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

Full Article  |  PDF Article
OSA Recommended Articles
Recursive methods for computing the Abel transform and its inverse

Eric W. Hansen and Phaih-Lan Law
J. Opt. Soc. Am. A 2(4) 510-520 (1985)

Attenuated Radon and Abel transforms

Anne V. Clough and Harrison H. Barrett
J. Opt. Soc. Am. 73(11) 1590-1595 (1983)

Abel inversion using fast Fourier transforms

Milan Kalal and Keith Nugent
Appl. Opt. 27(10) 1956-1959 (1988)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (1)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (47)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription