Optical systems capable of three-dimensional transmission imaging are considered; these systems employ a conventional tomographic setup with an added linear shift-invariant optical system between the sample and the detector. A theoretical analysis is presented of image formation and sample reconstruction in such systems, examples of which include diffraction tomography and phase-contrast tomography with the use of analyzer crystals. An example is introduced in which the image is obtained by scanning the beam along the line orthogonal to the optic axis and to the axis of rotation with a one-dimensional slit or grating parallel to the rotation axis. We show that under certain conditions the proposed system may allow quantitative local (region-of-interest) tomography.
© 2007 Optical Society of America
Original Manuscript: August 30, 2006
Revised Manuscript: February 28, 2007
Manuscript Accepted: March 17, 2007
Published: July 11, 2007
Timur E. Gureyev, Yakov I. Nesterets, Konstantin M. Pavlov, and Stephen W. Wilkins, "Computed tomography with linear shift-invariant optical systems," J. Opt. Soc. Am. A 24, 2230-2241 (2007)