Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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
Online
ISSN
2391-5471
See all formats and pricing
More options …
Volume 7, Issue 1 (Mar 2009)

Issues

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

Abstract

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)90052-2CrossrefGoogle Scholar

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

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

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

  • [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 Google Scholar

  • [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:2008049CrossrefGoogle Scholar

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

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

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

  • [10] W. Choi et al., Nat. Methods 4, 717 (2007) http://dx.doi.org/10.1038/nmeth1078CrossrefGoogle Scholar

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

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

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

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

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

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

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

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

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. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in