OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 24 — Nov. 24, 2008
  • pp: 19926–19933

Generation of hollow Gaussian beam by phase-only filtering

Zhengjun Liu, Jingmin Dai, Xiaogang Sun, and Shutian Liu  »View Author Affiliations

Optics Express, Vol. 16, Issue 24, pp. 19926-19933 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (936 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a novel phase retrieval algorithm in Hankel (or called Fourier-Bessel) transform domains by using Monte-Carlo method. Based on the proposed algorithm, we investigate the generation of Gaussian-like beams, such as hollow Gaussian beam, Bessel-Gaussian beam and Laguerre-Gaussian beam, with double phase filtering operations. The phase distributions of filters are determined by employing the proposed phase retrieval algorithm. The advantage of the method is that the total energy of the beam is conservative. Numerical simulations are shown to demonstrate the validity of the scheme.

© 2008 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(140.3300) Lasers and laser optics : Laser beam shaping
(350.5500) Other areas of optics : Propagation

ToC Category:
Image Processing

Original Manuscript: September 9, 2008
Revised Manuscript: November 3, 2008
Manuscript Accepted: November 9, 2008
Published: November 19, 2008

Zhengjun Liu, Jingmin Dai, Xiaogang Sun, and Shutian Liu, "Generation of hollow Gaussian beam by phase-only filtering," Opt. Express 16, 19926-19933 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713-4716 (1997). [CrossRef]
  2. H. Ito, T. Nakata, K. Sakaki, M. Ohtsu, K. I. Lee, and W. Jhe, "Laser spectroscopy of atoms guided by evanescent waves in micron-sized hollow optical fibers," Phys. Rev. Lett. 76, 4500 (1996). [CrossRef] [PubMed]
  3. Y. K. Wu, J. Li, and J. Wu, "Anomalous hollow electron beams in a storage ring," Phys. Rev. Lett. 94, 134802 (2005). [CrossRef] [PubMed]
  4. Y. Cai, X. Lu, and Q. Lin, "Hollow Gaussian beams and their propagation properties," Opt. Lett. 28, 1084 (2003). [CrossRef] [PubMed]
  5. Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, "Generation of hollow Gaussian beams by spatial filtering," Opt. Lett. 32, 2076 (2007). [CrossRef] [PubMed]
  6. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, "Spin-to-orbital angular momentum conversion in a strongly focused optical beam," Phys. Rev. Lett. 99, 073901 (2007). [CrossRef] [PubMed]
  7. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).
  8. Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, "Gerchberg-Saxton algorithm applied in the fractional Fourieror the Fresnel domain," Opt. Lett. 21, 842-844 (1996). [CrossRef] [PubMed]
  9. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, and M. G. Raymer, "Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms," Opt. Lett. 20, 1181-1183 (1995). [CrossRef] [PubMed]
  10. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barena, "Quantitative Phase Imaging using Hard X Rays," Phys. Rev. Lett. 77, 2961-2964 (1996). [CrossRef] [PubMed]
  11. J. Miao T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Hodgson, "High resolution 3D X-ray diffraction microscopy," Phys. Rev. Lett. 89, 088303 (2002). [CrossRef] [PubMed]
  12. F. Meng, H. Liu, and X. Wu, "An iterative phase retrieval algorithm for in-line x-ray phase imaging," Opt. Express 15, 8383-8390 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-13-8383. [CrossRef] [PubMed]
  13. J. M. Zuo I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, "Atomic resolution imaging of a carbon nanotube from diffraction intensities," Science 300, 1419 (2003). [CrossRef] [PubMed]
  14. R. Borghi, F. Gori, and M. Santarsiero, "Phase and amplitude retrieval in ghost diffraction from field-correlation measurements," Phys. Rev. Lett. 96, 183901 (2006). [CrossRef] [PubMed]
  15. A. Anand, G. Pedrini, W. Osten, and P. Almoro, "Wavefront sensing with random amplitude mask and phase retrieval," Opt. Lett. 32, 1584-1586 (2007). [CrossRef] [PubMed]
  16. P. Almoro, G. Pedrini, and W. Osten, "Wavefront sensing with random amplitude mask and phase retrieval," Opt. Lett. 32, 733-735 (2007). [CrossRef] [PubMed]
  17. A. K. Ellerbee and J. A. Izatt, "Phase retrieval in low-coherence interferometric microscopy," Opt. Lett. 32, 388-390 (2007). [CrossRef] [PubMed]
  18. J. Zhong and J. Weng, "Phase retrieval of optical fringe patterns from the ridge of a wavelet transform," Opt. Lett. 30, 2560-2562 (2005). [CrossRef] [PubMed]
  19. J. S. Wu, U. Weierstall, J. C. H. Spence, and C. T. Koch, "Iterative phase retrieval without support," Opt. Lett. 29, 2737 (2004). [CrossRef] [PubMed]
  20. N. Nakajima, "Phase and amplitude retrieval in ghost diffraction from field-correlation measurements," Phys. Rev. Lett. 98, 223901 (2007). [CrossRef] [PubMed]
  21. F. Zhang, G. Pedrini, and W. Osten, "Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation," Phys. Rev. A 75, 043805 (2007). [CrossRef]
  22. T. Latychevskaia and H.-W. Fink, "Solution to the twin image problem in holography," Phys. Rev. Lett. 98, 233901 (2007). [CrossRef] [PubMed]
  23. Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, "Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm," Opt. Express 11, 3234-3241 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-24-3234. [CrossRef] [PubMed]
  24. Z. Liu and S. Liu, "Double image encryption based on iterative fractional Fourier transform," Opt. Commun. 272, 324-329 (2007). [CrossRef]
  25. 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, 209 (1994). [CrossRef] [PubMed]
  26. B. Dong, Y. Zhang, B. Gu, and G. Yang, "Numerical investigation of phase retrieval in a fractional Fourier transform," J. Opt. Soc. Am. A 14, 2709-2714 (1997). [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