OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 26 — Dec. 20, 2010
  • pp: 27036–27047

Packed domain Rayleigh-Sommerfeld wavefield propagation for large targets

Andreas Wuttig, Mario Kanka, Hans Jürgen Kreuzer, and Rainer Riesenberg  »View Author Affiliations

Optics Express, Vol. 18, Issue 26, pp. 27036-27047 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1115 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



For applications in the domain of digital holographic microscopy, we present a fast algorithm to propagate scalar wave fields from a small source area to an extended, parallel target area of coarser sampling pitch, using the first Rayleigh-Sommerfeld diffraction formula. Our algorithm can take full advantage of the fast Fourier transform by decomposing the convolution kernel of the propagation into several convolution kernel patches. Using partial overlapping of the patches together with a soft blending function, the Fourier spectrum of these patches can be reduced to a low number of significant components, which can be stored in a compact sparse array structure. This allows for rapid evaluation of the partial convolution results by skipping over negligible components through the Fourier domain pointwise multiplication and direct mapping of the remaining multiplication results into a Fourier domain representation of the coarsly sampled target patch. The algorithm has been verified experimentally at a numerical aperture of 0.62, not showing any significant resolution limitations.

© 2010 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(180.0180) Microscopy : Microscopy
(090.1995) Holography : Digital holography
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Physical Optics

Original Manuscript: October 6, 2010
Revised Manuscript: November 15, 2010
Manuscript Accepted: November 19, 2010
Published: December 8, 2010

Andreas Wuttig, Mario Kanka, Hans Jürgen Kreuzer, and Rainer Riesenberg, "Packed domain Rayleigh-Sommerfeld wavefield propagation for large targets," Opt. Express 18, 27036-27047 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Gu, Advanced Optical Imaging Theory, vol. 75 of Optical Sciences (Springer, Berlin, Germany, 1999).
  2. P. P. Vaidyanathan, "Generalizations of the Sampling Theorem: Seven Decades After Nyquist," IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48, 1094-1109 (2001). [CrossRef]
  3. F. Shen, and A. Wang, "Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula," Appl. Opt. 45(6), 1102-1110 (2006). [CrossRef] [PubMed]
  4. D. Gabor, "A new microscopic principle," Nature 161(4098), 777 (1948). [CrossRef] [PubMed]
  5. U. Schnars, "Direct phase determination in hologram interferometry with use of digitally recorded holograms," J. Opt. Soc. Am. A 11(7), 2011-2015 (1994). [CrossRef]
  6. H. J. Kreuzer, "Low energy electron point source microscopy," Micron 26(6), 503-509 (1995). [CrossRef]
  7. H. J. Kreuzer, "Holographic microscope and method of hologram reconstruction," US 6,411,406 B1, June 25, 2002 (Canadian Patent CA2376395).
  8. R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 227-246 (1972).
  9. G.-Z. Yang, B.-Z. Dong, B.-Y. Gu, J.-Y. Zhuang, and O. K. Ersoy, "Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison," Appl. Opt. 33(2), 209-218 (1994). [CrossRef] [PubMed]
  10. A. Grjasnow, A. Wuttig, and R. Riesenberg, "Phase resolving microscopy by multi-plane diffraction detection," J. Microsc. 231(1), 115-123 (2008). [CrossRef] [PubMed]
  11. G. C. Sherman, "Application of the Convolution Theorem to Rayleigh’s Integral Formulas," J. Opt. Soc. Am. 57(4), 546-547 (1967) (Proof: Rayleigh-Sommerfeld-integral ) (CV) ( equals angular spectrum ) (AS). [CrossRef] [PubMed]
  12. J. Li, Z. Peng, and Y. Fu, "Diffraction transfer function and its calculation of classic diffraction formula," Opt. Commun. 280(2), 243-248 (2007). [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics, Electrical and Computer Engineering, 2nd ed. (McGraw-Hill Companies, Inc., USA, 1996).
  14. M. Kanka, R. Riesenberg, and H. J. Kreuzer, "Reconstruction of high-resolution holographic microscopic images," Opt. Lett. 34(8), 1162-1164 (2009). [CrossRef] [PubMed]
  15. M. Kanka, A. Wuttig, C. Graulig, and R. Riesenberg, "Fast exact scalar propagation for an in-line holographic microscopy on the diffraction limit," Opt. Lett. 35(2), 217-219 (2010). [CrossRef] [PubMed]
  16. V. Nascov, and P. C. Logofătu, "Fast computation algorithm for the Rayleigh-Sommerfeld diffraction formula using a type of scaled convolution," Appl. Opt. 48(22), 4310-4319 (2009). [CrossRef] [PubMed]
  17. M. Paturzo, P. Memmolo, L. Miccio, A. Finizio, P. Ferraro, A. Tulino, and B. Javidi, "Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase," Opt. Lett. 33(22), 2629-2631 (2008). [CrossRef] [PubMed]
  18. M. Frigo, and S. G. Johnson, "The Design and Implementation of FFTW3," in Proc. IEEE, vol. 93, pp. 216-231 (2005). [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
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited