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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 1 — Jan. 4, 2010

Image formation in holographic tomography: high-aperture imaging conditions

Shan Shan Kou and Colin J. R. Sheppard  »View Author Affiliations

Applied Optics, Vol. 48, Issue 34, pp. H168-H175 (2009)

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Three-dimensional (3D) imaging by holographic tomography can be performed for a fixed detector through rotation of either the object or the illumination beam. We have previously presented a paraxial treatment to distinguish between these two approaches using transfer function analysis. In particular, the cutoff of the transfer function when rotating the illumination about one axis was calculated analyt ically using one-dimensional Fourier integration of the defocused transfer function. However, high numerical aperture objectives are usually used in experimental arrangements, and the previous paraxial model is not accurate in this case. Hence, in this analysis, we utilize 3D analytical geometry to derive the imaging behavior for holographic tomography under high-aperture conditions. As expected, the cutoff of the new transfer function leads to a similar peanut shape, but we found that there was no line singularity as was previously observed in the paraxial case. We also present the theory of coherent transfer function for holographic tomography under object rotation while the detector is kept stationary. The derived coherent transfer functions offer quantitative insights into the image formation of a diffractive tomography system.

© 2009 Optical Society of America

OCIS Codes
(110.6960) Imaging systems : Tomography
(180.6900) Microscopy : Three-dimensional microscopy
(090.1995) Holography : Digital holography

Original Manuscript: July 2, 2009
Revised Manuscript: October 19, 2009
Manuscript Accepted: October 19, 2009
Published: November 5, 2009

Virtual Issues
Vol. 5, Iss. 1 Virtual Journal for Biomedical Optics

Shan Shan Kou and Colin J. R. Sheppard, "Image formation in holographic tomography: high-aperture imaging conditions," Appl. Opt. 48, H168-H175 (2009)

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  1. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial Mathematics, 2001). [CrossRef]
  2. H. Stark, Image Recovery: Theory and Application (Academic, 1987).
  3. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102-168104 (2006). [CrossRef] [PubMed]
  4. J. R. Price, P. R. Bingham, and C. E. Thomas, “Improving resolution in microscopic holography by computationally fusing multiple, obliquely illuminated object waves in the Fourier domain,” Appl. Opt. 46, 827-833 (2007). [CrossRef] [PubMed]
  5. G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe's limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905-213904 (2009). [CrossRef] [PubMed]
  6. S. S. Kou and C. J. R. Sheppard, “Imaging in digital holographic microscopy,” Opt. Express 15, 13640-13648 (2007). [CrossRef] [PubMed]
  7. V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. (Oxford) 205, 165-176 (2002). [CrossRef]
  8. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. Dasari, and M. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717-719 (2007). [CrossRef] [PubMed]
  9. F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178-180 (2006). [CrossRef] [PubMed]
  10. S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, “Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space,” Central Eur. J. Phys. 7, 22-31 (2009). [CrossRef]
  11. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153-156 (1969). [CrossRef]
  12. R. W. James, Optical Principles of the Diffraction of X-Rays, 1st ed. (G. Bell, 1982).
  13. D. W. Sweeney and C. M. Vest, “Reconstruction of three-dimensional refractive index fields from multidirectional interferometric data,” Appl. Opt. 12, 2649-2664 (1973). [CrossRef] [PubMed]
  14. A. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336-350 (1982). [CrossRef] [PubMed]
  15. R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323-328 (1970). [CrossRef]
  16. C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik (Jena) 72, 131-133 (1986).
  17. S. S. Kou and C. J. R. Sheppard, “Image formation in holographic tomography,” Opt. Lett. 33, 2362-2364(2008). [CrossRef] [PubMed]
  18. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  19. C. J. R. Sheppard and M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. 165, 377-390 (1991), [CrossRef]
  20. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).
  21. A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. (Chapman & Hall/CRC Press, 2006).
  22. A. J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Opt. Lett. 7, 111-112 (1982). [CrossRef] [PubMed]
  23. A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6, 374-376 (1981). [CrossRef] [PubMed]
  24. C. J. R. Sheppard, T. J. Connolly, and M. Gu, “Scattering by a one-dimensional rough surface and surface reconstruction by confocal imaging,” Phys. Rev. Lett. 70, 1409-1412(1993). [CrossRef] [PubMed]
  25. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, 1960).
  26. Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266-277 (2009). [CrossRef] [PubMed]

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