MATLAB implementation of an analytical model for the emission of x rays from an x-ray tube

Published: 2 September 2022| Version 4 | DOI: 10.17632/hjf5sctyt8.4
Artur Omar, Pedro Andreo, Gavin Poludniowski


An analytical model for the energy and angular distribution of bremsstrahlung and characteristic x rays emitted from an x-ray tube is provided for tungsten and molybdenum targets. The model includes photon mass attenuation coefficients, CSDA ranges, NIST bremsstrahlung cross sections, and bremsstrahlung shape functions extracted from the PENELOPE [v. 2014] materials database. Also included are Monte Carlo-calculated (PENELOPE) electron penetration data, describing the depth, energy, and angular distribution of electrons in thick x-ray targets. The emission of characteristic x rays is taken into account using a previously developed model, which includes Monte Carlo-calculated depth distributions of x-ray fluorescence (see the related link to dataset below). A Python implementation of the above model has been included in the following toolkit: Some of the key features of this toolkit are also available through a web-based graphical user interface (GUI):


Steps to reproduce

The electron penetration data entering into the model was determined as follows. The Monte Carlo system PENELOPE [v. 2014] was used to simulate a pencil beam of monoenergetic electrons normally incident onto tungsten and molybdenum slabs. A modified version of the penEasy user code was used to tally the electron kinetic energy and polar angle at depths of {0, 0.005, ..., 0.100, 0.125, 0.150, 0.200, ..., 0.500} times the electron CSDA range. The electron transport was simulated in detail with the parameter C1 (and C2) set equal to zero to treat the elastic scattering in detail (analogue technique). The electron and photon transport cut-off energies EABS(1-2) were set to 5 keV, and the energy transfer thresholds WCC and WCR were set to 1 keV. The generated Monte Carlo results were formulated as number and probability density functions using linear interpolation to express the continuous variables.


Karolinska Institutet Department of Oncology Pathology, Karolinska Universitetssjukhuset


Medical X-Ray Imaging, Monte Carlo Method, Analytical Modeling, Bremsstrahlung, Characteristic Radiation