Modelling the penumbra in Computed Tomography1

In computed tomography (CT), the spot geometry is one of the main sources of error in CT images. Since X-rays 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.

This paper proposes to use a penumbra model, derived from Beer's law, both to confirm spot geometry from penumbra data, and to quantify blurring in the image.

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.

The model consisting of a single Gaussian spot has a poor fit at the boundary. The mixture model (which adds a larger uniform spot) exhibits a much improved fit. 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.

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.