Comments and corrections on the use of polar sampling theorems in CT

In two recent papers, an exact polar interpolation formula was used to reconstruct computer tomography (CT) imagery by a procedure known as direct Fourier transform inversion. The resulting imagery compared favorably to CT imagery reconstructed by filtered convolution back projection. Strictly speaking, however, the interpolation formula was inappropriately used since it is valid only for an odd number of azimuthal samples while in CT one uses an even number of samples. When the number of samples N is large (say > 200 as in CT) the error is not noticeable and the "appropriateness" of the formula has no practical significance. However, when N is small, a large error can result. We derive, in this paper, exact azimuthal interpolation formulas for N even and arbitrary N.