Acoustical diffraction tomography in a finite form and its computer simulations

Until now, all acoustical diffraction reconstruction algorithms are in infinite forms. All of these algorithms have disadvantages: severe limitations on scatterers or tedious calculations. In this paper, we present a new reconstruction algorithm in a finite form using the method of formal parameter, which is very simple. This new algorithm gives an exact reconstruction when the amplitude of the scattered wave is smaller than that of the incident wave everywhere. This assumption is much less restrictive than that for the first- and second-order Born approximations. Although this new algorithm is in a finite form, it is still an approximate one when the amplitude of the scattered wave is not smaller than that of the incident wave everywhere. However, it still gives a good reconstruction when the amplitude of the scattered wave is a little greater than that of the incident wave in some area. Some numerical examples have confirmed these conclusions.