Scattering by complex inhomogeneous objects: a first-order reciprocity method

New developments in analytical calculation of first order scattering for 3D complex objects

The principle of the analytical calculation of first order scattering used in our simulation code named VXI (Virtual X-ray Imaging) is based on a double ray-tracing [1]. The first step consists in realizing a ray-tracing from the X-ray source point to each point of the object (an elementary volume in practice) including attenuation effect in the primary beam. This calculation gives the number o...

Fast, High-Order Methods for Scattering by Inhomogeneous Media

In this thesis, we introduce a new, fast, high-order method for scattering by inhomogeneous media in three dimensions. As in previously existing methods, the low (O(N logN)) complexity of our integral equation method is obtained through extensive use of the fast Fourier transform (FFT) in evaluating the required convolutions. Unlike previous FFT-based methods, however, this method yields high-o...

A method for solving first order fuzzy differential equation

Acoustic Scattering by Inhomogeneous Obstacles

Acoustic scattering problems are considered when the material parameters (density and speed of sound) are functions of position within a bounded region. An integro-differential equation for the pressure in this region is obtained. It is proved that solving this equation is equivalent to solving the scattering problem. Problems of this kind are often solved by regarding the effects of the inhomo...

Acoustic scattering by inhomogeneous spheres.

Acoustic scattering problems are considered when the material parameters (density rho and speed of sound c) are spherically symmetric functions of position. Explicit separated solutions are derived (i) when rho(r) = exp(beta r) and c(-2) is a linear function of r(-1), and (ii) when rho(r) = exp(-beta r2) and c(-2) is a linear function of r2. In both cases, the radial parts of the solutions are ...