Geodesic
Method of hyperplanes in the problem of identification of an unknown substance
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 39-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: radiography of a continuous medium, identification of chemical composition of a substance, calculation accuracy. 
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V. G. Nazarov. Method of hyperplanes in the problem of identification of an unknown substance. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 39-54. http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a3/

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