Abstract: The invention relates to a method for processing attenuation data to produce a tomographic image which requires only that each point within the scan circle be viewed from 180.degree. in order to produce a full set of data. Data from views beyond 180.degree. are redundant and do not improve the picture quality. The invention further relates to an X-ray source and detector arrangement in which the X-ray source is a fan-shaped beam of X-rays and the detectors are arranged about the scan circle for 180.degree. plus approximately the angle of the fan beam. The invention further relates to method and apparatus for back projecting data from a polar coordinate system into a rectangular coordinate system in which the matrix points in the rectangular coordinate system can be loaded sequentially with the appropriate density value from the data line expressed in the polar coordinate system.