OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 7 — Jul. 16, 2007

Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region

Jean Pierre Guigay, Max Langer, Renaud Boistel, and Peter Cloetens  »View Author Affiliations

Optics Letters, Vol. 32, Issue 12, pp. 1617-1619 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (253 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a method for phase retrieval in propagation-based x-ray imaging, based on the contrast transfer and transport of intensity equation approaches. We show that the contrast transfer model does not coincide with the transport of intensity in the limit of small propagation distances, and we derive a new model that alleviates this problem. Using this model, we devise an algorithm to retrieve the phase from slowly varying samples that is valid beyond the limit of small distances. We show its utility by imaging in three dimensions a biological sample that causes both strong absorption and phase shift.

© 2007 Optical Society of America

OCIS Codes
(000.2170) General : Equipment and techniques
(100.5070) Image processing : Phase retrieval
(110.0180) Imaging systems : Microscopy
(110.7440) Imaging systems : X-ray imaging
(180.0180) Microscopy : Microscopy

ToC Category:
Imaging Systems

Original Manuscript: February 21, 2007
Manuscript Accepted: March 26, 2007
Published: June 5, 2007

Virtual Issues
Vol. 2, Iss. 7 Virtual Journal for Biomedical Optics

Jean Pierre Guigay, Max Langer, Renaud Boistel, and Peter Cloetens, "Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region," Opt. Lett. 32, 1617-1619 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006). [CrossRef]
  2. A. Momose and J. Fukuda, Med. Phys. 22, 375 (1995). [CrossRef] [PubMed]
  3. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, Rev. Sci. Instrum. 66, 5486 (1995). [CrossRef]
  4. M. R. Teague, J. Opt. Soc. Am. 72, 1199 (1982). [CrossRef]
  5. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996). [CrossRef] [PubMed]
  6. J.-P. Guigay, Optik (Stuttgart) 49, 121 (1977).
  7. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999). [CrossRef]
  8. S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, Rev. Sci. Instrum. 76, 1 (2005). [CrossRef]
  9. X. Wu and H. Liu, J. X-Ray Sci. Technol. 11, 33 (2003).
  10. L. D. Turner, B. B. Dhal, J. P. Hayes, A. P. Mancuso, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, Opt. Express 12, 2690 (2004). [CrossRef]
  11. D. M. Paganin, Coherent X-Ray Optics (Oxford U. Press, 2006). [CrossRef]

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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited