Mathematical aspects of divergent beam radiography.

At the present time, largely because of a breakthrough in radiology called computed tomography, the attenuation of x-ray beams is measured in extremely sensitive quantitative ways, and the information from many x-ray sources is assembled and analyzed on a computer. In this situation mathematics can make significant contributions concerning the nature of the information conveyed by x-rays from many sources, the extent to which this information determines the object x-rayed, suitable configurations of sources, methods for using the data to build a detailed reconstruction of the object, etc. This article announces results on these topics for the divergent x-ray beam. The three-dimensionally divergent beam, or cone beam, presents new problems that do not appear in the two-dimensional, or fan beam, case.