OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 13 — Jun. 20, 2011
  • pp: 12066–12073

Single-distance phase retrieval at large phase shifts

Julian Moosmann, Ralf Hofmann, and Tilo Baumbach  »View Author Affiliations

Optics Express, Vol. 19, Issue 13, pp. 12066-12073 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (2778 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



For coherent X-ray imaging of pure phase objects we study the reliability of linear relations in phase-retrieval algorithms based on a single intensity map after free-space propagation. For large phase changes and/or large propagation distances we propose two venues of working beyond linearity: Projection onto an effective, linear and local model in Fourier space and expansion of intensity contrast in powers of object-detector distance. We apply both algorithms successfully to simulated data.

© 2011 OSA

OCIS Codes
(100.2960) Image processing : Image analysis
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Image Processing

Original Manuscript: March 21, 2011
Revised Manuscript: May 17, 2011
Manuscript Accepted: May 23, 2011
Published: June 7, 2011

Julian Moosmann, Ralf Hofmann, and Tilo Baumbach, "Single-distance phase retrieval at large phase shifts," Opt. Express 19, 12066-12073 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. Henke, E. Gullikson, and J. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, z=1–92,” At. Data. Nucl. Data Tables 54, 181–342 (1993). [CrossRef]
  2. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995). [CrossRef]
  3. P. Cloetens, “Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation,” PhD dissertation, Vrije Universiteit Brussel (1999).
  4. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384, 335–338 (1996). [CrossRef]
  5. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. M. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996). [CrossRef] [PubMed]
  6. A. Momose and J. Fukuda, “Phase-contrast radiographs of nonstained rat cerebellar specimen,” Med. Phys. 22, 375–379 (1995). [CrossRef] [PubMed]
  7. The cone-beam case relates to the parallel-beam case via a simple rescaling operation, see D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006). [CrossRef]
  8. M. R. Teague, “Deterministic phase retrieval: a Greens function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  9. J.-P. Guigay, “Fourier transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik 49, 121–125 (1977).
  10. P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Rejmankova-Pernot, M. Salome, M. Schlenker, J. Y. Buffiere, E. Maire, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D: Appl. Phys. 32, A145–A151 (1999). [CrossRef]
  11. L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12, 2960–2965 (2004). [CrossRef] [PubMed]
  12. T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89, 034102 (2006). [CrossRef]
  13. T. E. Gureyev, Y. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. partially coherent illumination,” Opt. Commun. 259, 569–580 (2006). [CrossRef]
  14. S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, “Optimization of phase contrast imaging using hard X rays,” Rev. Sci. Instrum. 76, 073705 (2005). [CrossRef]
  15. L. Waller, L. Tian, and G. Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express 18, 12552–12561 (2010). [CrossRef] [PubMed]
  16. J. Moosmann, R. Hofmann, A. V. Bronnikov, and T. Baumbach, “Nonlinear phase retrieval from single-distance radiograph,” Opt. Express 18, 25771–25785 (2010). [CrossRef] [PubMed]
  17. J. Moosmann, R. Hofmann, and T. Baumbach, “Nonlinear, single-distance phase retrieval and Schwinger regularization,” To appear in Phys. Status. Solidi A.
  18. L. D. Landau, “The theory of a Fermi liquid,” Sov. Phys. JETP 3, 920–925 (1957).
  19. M. Langer, P. Cloetens, and F. Peyrin, “Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography,” IEEE Transactions on Image Processing 19, 2429–2436 (2010). [CrossRef]
  20. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  21. V. Altapova, D. Hänschke, J. Moosmann, R. Hofmann, and T. Baumbach, “Imaging in evolutionary biology: Single-distance phase contrast, nonlinear-noniterative retrieval, and tomographic reconstruction,” In preparation (2011).

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited