Résumé
Urban trees present numerous benefits at ecological and sanitary levels in modern cities. To manage this resource, urban operators need tools to evaluate their phytosanitary state [1]. Aiming to analyse the inner structures of trees without altering their condition, non-destructive imaging methods have been proposed, such as ultrasonic tomography [2]. Here we are interested on the influence of the wood orthotropic behaviour on the ultrasonic waves transit time, and more precisely, how the tomography image reconstruction process (inverse problem) should be adapted to the standing tree constraints. For wood, the ray paths between the ultrasonic transmitter and the receivers are not straight as for isotropic media; therefore, the image reconstruction method should be adapted to deal with curved rays. The aim of this study is to present a methodology for the solution of the inverse problem in anisotropic media such as wood, considering curved rays. Time-of-flight (TOF) estimation was obtained either by numerical simulations (by raytracing approach) and from experimental data. Experiment configurations included healthy and defective disk wood disks; defects were simulated by drilling circular holes on the disks. Centric and eccentric defect positions were tested. Considering that ray paths are not known a priori when performing ultrasonic tomography, solution to the inverse problem requires an optimization procedure to adapt iteratively the trajectories, to minimize a functional of the time-of-flight. Subsequently, for each pixel in each trajectory, the corresponding velocity or slowness value can be used to compute the inner wood mechanical parameters, using the Christoffel formulation.