaneous velocity field of a fluid flow previously seeded with small particles. It consists in imaging the flow with an ultrasonic array at a high frame rate. Topological imaging is a method that benefits from the refocusing properties of the time-reversal principle in a systematic way, so that a single plane wave illumination of the medium leads to a fine resolution. Multiple insonifications are then possible at very high speed allowing not only static images of the medium but successive images of a moving medium. Experimental results are presented for a fluid seeded with stone powder. Two cases are studied: a vortex flow and the propagation of water surface waves.

The three-measurement two-calibration method for measuring the transfer matrix

Extensive use of transfer matrices (TMs) is made in determining the acoustic properties of a duct and in in-duct acoustic propagation models in the automotive industry and for musical acoustics purposes. The experimental apparatuses of classical TM measurement methods feature two measurement heads. Two microphones are flush with the walls of each head. The pressure signals are processed following the transfer function method constructed on an analytical model of acoustic propagation in measurement heads. The present paper aims at presenting a measurement method based on a three-microphone experimental apparatus and on its acoustic calibration through two reference measurements: the three-measurement two-calibration method for measuring the TM (3M2C-TM). Two microphones are flush with the measurement head walls and one is in the cap closing one side of the measured duct. 3M2C-TM proved essential for an accurate measurement of the four TM elements of two different ducts: a cylindrical duct and an expansion chamber.

Selective focusing through target identification and experimental acoustic signature extraction: Numerical experiments

Using transducer arrays and appropriate emission delays allow to focus acoustic waves at a chosen location in a medium. The focusing spatial accuracy depends on the accurate knowledge of its acoustic properties. When those properties are unknown, methods based on the Time-Reversal principle allow accurate focusing. Still, these methods are either intrusive (an active source has to be introduced at the target location first), either blind (the target cannot be selected in the presence of several objects.) The purpose of the present work is to achieve non-invasive accurate focusing on a selected target using inaccurate acoustic properties for the investigated medium. Potential applications are for instance noninvasive surgery based on High Intensity Focused Ultrasound (HIFU). Numerical experiments are presented and demonstrate accurate focusing on a previously designated target located in an unknown heterogeneous medium.

Three-dimensional and real-time two-dimensional topological imaging using parallel computing

We present the Fast Topological IMaging that has shown promising results to quickly process a picture by sending an ultrasonic plane wave within an unknown medium. This imaging algorithm is close to adjoint-based inversion methods but relies on a fast calculation of the direct and adjoint fields formulated in the frequency domain. The radiation pattern of a transducer array is computed once and for all, and then the direct and adjoint fields are obtained as a simple multiplication with the emitted or received signals, in Fourier domain. The resulting image represents the variations of acoustic impedance, and therefore highlights interfaces or flaws. Real-time imaging and high definition visualization both imply an expensive computation cost, that led us to implement this method on GPU (Graphics Processing Unit). Thanks to a massively parallel architecture, GPUs have become for ten years a new way to implement high performance algorithms. We used interoperability between OpenGL and CUDA to enable a real-ti...

Input impedance in flow ducts: Theory and measurement

This paper presents both a theoretical and an experimental investigation of the influence of the mean flow on the input impedance of a duct. The input impedance of an axisymetrical flow duct is calculated, taking into account the convective effect of a uniform flow, the dissipative effect of a turbulent flow and the radiation in an open jet. Each of these effects is separately studied. An experimental apparatus has been specifically designed to lower flow noise on the transducers, taking advantage of the Two-Microphone-Three-Calibration (TMTC) method [V. Gibiat and F. Laloë, J. Acoust. Soc. Am. 88, 2533-2545 (1990)], whose full calibration process allows any geometry for the measurement head. Theory and experiments are compared for a 1 m long cylindrical duct carrying a flow whose Mach number equals up to 0.15. The resonant frequencies are in close agreement, within 3%. The relative evolution of the magnitude maxima with increasing flow are in good agreement, within 10%. Despite similar tendencies when modifying the mean flow velocity, the amplitude of variation of the magnitude is 2 to 5 times smaller in the experiments.

Imaging of a fractal pattern with time and frequency domain topological derivative

While fractal boundaries and their ability to describe irregularity have been intensively studied, only a few studies are available on wave propagation in a medium where a fractal or quasi fractal pattern is embedded. Acoustical propagation in 1D or 2D domains can be modeled using Time Domain Finite Differences or in Frequency domain with Finite element methods. The fractal object is then considered as a subwavelength set of scatterers, and the problem becomes a multiple scattering one leading to acoustic localization. So, as some important part of the energy remains trapped inside the fractal pattern, imaging such a medium becomes difficult and imaging such complex media with classical tools as B-scan or comparable methods is not sufficient. The resolution of the inverse problem of wave propagation can then be achieved with the help of the more efficient imaging methods related with Time Reversal. Using the concept of topological derivative as defined in Time Domain Topological Energy and Fast Topologica...

From frequency to time domain: Signal features and physical characteristics for resonant acoustical systems

The determination of the impulse response or the reflection function of an acoustical system from data expressed in the frequency domain is not immediate. Signal processing from frequency domain to time domain should involve phenomena of large amplitude as oscillations known as ”ripple” that does not correspond to any physical phenomenon. The ”ripple phenomenon” will be analyzed from both a signal processing and a physical point of view with the help of simple duct acoustic examples. A map designed as a new time-frequency tool helps us to show that it cannot be removed in most cases without the use of processing techniques involving modifications in the computed signal. This work has been developed for the automotive research, but can be applied to musical acoustics or to any field connected with time domain exploration of acoustic cues.