• 2022 (Vol.36)
  • 1990 (Vol.4)
  • 1989 (Vol.3)
  • 1988 (Vol.2)
  • 1987 (Vol.1)

Spectral model of a single-channel X-ray measuring instruments with polychromatic radiation

© 2019 A. S. Ingacheva

Institute for Information Transmission Problem RAS, 127051 Moscow, B. Karetny per., 19, Russia

Received 12 Feb 2019

In this paper we study the model of the optical path in devices which measure transmission coefficient of the objects for X-Ray emission. These devices include transmission tomographs, X-Ray microscopes and other X-Ray related devices. In the task of CT this model describes “Beam hardening” effect which occurs when polychromatic probe is used. We introduce function of the integral attenuation of the polychromatic beam and discuss its relation with equations for correction of polyenergetic ray sums. The model is implemented as python package “XRayUtil” with open source. This package is used to model spectral distribution of the emission for X-Ray tubes with different anodes (chrome, cuprum, molibden, silver, wolfram and others if user provides properties of the emission). With this package one can simulate presence of the filters of different thickness and material according to its chemical description. This functionality is implemented using XRAYLIB package. Using this one can estimate attenuation of the probing beam with objects of defined size and material using specific filters. The model includes single-channel detectors of the X-Ray emission with scintillators which are described with equations for spectral scintillator efficiency and spectral detector sensitivity. The used mathematical model evaluates emission attenuation only due to absorption and does not count reflection, diffraction and fluorescence. To evaluate quality of the simulated data we used experimental data from the laboratory microtomograph constructed and located in FSRC “Crystallography and Photonics” RAS. In the paper we estimate difference between experimental and simulated data and provide approximation of the function of the integral attenuation for the polychromatic emission for different anodes and objects.

Key words: X-Ray optical path, cupping effect, beam hardening, polychromatic X-Rays, integral attenuation of a polychromatic X-Rays, polyenergetic ray sum, correction formulas of polyenergetic ray sums

DOI: 10.1134/S0235009219030028

Cite: Ingacheva A. S. Spektralnaya model signala odnokanalnykh rentgenovskikh izmeritelnykh priborov, ispolzuyushchikh polikhromaticheskoe zondiruyushchee izluchenie [Spectral model of a single-channel x-ray measuring instruments with polychromatic radiation]. Sensornye sistemy [Sensory systems]. 2019. V. 33(3). P. 212-221 (in Russian). doi: 10.1134/S0235009219030028


