Optimum spread functions in linear tomography.

Recent attempts to reduce artefacts in tomographic blurring, using a transfer function approach, have so far taken little explicit account of the lessening in the degree of blurring which accompanies transfer function correction. A simple comparative measure R of the blurring effect of a linear tomographic movement is proposed. The parameter R is related to the ratio of the area of the point spread function (PSF) to its peak height. It is shown that the PSF having the greatest value of R (maximum blurring), whilst having an entirely positive transform, is of triangular form. Conversely, any PSF for which the value of R exceeds Rtriangle is inevitably associated with phase reversals. The problem of finding the PSF with R greater than Rtriangle, which leads to the minimum degree of phase reversal, has been tackled by determining the transfer function which, for the given value of R, has the minimum area under its subsidiary maxima. Transfer functions optimized in this way, and their corresponding PSFS, are calculated for four values of R using the method described by Jacquinot and Roizen-Dossier. The results of this procedure are discussed and its possible extensions noted.