Integration Errors in Image Reconstruction of Circularly Symmetric Objects in Computer Assisted Tomography

Abstract

Computer assisted tomography is a new technique for producing X-ray images of exceptional clarity. The basic data consist of transmitted intensities at a series of uniformly spaced positions and angles. These data can then be used to reconstruct the image by a Fourier transform algorithm first developed in the context of radio- astronomy. A brief summary of the general technique is given. We then discuss the discretization error arising from the necessity of using a discrete approximation to the final integral in the reconstruction, restricting ourselves to objects with circular symmetry. We show that the analysis is considerably simplified if one works in the Fourier domain, and consider the error made by constructing an approximation to the desired kernel by linear interpolation. We show that the error is roughly proportional to 1/m², where m is the number of scans.