  • Buzmakov A.V., Asadchikov V.E., Zolotov D.A., Chukalina M.V., Ingacheva A.S., Krivonosov Y.S. Laboratornye rentgenovskie mikrotomografy: metody predobrabotki eksperimental’nyh dannyh [Laboratory X-ray Microtomography: Ways of Processing Experimental Data]. Izvestiya RAN. Seriya Fizicheskaya [Bulletin of the Russian Academy of Sciences: physics]. 2018. V. 83. № 2. 2018. P. 194–197 (in Russian).
  • Trofimchuk A.M. Komp’yuternoe modelirovanie rentgenovskih izobrazhenij poluchennyh s pomoshch’yu inspekcionno-dosmotrovyh kompleksov [Computer simulation of x-ray images obtained with the help of inspection and inspection complexes]. Inzhenernyj vestnik Dona [Engineering Bulletin of the Don]. 2017. V. 44 (1). URL: https://cyberleninka.ru/article/n/kompyuternoe-modelirovanie-rentgenovskih-izobrazheniy-poluchennyh-s-pomoschyu-inspektsionno-dosmotro-vyh-kompleksov (accessed: 09.04.2019) (in Russian).
  • Feldman L., James M. Osnovy analiza poverhnosti i tonkih plenok. [Basics of surface and thin film analysis] Moscow, Mir, 1989. 344 p. (in Russian).
  • Pavlinsky G. Osnovy fiziki rentgenovskogo izlucheniya [Fundamentals of x-ray physics]. Moscow, FIZMALIT, 2007. 240 p. ISBN 978-5-9221-0783-9 (in Russian).
  • Bam Lunga Cleartone, Jodie Ann Miller, Megan Becker, Ian James Basson. X-ray computed tomography: Practical evaluation of beam hardening in iron ore samples. Minerals Engineering. 2019. V.131. P. 206–215. https://doi.org/10.1016/j.mineng.2018.11.010
  • Beckhoff B., Kanngießer B., Langhoff N., Wedell R. and Wolff H. Handbook of practical X-ray fluorescence analysis. Springer Science & Business Media. 2007. P.878.
  • Buzmakov A., Chukalina M., Nikolaev D., Gulimova V., Saveliev S., Tereschenko E., Seregin A., Senin R., Zolotov D., Prun V., Shaefer G. Monochromatic computed microtomography using laboratory and synchrotron sources and X-ray fluorescence analysis for comprehensive analysis of structural changes in bones. Journal of applied crystallography. 2015. V. 48. № 3. P. 693–701. https://doi.org/10.1107/S1600576715006214
  • Byun S.H. Radioisotopes and Radiation Methodology I, II. Lecture Notes. Radiation Sciences Graduate Program. McMaster University Hamilton, Ontario Canada. 2017. P. 4–10.
  • Crystals S.G. Efficiency calculations for selected scintillators. Saint-Gobain Ceramics & Plastics. 2016. P. 12.
  • Dewulf Wim, Ye Tan, Kim Kiekens. Sense and non-sense of beam hardening correction in CT metrology. CIRP Annals-Manufacturing Technology. 2012. V. 61. № 1. P.495–498. https://doi.org/10.1016/j.cirp.2012.03.013
  • Duvauchelle P., Freud N., Kaftandjian V., Babot D. A computer code to simulate X-ray imaging techniques. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. 2000. V. 170 (1–2). P. 245–258. https://doi.org/10.1016/S0168-583X(00)00185-3
  • Farago Tomáš, Petr Mikulík, Alexey Ershov, Matthias Vogelgesang, Daniel Hänschke, Tilo Baumbach. Syris: a flexible and efficient framework for X-ray imaging experiments simulation. Journal of synchrotron radiation. 2017. V. 24 (6). P. 1283–1295. https://doi.org/10.1107/S1600577517012255
  • Gokhale B.G. Contribution a l'etude de la largeur des raies dans les spectres de rayons X. In Annales de Physique. 1952. V. 12. № 7. P. 852–902. https://doi.org/10.1051/anphys/195212070852
  • Ingacheva A.S., Chukalina M.V. Polychromatic CT Data Improvement with One-Parameter Power Correction. Mathematical Problems in Engineering. 2019. ID 1405365. P. 12. https://doi.org/10.1155/2019/1405365
  • Kachelrieß M, Sourbelle K, Kalender W.A. Empirical cupping correction: A first-order raw data precorrection for cone-beam computed tomography. Medical physics. 2006. V. 33 (5). P. 1269–74. https://doi.org/10.1118/1.2188076
  • Nikolaev D.P., Gladkov A., Chernov T., Bulatov K. Diamond recognition algorithm using two-channel x-ray radiographic separator. In Seventh International Conference on Machine Vision (ICMV 2014). 2015. V. 9445. P.944507. https://doi.org/10.1117/12.2181204
  • Punnoose J., Xu J., Sisniega A., Zbijewski W., Siewerdsen J.H. spektr 3.0 – A computational tool for x-ray spectrum modeling and analysis. Medical physics. 2016. V.43. №8 Part 1. P. 4711–7. https://doi.org/10.1118/1.4955438
  • Salem S.I., Lee P.L. Experimental widths of K and L x-ray lines. Atomic Data and Nuclear Data Tables. 1976. V. 18. № 3. P. 233–241.
  • Schoonjans T., Brunetti A., Golosio B., del Rio M.S., SoléV.A., Ferrero C., Vincze L. The xraylib library for X-ray–matter interactions. Recent developments. Spectrochimica Acta Part B: Atomic Spectroscopy. 2011. V. 6. № 11–12. P. 776–784. https://doi.org/10.1016/j.sab.2011.09.011
  • Seferis I., Michail C., Valais I., Zeler J., Liaparinos P., Fountos G., Kalyvas N. Light emission efficiency and imaging performance of Lu2O3: Eu nanophosphor under X-ray radiography conditions: comparison with Gd2O2S: Eu. Journal of Luminescence. 2014. V. 151. P.229–234. https://doi.org/10.1118/1.3451113
  • Siewerdsen J.H., Waese A.M., Moseley D.J., Richard S., Jaffray D.A. Spektr: A computational tool for x-ray spectral analysis and imaging system optimization. Medical physics. 2004. V. 31. № 11. P. 3057–67. https://doi.org/10.1118/1.1758350
  • Sorum H. The Kα1, 2 x-ray spectra of the 3d transition metals Cr, Fe, Co, Ni and Cu. Journal of Physics F: Metal Physics. 1987. V. 1. № 2. P. 417. https://doi.org/10.1088/0305-4608/17/2/011
  • Thompson A., Attwood D., Gullikson E., Howells M., Kortright J., Robinson A. X-ray data booklet (2009). URL: http://xdb. lbl. gov. 2009. https://doi.org/10.1016/0092-640X(76)90026-7