Proceedings of the Estonian Academy of Sciences, 2010, 59, 2, 108–117 doi: 10.3176/proc.2010.2.08 Available online at www.eap.ee/proceedings Nonlinear signal processing for ultrasonic imaging of material complexity Serge Dos Santos a ∗ , Sarka Vejvodova b , and Zdenek Prevorovsky c a ENI Val de Loire, Unit´ e Mixte de Recherche “Imagerie et Cerveau”, INSERM U930 - CNRS ERL 3106, Universit´ e Franc ¸ois, Rabelais Rue de la Chocolaterie, BP3410, 41034 Blois cedex, France b Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Brehova 7, CZ-11519 Prague 1, Czech Republic; sarka.vejvodova@centrum.cz c Institute of Thermomechanics AS CR, v.v.i., Dolejskova 5, CZ-18200, Prague 8, Czech Republic; zp@it.cas.cz Received 15 December 2009, accepted 3 February 2010 Abstract. Ultrasonic imaging of material complexity is investigated theoretically and experimentally using the concept of symmetry analysis based signal processing in symbiosis with nonlinear elastic wave spectroscopy. These concepts were tested experimentally on several complex media with an advanced electronic system. This system exploits TR invariance, reciprocity, and coded excitation for an accurate extraction of the nonlinear signature of the medium under ultrasonic monitoring. Tested both in the context of the medical imaging of a tooth and in those of nondestructive testing of aeronautic composites, the basis of a new tomographic imaging of material complexity is presented with the help of algebraic concepts describing the TR operators. Key words: nonlinear signal processing, TR-NEWS, symmetry analysis, DORT, echodentography, nonlinear acoustics, coded excitation, complex imaging, solitonic waves. 1. INTRODUCTION Ultrasonic imaging methods based on the analysis of nonlinear effects of ultrasound propagation are today referred to nonlinear elastic wave spectroscopy (NEWS). Their advantages reside in their capacity for detecting smaller defects below the wavelength limit, so their sensitivity is much greater than that of traditional imaging methods based on measurements of wave velocity and attenuation [1]. Associated to the advanced NEWS techniques, enhanced signal processing should be chosen for the extraction of the nonlinear signature. The pulse-inversion (PI) technique is one of the most applied nonlinear signal processing tools in second harmonic imaging because of its ability to separate second-order harmonic components regardless of the transmitted bandwidth [2]. The framework of symmetry analysis (SA) constitutes the basis [3] of a systemic approach aimed at using absolute invariants such as time reversal (TR), reciprocity between emitters and receivers, and other nonlinear properties so as to optimize coded excitations (e.g., pulse- inversion PI or chirp-coded processes, etc.). Invariance with respect to TR and reciprocity between sources and receivers combined with PI was fully elaborated as the TR-NEWS techniques [4], which supplement and improve classical NEWS methodology. The concept of TR-NEWS symbiosis has a large potential of application in ultrasonic imaging, particularly in nondestructive testing (NDT), and it has been the subject of several investigations for the last five years, both from an experimental and a numerical point of view [4–7]. These TR-NEWS methods can be implemented in a scanning system for adequate localization of ∗ Corresponding author, serge.dossantos@univ-tours.fr