Journal of the Institute of Electronics Engineers of Korea SD (대한전자공학회논문지SD)

The Institute of Electronics and Information Engineers (대한전자공학회)
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A study on the Convergence of Iterative Fourier Transform Algorithm for Optimal Design of Diffractive Optical Elements

회절광학소자의 최적 설계를 위한 Iterative Fourier Transform Algorithm의 수렴성에 관한 연구

  • Kim, Hwi (National Research Laboratory of Holography Technologies, School of Electrical Engineering, Seoul National University) ;
  • Yang, Byung-Choon (National Research Laboratory of Holography Technologies, School of Electrical Engineering, Seoul National University) ;
  • Park, Jin-Hong (National Research Laboratory of Holography Technologies, School of Electrical Engineering, Seoul National University) ;
  • Lee, Byoung-Ho (National Research Laboratory of Holography Technologies, School of Electrical Engineering, Seoul National University)
  • 김휘 (서울대학교 전기공학부) ;
  • 양병춘 (서울대학교 전기공학부) ;
  • 박진홍 (서울대학교 전기공학부) ;
  • 이병호 (서울대학교 전기공학부)
  • Published : 2003.05.01
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Abstract

Iterative Fourier transform algorithm, (IFTA) is tile iterative numerical algorithm for the design of the diffractive optical elements (DOE), by which the phase distribution of a DOE converges on a local optimal solution. The convergence of IFTA depends on several factors 3s initial phase distribution, the structure of the degree of freedom on the observation plane, and the values of internal parameters. In this paper, we analyze tile dependence of the convergence of IFTA on an internal parameter of IFTA, the relaxation parameter, and propose a new hybrid scheme of genetic algorithm and IFTA to obtain more accurate solution.

Iterative Fourier transform algorithm (IFTA)은 회절광학소자 (DOE)의 위상 분포를 구하기 위한 반복적 수치 해석 알고리즘으로서 회절광학소자의 위상 분포는 반복 과정을 통하여 국소 최적해로 수렴하게 된다. Ink의 수렴은 위상 분포 초기치, 관측면에서의 자유도의 허용 범위 및 알고리즘에 내재된 매개 변수들의 설정 값에 영향을 받는다. 본 논문에서는 IFTA의 내부적 매개 변수인 완화 변수(relaxation parameter)가 IFTA의 수렴에 미치는 영향을 분석하고 이를 토대로 보다 정확한 최적화 해를 얻기 위한 유전 알고리즘과 IFTA의 하이브리드 알고리즘을 제안한다.

Keywords

References

  1. R. W. Gerchberg and W. O. Saxton, 'A practical algorithm of the determination of the phase from image and diffraction plane pictures,' Optik, vol. 35, no. 2, pp. 237-46, 1972
  2. V. A. Soifer, V. V. Kotlyar, and L. L. Doskolovich, Iterative methods for diffractive optical elements computation(Taylor & Francis Publishers, London, 1997)
  3. R. W. Gerchberg, 'Super resolution through error energy reduction,' Optica Acta., vol. 21, no. 9, pp. 709-720, 1972
  4. A. Papoulis, 'A new algorithm in spectra analysis and band-limited signal extrapolation,' IEEE Transactions on Circuits and Systems, vol. CAS-22, pp. 735-742,1975 https://doi.org/10.1109/TCS.1975.1084118
  5. F. Wyrowski, 'Diffractive optical elements: iterative calculation of quantized blazed phase structures,' Journal of Optical Society of America A, vol. 7, no. 6, pp. 961-969, 1990 https://doi.org/10.1364/JOSAA.7.000961
  6. J. R. Fineup, 'Phase-retrieval algorithm for a complicated optical system,' Applied Optics, vol. 32, no. 10, pp. 1737-1746, 1993 https://doi.org/10.1364/AO.32.001737
  7. Z. Michalewicz, Genetic Algorithms+Data Structures = Evolution Programs, Berlin,1992
  8. E. G. Jonson and M. A. G. Abushagur, 'Microgenetic-algorithm optimization methods applied to dielectric gratings,' J. Opt. Am. A., vol. 12, pp. 1152-1160, 1995 https://doi.org/10.1364/JOSAA.12.001152
  9. S. Rudnaya, Analysis and Optimal Design of Diffractive Optical Elements, Ph. D. thesis, Univ. of Minnesota, 1999
  10. J. Goodman, Introduction to Fourier Optics, 2nd ed.(McGraw-Hill Book Co., New York, 1996)
  11. H. Kim, B. Yang, and B. Lee, 'Iterative Fourier transform algorithm with Tikhonov's regularization for the optical design of diffractive optical elements,' International Workshop on Optical Display and Information Processing, pp. 271-272, Gyeoungju, Korea, May 2002
  12. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems(Kluwer Academic Publishers, Dordrecht, Boston, London,1996)
  13. V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, 'An iterative algorithm for designing diffractive optical elements with regularization', Opt. Las. Eng., vol 29, pp. 261-268, 1998 https://doi.org/10.1016/S0143-8166(97)00114-0
  14. 김휘, 양병춘, 박진홍, 이병호, '회절광학소자 설계를 위한 반복 푸리에 알고리즘의 최척활용에 대한 연구', 제8회 광전자 및 광통신 학술회의, FD2-2, pp. 357-358, 2001
  15. A. M. Cohen and M. Woodring, Win32 Multithreaded Programming(O'Reilly & Associated Inc., Sebastopol, CA, 1998)