Abstract

The standard fan beam geometry is extended to a generalized geometry accounting for source, detector, and axis of rotation displacements as well as detector tilting. The standard fan beam convolution backprojection algorithm is modified so as to reconstruct from projections recorded in an arbitrary fan beam geometry. The new generalized fan beam algorithm is applied to various nonideal geometries, such as reconstruction from center-displaced projections, nonredundant single-sided projections, and partially redundant projections. It is shown that the algorithm is capable of reconstructing from truncated and partial projection data and can be applied to tomographic synthetic scanner arrays. A novel method of resolution enhancement in microtomography is presented. The generalized fan beam algorithm is shown to reconstruct from projection data recorded with a tilted detector arbitrarily stretching tiny projection images over a larger portion of the available detector range. Optimal detector use is achieved through horizontal scanner displacement compensating for the asymmetric magnification of fan beam projections onto tilted detectors. It is shown that tilted-detector microtomography possesses a number of desirable properties such as superior signal-to-noise ratio, contrast, stability, and artifact suppression in the reconstructed images. Moreover, the new algorithm substantially reduces blurring artifacts in the presence of penumbral broadening that is due to finite-size point sources. The generalized fan beam algorithm is efficiently implemented, and its run-time performance compares with that of the standard fan beam method.

© 1994 Optical Society of America

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