### Modelling the Penumbra in Computed Tomography

Kueh, A., Warnett, J. W., Gibbons, G. J., Brettschneider, J., Nichols, T. E., Williams, M. A., & Kendall, W. S. (2016). Modelling the Penumbra in Computed Tomography. *Journal of X-Ray Science and Technology*, to appear, 14pp.

BACKGROUND: In computed tomography (CT), spot geometry is one of the main sources of error in CT images. Since X-ray tubes do not arise from a point source, artefacts are produced. In particular there is a penumbra effect, leading to poorly defined edges within a reconstructed volume. Penumbra models can be simulated given a fixed spot geometry and the known experimental setup.

OBJECTIVE: This paper proposes to use a penumbra model, derived from Beer’s law, to confirm spot geometry from penumbra data, as well as quantify blurring in the image.

METHODS: Two models for the spot geometry are considered; one consists of a single Gaussian spot, the other is a mixture model consisting of a Gaussian spot together with a larger uniform spot.

RESULTS: The model consisting of a single Gaussian spot has fits which are poor. The mixture model (which adds a larger uniform spot) exhibits much improved fits. The parameters corresponding to the uniform spot are similar across all powers, and further experiments suggest that the uniform spot produces only soft X-rays of relatively low-energy.

CONCLUSIONS: Thus, the precision of radiographs can be estimated from the penumbra effect in the image. The use of a thin copper filter reduces the size of the effective penumbra.

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