Data for Modelling the Penumbra in Computed Tomography

Background: 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. Objective: 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. 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 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. 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. Penumbra data ========== These data files correspond to the data discussed in Kueh et al (2016). A 3mm ceramic rod was placed centrally on the manipulator in an approximately vertical alignment such that the magnification was x4.45. Images were taken at a constant voltage of 140kV, at each of the following 7 different exposure/power settings: 0.177s/44W, 0.25s/30.6W, 0.354s/21W, 0.5s/14.6W, 0.708s/9.6W, 1s/6.4W, 1.415s/4W. Three images were taken for each parameter set, and these are placed within their respective folder (labelled by magnification) as TIFF files. Code which imports these files into the R environment is provided in Import.R. File structure ======== Description.txt Import.R 0.177s_44W: 44W_177ms_1.tif 44W_177ms_2.tif 44W_177ms_3.tif 0.25s_30.6W: 30-6W_250ms_1.tif 30-6W_250ms_2.tif 30-6W_250ms_3.tif 0.354s_21W: 21W_354ms_1.tif 21W_354ms_2.tif 21W_354ms_3.tif 0.5s_14.6W: 14.6W_500ms_1.tif 14.6W_500ms_2.tif 14.6W_500ms_3.tif 0.708s_9.6W: 9.6W_708ms_1.tif 9.6W_708ms_2.tif 9.6W_708ms_3.tif 1.415s_4W: 4.0W_1415ms_1.tif 4.0W_1415ms_2.tif 4.0W_1415ms_3.tif 1s_6.4W: 6.4W_1000ms_1.tif 6.4W_1000ms_2.tif 6.4W_1000ms_3.tif