Determining the chemical composition of an inhomogeneous body by multi-energy radiography

We consider the question of determining the chemical composition of an inhomogeneous body consisting of several homogeneous parts using multi-energy radiography. The interior structure of the body is assumed known. At the first stage of the solution the body is illuminated by collimated X-ray beams along a collection of specifically chosen directions at a prescribed set of energies, and by solving systems of linear algebraic equations we find the values of attenuation coefficients in each homogeneous part of the body. Then under certain additional assumptions we find the possible chemical composition of these parts. We analyze the effect of measurement errors on the quality of the solution. We illustrate the results with particular simulations. The proposed method can be used in the nondestructive control of products, customs control, and medicine.