OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 40, Iss. 11 — Apr. 10, 2001
  • pp: 1795–1805

Cone-beam tomography with a digital camera

Daniel L. Marks, Ronald Stack, Andrew J. Johnson, David J. Brady, and David C. Munson, Jr.  »View Author Affiliations

Applied Optics, Vol. 40, Issue 11, pp. 1795-1805 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (4035 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We show that x-ray computer tomography algorithms can be applied with minimal alteration to the three-dimensional reconstruction of visible sources. Diffraction and opacity affect visible systems more severely than x-ray systems. For camera-based tomography, diffraction can be neglected for objects within the depth of field. We show that, for convex objects, opacity has the effect of windowing the angular observation range and thus blurring the reconstruction. For concave objects, opacity leads to nonlinearity in the transformation from object to reconstruction and may cause multiple objects to map to the same reconstruction. In x-ray tomography, the contribution of an object point to a line integral is independent of the orientation of the line. In optical tomography, however, a Lambertian assumption may be more realistic. We derive an expression for the blur function (the patch response) for a Lambertian source. We present experimental results showing cone-beam reconstruction of an incoherently illuminated opaque object.

© 2001 Optical Society of America

OCIS Codes
(100.6890) Image processing : Three-dimensional image processing
(100.6950) Image processing : Tomographic image processing
(110.6880) Imaging systems : Three-dimensional image acquisition
(150.6910) Machine vision : Three-dimensional sensing

Original Manuscript: May 16, 2000
Revised Manuscript: November 27, 2000
Published: April 10, 2001

Daniel L. Marks, Ronald Stack, Andrew J. Johnson, David J. Brady, and David C. Munson, "Cone-beam tomography with a digital camera," Appl. Opt. 40, 1795-1805 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. Ahuja, A. L. Abbott, “Active stereo: integrating disparity, vergence, focus, aperture, and calibration for surface estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1007–1029 (1993). [CrossRef]
  2. A. Pentland, S. Scherock, T. Darrell, B. Girod, “Simple range cameras based on focal error,” J. Opt. Soc. Am. A 11, 2925–2934 (1994). [CrossRef]
  3. S. K. Nayar, Y. Nakagama, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824–831 (1994). [CrossRef]
  4. S. K. Nayar, M. Watanabe, M. Noguchi, “Real-time focus range sensor,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186–1198 (1996). [CrossRef]
  5. T. Wilson, ed., Confocal Microscopy (Academic, San Diego, Calif., 1990).
  6. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991). [CrossRef] [PubMed]
  7. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence tomography in scattering media,” Opt. Lett. 19, 590–592 (1994). [CrossRef] [PubMed]
  8. B. L. Stann, W. C. Ruff, Z. G. Sztankay, “Intensity-modulated diode laser radar using frequency modulation/continuous wave ranging techniques,” Opt. Eng. 35, 3270–3278 (1996). [CrossRef]
  9. D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284, 2164–2166 (1999). [CrossRef] [PubMed]
  10. J. Rosen, A. Yariv, “Reconstruction of longitudinal distributed incoherent sources,” Opt. Lett. 21, 1803–1806 (1996). [CrossRef] [PubMed]
  11. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).
  12. D. I. Marks, D. J. Brady, “Three-dimensional source reconstruction with a scanned pinhole camera,” Opt. Lett. 23, 820–822 (1998). [CrossRef]
  13. D. L. Marks, R. A. Stack, D. J. Brady, J. van der Gracht, “Three-dimensional tomography using a cubic-phase plate extended depth-of-field system,” Opt. Lett. 24, 253–255 (1999). [CrossRef]
  14. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1980).
  15. E. R. Dowski, W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995). [CrossRef] [PubMed]
  16. S. Bradburn, W. T. Cathey, E. R. Dowski, “Realizations of focus invariance in optical-digital systems with wave-front coding,” Appl. Opt. 36, 9157–9166 (1997). [CrossRef]
  17. H. K. Tuy, “An inversion formula for cone-beam tomography,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 43, 546–552 (1983). [CrossRef]
  18. L. A. Feldkamp, L. C. Davis, J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. A 1, 612–619 (1984). [CrossRef]
  19. P. A. Rattey, A. G. Lindgren, “Sampling the 2-D Radon transform,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 994–1002 (1981). [CrossRef]
  20. A. J. Johnson, “Patch response of cone-beam tomography,” M. S. thesis (University of Illinois at Urbana-Champaign, Urbana, Illinois, 1999).
  21. A. J. Johnson, D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, “Three-dimensional surface reconstruction of optical Lambertian objects using cone-beam tomography,” in Proceedings of the IEEE Conference on image processing (Institute for Electrical and Electronics Engineers, New York, 1999), pp. 663–667.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited