Modelling the penumbra in Computed Tomography1.
Kueh A., Warnett JM., Gibbons GJ., Brettschneider J., Nichols TE., Williams MA., Kendall WS.
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.