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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.

Original publication




Journal article


Journal of X-ray science and technology

Publication Date





583 - 597


Statistics Department, University of Warwick, Warwick, UK.


Tomography, X-Ray Computed, Nonlinear Dynamics, Models, Theoretical, Image Processing, Computer-Assisted