An Inverse Approach for Ultrasonic Imaging by Total Focusing Point for Close Reflectors Separation

The total focusing method (TFM) becomes a common approach in order to process full matrix capture data in nondestructive testing. This method consists in transmitting an unfocused beam and performing focusing in reception at each point of a reconstruction grid. The quality of TFM images is generally better than conventional phased array focusing that can focus at only a few points. Nevertheless, resolution in TFM images is not always sufficient, in particular when reflectors are close or in the case of a low signal to noise ratio. We propose to model the full matrix capture data as a linear operation between the reconstructed image vector and a matrix of waveforms. This matrix depends on the geometry of the inspection, the acoustical properties of the transducers and the medium under inspection. This inverse problem is ill-posed, therefore, a priori information on the final image must be introduced in order to regularize the problem. Our proposal consists in minimizing a penalized least-squares criterion within an iterative procedure under a sparse assumption. The first example shows the ability of the inverse approach to resolve flaws separated by a distance of λ/4 on synthetic data. The second example uses experimental data acquired from two close side drilled holes (SDH) in an aluminum block. The proposed algorithm clearly resolves the two SDH that are also separated by a distance of λ/4. The proposed method is able to resolve close flaws despite their sub wavelength separation distance, which significantly outperforms the well known Rayleigh's criterion.