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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 4 — Apr. 1, 2001
  • pp: 791–800

Design of diffractive phase elements for beam shaping: hybrid approach

Guangya Zhou, Xiaocong Yuan, Philip Dowd, Yee-Loy Lam, and Yuen-Chuen Chan  »View Author Affiliations

JOSA A, Vol. 18, Issue 4, pp. 791-800 (2001)

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Hybrid approaches that combine genetic algorithms (GA’s) with traditional gradient-based local search techniques are proposed for the optimization design of diffractive phase elements (DPE’s) for laser beam shaping. These hybrid methods exploit the global nature of the GA’s as well as the local improvement capabilities of the gradient-based local search techniques and will perform a more improved search in comparison with each of the individual approaches. The incorporated local search technique that we used here is the Davidon–Fletcher–Powell method. A cost function that can directly control the performance of the final solutions is also used. By performing the DPE design with different desired diffraction efficiencies, we obtain a set of results that approximately reflect the trade-off between the design objectives, namely, signal-to-noise ratio (SNR) and diffraction efficiency. Reasonable solutions can be chosen on the basis of the knowledge of the problem. Simulation computations are detailed for two rotationally symmetric beam-shaping systems, in which an incident Gaussian profile laser beam is converted into a uniform beam and a zero-order Bessel beam. Numerical results demonstrate that the proposed algorithm is highly efficient and robust. DPE’s that have high diffraction efficiency and excellent SNR can be achieved by using the algorithm that we propose.

© 2001 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1970) Diffraction and gratings : Diffractive optics
(140.3300) Lasers and laser optics : Laser beam shaping

Original Manuscript: June 5, 2000
Revised Manuscript: October 19, 2000
Manuscript Accepted: November 1, 2000
Published: April 1, 2001

Guangya Zhou, Xiaocong Yuan, Philip Dowd, Yee-Loy Lam, and Yuen-Chuen Chan, "Design of diffractive phase elements for beam shaping: hybrid approach," J. Opt. Soc. Am. A 18, 791-800 (2001)

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  1. W. B. Veldkamp, C. J. Kastner, “Beam profile shaping for laser radars that use detector arrays,” Appl. Opt. 21, 345–356 (1982). [CrossRef] [PubMed]
  2. J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32, 2538–2542 (1993). [CrossRef] [PubMed]
  3. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of lasers for uniform target acceleration and plasma instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984). [CrossRef]
  4. M. Arif, M. M. Hossain, A. A. S. Awwal, M. N. Islam, “Refracting system for annular Gaussian-to-Bessel beam transformation,” Appl. Opt. 37, 649–652 (1998). [CrossRef]
  5. M. Kuittinen, P. Vahimaa, M. Honkanen, J. Turunen, “Beam shaping in the nonparaxial domain of diffractive optics,” Appl. Opt. 36, 2034–2041 (1997). [CrossRef] [PubMed]
  6. J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995). [CrossRef]
  7. G. J. Swanson, W. B. Weldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989). [CrossRef]
  8. O. Bryngdahl, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974). [CrossRef]
  9. O. Bryngdahl, “Optical map transformations,” Opt. Commun. 10, 164–166 (1974). [CrossRef]
  10. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  11. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980). [CrossRef]
  12. F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991). [CrossRef]
  13. F. Wyrowski, O. Bryngdahl, “Iterative Fourier transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988). [CrossRef]
  14. J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1176 (1989). [CrossRef]
  15. B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989). [CrossRef]
  16. E. G. Johnson, A. D. Kathman, D. H. Hochmuth, A. Cook, D. R. Brown, B. Delaney, “Advantages of genetic algorithm optimization methods in diffractive optic design,” in Diffractive and Miniaturized Optics, S.-H. Lee, ed., Vol. CR49 of Critical Review Series (SPIE Press, Bellingham, Wash.,1993), pp. 54–74.
  17. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983). [CrossRef] [PubMed]
  18. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953). [CrossRef]
  19. X. Qi, F. Palmieri, “Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space: Part I. Basic properties of selection and mutation,” IEEE Trans. Neural Netw. 5, 102–119 (1994). [CrossRef]
  20. J. M. Renders, S. P. Flasse, “Hybrid methods using genetic algorithms for global optimization,” IEEE Trans. Syst. Man Cybern. 26, 243–258 (1996). [CrossRef]
  21. G. Zhou, Y. Chen, Z. Wang, H. Song, “Genetic local search algorithm for optimization design of diffractive optical elements,” Appl. Opt. 38, 4281–4290 (1999). [CrossRef]
  22. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4, pp. 63–90.
  23. A. M. S. Zalzala, P. J. Fleming, eds., Genetic Algorithms in Engineering Systems (Institution of Electrical Engineers, London, 1997), Chap. 1, pp. 10–12.
  24. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989), Chap 5, pp. 148–214.
  25. M. A. Wolfe, Numerical Methods for Unconstrained Optimization: An Introduction (Van Nostrand Reinhold, New York, 1978), Chap. 6, pp. 161–167.
  26. A. E. Siegman, “Quasi fast Hankel transform,” Opt. Lett. 1, 13–15 (1977). [CrossRef] [PubMed]
  27. H. H. Hopkins, “The numerical evaluation of the frequency response of optical systems,” Proc. Phys. Soc. London Sect. B 70, 1002–1005 (1957). [CrossRef]
  28. S. N. Dixit, I. M. Thomas, B. W. Woods, A. J. Morgan, M. A. Henesian, P. J. Wegner, H. T. Powell, “Random phase plates for beam smoothing on the Nova laser,” Appl. Opt. 32, 2543–2554 (1993). [CrossRef] [PubMed]
  29. C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991). [CrossRef]
  30. P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance distribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980). [CrossRef] [PubMed]
  31. X. Tan, B. Y. Gu, G. Z. Yang, B. Z. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34, 1314–1320 (1995). [CrossRef] [PubMed]
  32. J. E. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987). [CrossRef]
  33. J. E. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beam,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef] [PubMed]
  34. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988). [CrossRef] [PubMed]
  35. W. X. Cong, N. X. Chen, B. Y. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. A 15, 2362–2364 (1998). [CrossRef]

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