Modelling of the focal spot intensity distribution and the off-focal spot radiation in kilovoltage x-ray tubes for imaging

Brent van der Heyden, Gabriel Paiva Fonseca, Mark Podesta, Ivan Messner, Niklas Reisz, Ana Vaniqui, Heinz Deutschmann, Phil Steininger, Frank Verhaegen*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


X-ray tubes for medical applications typically generate x-rays by accelerating electrons, emitted from a cathode, with an interelectrode electric field, towards an anode target. X-rays are not emitted from one point, but from an irregularly shaped area on the anode, the focal spot. Focal spot intensity distributions and off-focal radiation negatively affect the imaging spatial resolution and broadens the beam penumbra. In this study, a Monte Carlo simulation model of an x-ray tube was developed to evaluate the spectral and spatial characteristics of off-focal radiation for multiple photon energies. Slit camera measurements were used to determine the horizontal and vertical intensity profiles of the small and the large focal spot of a diagnostic x-ray tube. First, electron beamlet weighting factors were obtained via an iterative optimization method to represent both focal spot sizes. These weighting factors were then used to extract off-focal spot radiation characteristics for the small and large focal spot sizes at 80, 100, and 120 kV. Finally, 120 kV simulations of a steel sphere (d = 4 mm) were performed to investigate image blurring with a point source, the small focal spot, and the large focal spot. The magnitude of off-focal radiation strongly depends on the anode size and the electric field coverage, and only minimally on the tube potential and the primary focal spot size. In conclusion, an x-ray tube Monte Carlo simulation model was developed to simulate focal spot intensity distributions and to evaluate off-focal radiation characteristics at several energies. This model can be further employed to investigate focal spot correction methods and to improve cone-beam CT image quality.

Original languageEnglish
Article number025002
Number of pages10
JournalPhysics in Medicine and Biology
Issue number2
Publication statusPublished - Jan 2020


  • x-ray tube
  • focal spot
  • off-focal radiation
  • Monte Carlo
  • Geant4
  • cone-beam CT
  • BEAM
  • SIZE

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