Method of hyperplanes in the problem of identification of an unknown substance

Under consideration is the problem of partial identification of the chemical composition of an unknown medium by using the method of transillumination of the medium with a collimated X-ray flux. A new method for solving the problem is proposed that consists in constructing a special set and a function that determines its boundary. The method is distinguished by its essential simplicity, it allows us to find the energy values that are the best to X-ray the unknown medium and in many cases makes it possible to use just a single transillumination. Some sufficient conditions are obtained under which the difference between two substances will certainly be established as a result of measurements with a single transillumination of the medium. The method also takes into account the influence of measurement errors on the possibility of successful solution of a specific identification problem. A sufficient condition is obtained for the maximum permissible total relative error under which two specific substances can be «distinguished» by the results of a single radioscopy experiment. Using an example of a specific group of hydrocarbons, which includes 40 substances, it is shown that every pair of these substances becomes «well distinguishable» at a sufficiently low energy of the medium transillumination. The result was obtained with the at most 10% total relative error of measuring the radiation entering and leaving the medium.