OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 26 — Dec. 24, 2007
  • pp: 17592–17612

Holography with extended reference by autocorrelation linear differential operation

Manuel Guizar-Sicairos and James R. Fienup  »View Author Affiliations

Optics Express, Vol. 15, Issue 26, pp. 17592-17612 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (3504 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We introduce a generalization of Fourier transform holography that allows the use of the boundary waves of an extended object to act as a holographic-like reference. By applying a linear differential operator on the field autocorrelation, we use a sharp feature on the extended reference to reconstruct a complex-valued image of the object of interest in a single-step computation. We generalize the approach of Podorov et al. [Opt. Express 15, 9954 (2007)] to a much wider class of extended reference objects. Effects of apertures in Fourier domain and imperfections in the reference object are analyzed. Realistic numerical simulations show the feasibility of our approach and its robustness against noise.

© 2007 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(100.5070) Image processing : Phase retrieval
(110.7440) Imaging systems : X-ray imaging
(090.1995) Holography : Digital holography
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:

Original Manuscript: October 5, 2007
Revised Manuscript: November 29, 2007
Manuscript Accepted: December 1, 2007
Published: December 11, 2007

Manuel Guizar-Sicairos and James R. Fienup, "Holography with extended reference by autocorrelation linear differential operation," Opt. Express 15, 17592-17612 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. N. Leith and J. Upatnieks, "Reconstructed wavefronts and communication theory," J. Opt. Soc. Am. 52, 1123-1130 (1962). [CrossRef]
  2. J. W. Goodman, Introduction to Fourier Optics, 3rd Ed. (Roberts & Company, Englewood, 2005).
  3. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  4. J. R. Fienup, "Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint," J. Opt. Soc. Am. A 4, 118-123 (1987). [CrossRef]
  5. P. S. Idell, J. R. Fienup and R. S. Goodman, "Image synthesis from nonimaged laser-speckle patterns," Opt. Lett. 12, 858-860 (1987). [CrossRef] [PubMed]
  6. J. N. Cederquist, J. R. Fienup, J. C. Marron and R. G. Paxman, "Phase retrieval from experimental far-field speckle data," Opt. Lett. 13, 619-621 (1988). [CrossRef] [PubMed]
  7. J. R. Fienup, "Lensless coherent imaging by phase retrieval with an illumination pattern constraint," Opt. Express 14, 498-508 (2006). [CrossRef] [PubMed]
  8. J. Miao, P. Charalambous, J. Kirz and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature 400, 342-344 (1999). [CrossRef]
  9. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101 (2003). [CrossRef]
  10. S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt and J. Stöhr, "Lensless imaging of magnetic nanostructures by x-ray spectro-holography," Nature 432, 885-888 (2004). [CrossRef] [PubMed]
  11. D. Shapiro et al., "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005). [CrossRef] [PubMed]
  12. H. N. Chapman et al., "Femtosecond diffractive imaging with a soft-x-ray free-electron laser," Nat. Phys. 2, 839-843 (2006). [CrossRef]
  13. L.M. Stadler, R. Harder, I. K. Robinson, C. Rentenberger, H. P. Karnthaler, B. Sepiol and G. Vogl, "Coherent x-ray diffraction imaging of grown-in antiphase boundaries in Fe65Al35," Phys. Rev. B 76, 014204 (2007). [CrossRef]
  14. H. N. Chapman et al., "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
  15. J. R. Fienup, T. R. Crimmins and W. Holsztynski, "Reconstruction of the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 72, 610-624 (1982). [CrossRef]
  16. T. R. Crimmins, J. R. Fienup and B. J. Thelen, "Improved bounds on object support from autocorrelation support and application to phase retrieval," J. Opt. Soc. Am. A 7, 3-13 (1990). [CrossRef]
  17. J. R. Fienup and C. C. Wackerman, "Phase-retrieval stagnation problems and solutions," J. Opt. Soc. Am. A 3, 1897-1907 (1986). [CrossRef]
  18. H. He, U. Weierstall, J. C. H. Spence, M. Howells, H. A. Padmore, S. Marchesini and H. N. Chapman, "Use of extended and prepared reference objects in experimental Fourier transform x-ray holography," Appl. Phys. Lett. 85, 2454-2456 (2004). [CrossRef]
  19. O. Hellwig, S. Eisebitt, W. Eberhardt, W. F. Schlotter, J. Lüning and J. Stöhr, "Magnetic imaging with soft x-ray spectroholography," J. Appl. Phys. 99, 08H307 (2006). [CrossRef]
  20. I. McNulty, J. Kirz, C. Jacobsen, E. H. Anderson, M. R. Howells and D. P. Kern, "High-Resolution Imaging by Fourier Transform X-ray Holography," Science 256, 1009-1012 (1992). [CrossRef] [PubMed]
  21. W. F. Schlotter et al., "Multiple reference Fourier transform holography with soft x rays," Appl. Phys. Lett. 89, 163112 (2006). [CrossRef]
  22. S. G. Podorov, K. M. Pavlov and D. M. Paganin, "A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging," Opt. Express 15, 9954-9962 (2007). [CrossRef] [PubMed]
  23. G.W. Stroke, R. Restrick, A. Funkhouser and D. Brumm, "Resolution-retrieving compensation of source effects by correlative reconstruction in high-resolution holography," Phys. Lett. 18, 274-275 (1965). [CrossRef]
  24. M. R. Howells, C. J. Jacobsen, S. Marchesini, S. Miller, J. C. H. Spence and U. Weirstall, "Toward a practical X-ray Fourier holography at high resolution," Nucl. Instrum. Methods Phys. Res. A 467, 864-867 (2001). [CrossRef]
  25. R. N. Bracewell, K.-Y. Chang, A. K. Jha and Y.-H. Wang, "Affine theorem for two-dimensional Fourier transform," Electron. Lett. 29, 304 (1993). [CrossRef]
  26. R. N. Bracewell, The Fourier Transform and its Applications, 2nd Ed. (McGraw-Hill, New York, 1978).
  27. J. D. Gaskill and J. W. Goodman, "Use of multiple reference sources to increase the effective field of view in lensless Fourier-transform holography," Proc. IEEE 57, 823-825 (1969). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited