The problem of identification an unknown substance by the radiographic method

Abstract

Abstract This paper considers the problem of partial identification of the chemical composition of an unknown medium by the multiple X-ray of this medium. A sample of an unknown substance is assumed to be homogeneous in its chemical composition, and the photon flux, collimated both in direction and in energy. A mathematical model for the identification problem is formulated. The approach proposed to solving the problem is based on the method of singular value decomposition of a matrix. At the first stage of the solution the problem is reduced to finding singular numbers and singular vectors for the series systems of algebraic equations linear with respect to products of unknown quantities. Then, based on the data obtained, a special function is built, called an indicator to the distinguishability of substances, which enables the sufficient conditions for the distinguishability of various substances. Based on the tabular data, calculations were made for a number of specific groups of chemical elements.