A model for the energy and angular distribution of x rays emitted from an x-ray tube. Part II. Validation of x-ray spectra from 20 to 300 kV

Abstract

Purpose: To present and validate a complete x-ray emission model (bremsstrahlung and characteristic x-ray emission) for the energy range 20–300 kV. Methods: An analytical x-ray spectrum model that combines the bremsstrahlung emission model developed in Part I with a previously developed characteristic x-ray emission model is validated by comparison with Monte Carlo calculations, published measured spectra, and models developed by other authors. Furthermore, the assumptions and limitations of previous spectrum models are summarized, and their predictions are compared with results obtained by Monte Carlo simulations of x rays emitted from tungsten and molybdenum targets. Results: The model is able to reproduce narrow-beam Monte Carlo calculations to within 0.5% in terms of the first and second aluminum half-value layer thickness (HVL). Compared with measured spectra, the difference in HVL is < 2% for typical diagnostic and therapeutic beam qualities available at primary standard laboratories. Compared with previous spectrum models, the present model performs especially well for low kilovoltage x-ray beams (below 50 kV), and is reliable for a wider range of take-off angles, that is, the angle between the target surface and the direction of emission. The difference in model and Monte Carlo predictions of the energy-fluence weighted air kerma (i.e., the photon energy absorption in air) is < 0.5% using the present model, while previous spectrum models can differ by more than 10%. Conclusions: The x-ray emission model developed in this work has been validated against Monte Carlo calculations and measured results. The model provides an efficient alternative to comprehensive Monte Carlo simulations and is an improvement over previous models. The model can be used to predict both central- and off-axis spectra, as well as off-axis effects such as the (anode) heel effect.