Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Feng, Jonathan

Managing Editor: Lesna-Szreter, Paulina

1 Issue per year

IMPACT FACTOR 2016 (Open Physics): 0.745
IMPACT FACTOR 2016 (Central European Journal of Physics): 0.765

CiteScore 2016: 0.82

SCImago Journal Rank (SJR) 2015: 0.458
Source Normalized Impact per Paper (SNIP) 2015: 1.142

Open Access
See all formats and pricing
In This Section
Volume 7, Issue 1 (Mar 2009)


Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space

Stanislas Vertu
  • Department of Engineering Synthesis, School of Engineering, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo, 113-8656, Japan
  • Email:
/ Jean-Jacques Delaunay
  • Department of Engineering Synthesis, School of Engineering, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo, 113-8656, Japan
  • Email:
/ Ichiro Yamada
  • Department of Engineering Synthesis, School of Engineering, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo, 113-8656, Japan
  • Email:
/ Olivier Haeberlé
  • Laboratory MIPS - University of Haute Alsace, IUT Mulhouse, 61 rue Albert Camus, 68093, Mulhouse Cedex, France
  • Email:
Published Online: 2009-01-08 | DOI: https://doi.org/10.2478/s11534-008-0154-6


Diffraction microtomography in coherent light is foreseen as a promising technique to image transparent living samples in three dimensions without staining. Contrary to conventional microscopy with incoherent light, which gives morphological information only, diffraction microtomography makes it possible to obtain the complex optical refractive index of the observed sample by mapping a three-dimensional support in the spatial frequency domain. The technique can be implemented in two configurations, namely, by varying the sample illumination with a fixed sample or by rotating the sample using a fixed illumination. In the literature, only the former method was described in detail. In this report, we precisely derive the three-dimensional frequency support that can be mapped by the sample rotation configuration. We found that, within the first-order Born approximation, the volume of the frequency domain that can be mapped exhibits a missing part, the shape of which resembles that of an apple core. The projection of the diffracted waves in the frequency space onto the set of sphere caps covered by the sample rotation does not allow for a complete mapping of the frequency along the axis of rotation due to the finite radius of the sphere caps. We present simulations of the effects of this missing information on the reconstruction of ideal objects.

Keywords: image reconstruction; tomography; Fourier optics; holographic interferometry

PACS: 42.; 42.30.-d; 42.40.-i; 42.90.+m

  • [1] E. Wolf, Opt. Commun. 1, 153 (1969) http://dx.doi.org/10.1016/0030-4018(69)90052-2 [Crossref]

  • [2] R. Da̋ndliker, K. Weiss, Opt. Commun. 1, 323 (1970) http://dx.doi.org/10.1016/0030-4018(70)90032-5 [Crossref]

  • [3] V. Lauer, J. Microsc. 205, 165 (2002) http://dx.doi.org/10.1046/j.0022-2720.2001.00980.x [Crossref]

  • [4] S. Kawata, O. Nakamura, S. Minami, J. Opt. Soc. Am. A 4, 292 (1987) http://dx.doi.org/10.1364/JOSAA.4.000292 [Crossref]

  • [5] O. Haeberlé, A. Santenac, H. Giovaninni, In: A.M. Vilas, J.D. Alvarez (Eds.), Modern Research and Educational Topics in Microscopy 3, Vol. II (Formatex, Badajoz, Spain, 2007) 956

  • [6] B. Simon, M. Debailleul, V. Georges, V. Lauer, O. Haeberlé, Eur. Phys. J.-Appl. Phys. 44, 29 (2008) http://dx.doi.org/10.1051/epjap:2008049 [Crossref]

  • [7] M. Debailleul, B. Simon, V. Georges, O. Haeberlé, V. Lauer, Meas. Sci. Technol. 19, 074009 (2008) http://dx.doi.org/10.1088/0957-0233/19/7/074009 [Crossref]

  • [8] F. Charrière et al., Opt. Lett. 31, 178 (2006) http://dx.doi.org/10.1364/OL.31.000178 [Crossref]

  • [9] W. Gorski, W. Osten, Opt. Lett. 32, 1977 (2007) http://dx.doi.org/10.1364/OL.32.001977 [Crossref]

  • [10] W. Choi et al., Nat. Methods 4, 717 (2007) http://dx.doi.org/10.1038/nmeth1078 [Crossref]

  • [11] S. Vertu et al., Proc. SPIE 6627, 66271A (2007)

  • [12] S. Vertu et al., Proc. SPIE 6861, 686103 (2008)

  • [13] A. C. Kak, M. Slaney, Principles of Computerized Tomography Imaging (IEEE Press, New York, 1988)

  • [14] M. Born, E. Wolf, Principles of Optics (Pergamond Press, Exeter, 1991)

  • [15] M. K. Kreysing et al., Opt. Express, 16, 16984 (2008) http://dx.doi.org/10.1364/OE.16.016984 [Crossref]

  • [16] A. Chomik et al., J. Opt. 28, 225 (1997) http://dx.doi.org/10.1088/0150-536X/28/6/001 [Crossref]

  • [17] B. Colicchio, O. Haeberlé, C. Xu, A. Dieterlen, G. Jung, Opt. Commun. 244, 37 (2005) http://dx.doi.org/10.1016/j.optcom.2004.08.039 [Crossref]

  • [18] N. Streibl, J. Opt. Soc. Am. A 2, 121 (1985) http://dx.doi.org/10.1364/JOSAA.2.000121 [Crossref]

About the article

Published Online: 2009-01-08

Published in Print: 2009-03-01

Citation Information: Open Physics, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-008-0154-6. Export Citation

© 2009 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac
Journal of Modern Optics, 2010, Volume 57, Number 9, Page 686
Stanislas Vertu, Jens Flügge, Jean-Jacques Delaunay, and Olivier Haeberlé
Open Physics, 2011, Volume 9, Number 4
C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte
Laser & Photonics Reviews, 2011, Volume 5, Number 1, Page 81
E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac
Optics Letters, 2010, Volume 35, Number 11, Page 1857
Shan Shan Kou and Colin J. R. Sheppard
Applied Optics, 2009, Volume 48, Number 34, Page H168
Reto Fiolka, Kai Wicker, Rainer Heintzmann, and Andreas Stemmer
Optics Express, 2009, Volume 17, Number 15, Page 12407

Comments (0)

Please log in or register to comment.
Log in