## Abstract

An axisymmetric object is reconstructed from its transaxial line-integral projection by the inverse Abel transform. An interesting variation of the Abel inversion problem is the finite-length line-spread function introduced by Dallas *et at.* [
J. Opt. Soc. Am. A **4**,
2039 (
1987)], in which the path of integration does not extend completely across the object support, resulting in incomplete projections. We refer to this operation as the incomplete Abel transform and derive a space-domain inversion formula for it. It is shown that the kernel of the inverse transform consists of the usual Abel inversion kernel plus a number of correction terms that act to complete the projections. The space-domain inverse is shown to be equivalent to Dallas’s frequency-domain inversion procedure. Finally, the space-domain inverse is demonstrated by numerical simulation.

© 1992 Optical Society of America

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