CAT scans Computed Axial Tomography uses narrow X-ray beams directed though the body at

Chapter 8, Problem 26

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CAT scans Computed Axial Tomography uses narrow X-ray beams directed though the body at several angles to construct an image of internal organs and structures. The density of the material through which the beam passes affects the extent to which it is diminished before exiting the body. In most cases the part of the body to be scanned is overlaid with a grid, and X-ray beams are directed through the elements of this grid at different angles. Measurements of the exiting beams can then be used to calculate the density of each element of the grid. (a) Consider a simple grid with three elements, and three X-ray beams directed through them at different angles, as shown in the figure. The unknown densities of the material in each element are x1, x2 and x3.