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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 5 — May. 1, 2011
  • pp: 766–769

Projection-slice theorem: a compact notation

Daissy H. Garces, William T. Rhodes, and Nestor M. Peña  »View Author Affiliations


JOSA A, Vol. 28, Issue 5, pp. 766-769 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000766


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Abstract

The notation normally associated with the projection-slice theorem often presents difficulties for students of Fourier optics and digital image processing. Simple single-line forms of the theorem that are relatively easily interpreted can be obtained for n-dimensional functions by exploiting the convolution theorem and the rotation theorem of Fourier transform theory. The projection-slice theorem is presented in this form for two- and three-dimensional functions; generalization to higher dimensionality is briefly discussed.

© 2011 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(100.6950) Image processing : Tomographic image processing
(110.6960) Imaging systems : Tomography

ToC Category:
Image Processing

History
Original Manuscript: December 10, 2010
Manuscript Accepted: December 14, 2010
Published: April 8, 2011

Virtual Issues
Vol. 6, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Daissy H. Garces, William T. Rhodes, and Nestor M. Peña, "Projection-slice theorem: a compact notation," J. Opt. Soc. Am. A 28, 766-769 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-5-766


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References

  1. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1989).
  2. G. T. Harman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd ed. (Springer, 2009).
  3. R. N. Bracewell, Two-Dimensional Imaging (Prentice-Hall, 1995), Chap. 14.
  4. N. Baddour, “Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates,” J. Opt. Soc. Am. A 26, 1767–1777 (2009). [CrossRef]
  5. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2004), Section 2.1.5.
  6. See, e.g., J. L. Prince and J. M. Links, Medical Imaging Signals and Systems (Prentice Hall, 2005), Section 6.3. A conventional treatment of the projection-slice theorem is also presented in this section.
  7. N. Baddour, “Operational and convolution properties of three-dimensional Fourier transforms in spherical polar coordinates,” J. Opt. Soc. Am. A 27, 2144–2155 (2010). [CrossRef]

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