The exponential edge-gradient effect in x-ray computed tomography.

The exponential edge-gradient effect must arise in any x-ray transmission CT scanner whenever long sharp edges of high contrast are encountered. The effect is non-linear and is due to the interaction of the exponential law of x-ray attenuation and the finite width of the scanning beam in the x-y plane. The error induced in the projection values is proved to be always negative. While the most common effect is lucent streaks emerging from single straight edges, it is demonstrated that dense streaks from pairs of edges are possible. It is shown that an exact correction of the error is possible only under very special (and rather unrealistic) circumstances in which an infinite number of samples per beam width are available and all thin rays making up the beam can be considered parallel. As a practical matter, nevertheless, increased sample density is highly desirable in making good approximate corrections; this is demonstrated with simulated scans. Two classes of approximate correction algorithms are described and their effectiveness evaluated on simulated CT phantom scans. One such algorithm is also shown to work well with a real scan of a physical phantom on a machine that provides approximately four samples per beam width.