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Optics Letters

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  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 15 — Aug. 1, 2006
  • pp: 2281–2283

Chromotomography for a rotating-prism instrument using backprojection, then filtering

Ross W. Deming  »View Author Affiliations


Optics Letters, Vol. 31, Issue 15, pp. 2281-2283 (2006)
http://dx.doi.org/10.1364/OL.31.002281


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Abstract

A simple closed-form solution is derived for reconstructing a 3D spatial-chromatic image cube from a set of chromatically dispersed 2D image frames. The algorithm is tailored for a particular instrument in which the dispersion element is a matching set of mechanically rotated direct vision prisms positioned between a lens and a focal plane array. By using a linear operator formalism to derive the Tikhonov-regularized pseudoinverse operator, it is found that the unique minimum-norm solution is obtained by applying the adjoint operator, followed by 1D filtering with respect to the chromatic variable. Thus the filtering and backprojection (adjoint) steps are applied in reverse order relative to an existing method. Computational efficiency is provided by use of the fast Fourier transform in the filtering step.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(100.6950) Image processing : Tomographic image processing
(300.6340) Spectroscopy : Spectroscopy, infrared
(300.6550) Spectroscopy : Spectroscopy, visible

ToC Category:
Image Processing

History
Original Manuscript: March 27, 2006
Revised Manuscript: May 16, 2006
Manuscript Accepted: May 19, 2006
Published: July 10, 2006

Virtual Issues
Vol. 1, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Ross W. Deming, "Chromotomography for a rotating-prism instrument using backprojection, then filtering," Opt. Lett. 31, 2281-2283 (2006)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-15-2281


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References

  1. J. M. Mooney, V. E. Vickers, M. An, and A. K. Brodzik, J. Opt. Soc. Am. A 14, 2951 (1997). [CrossRef]
  2. A. K. Brodzik and J. M. Mooney, J. Opt. Soc. Am. A 16, 246 (1999). [CrossRef]
  3. P. A. Bernhardt, J. Opt. Soc. Am. A 12, 1884 (1995). [CrossRef]
  4. M. Bertero, C. De Mol, and E. R. Pike, Inverse Probl. 1, 301 (1985). [CrossRef]
  5. M. Bertero, C. De Mol, and E. R. Pike, Inverse Probl. 4, 573 (1988). [CrossRef]
  6. A. N. Tikhonov, A. V. Goncharsky, V. V. Steponov, and A. G. Yagola, Mathematical Methods for the Solution of Ill-Posed Problems (Kluwer, 1995).
  7. Y. P. Petrov and V. S. Sizikov, Well-Posed, Ill-Posed, and Intermediate Problems with Applications (VSP, 2005).
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), Chap. 2.
  9. M.Abramowitz and I.A.Stegun, eds., Handbook of Mathematical Functions, Vol. 55 of Applied Mathematics Series (National Bureau of Standards, 1972).

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