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A study on the Convergence of Iterative Fourier Transform Algorithm for Optimal Design of Diffractive Optical Elements  

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)
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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.
Keywords
Iterative Fourier transform algorithm; diffractive optical element; relaxation Parameter; genetic algorithm;
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1 R. W. Gerchberg, 'Super resolution through error energy reduction,' Optica Acta., vol. 21, no. 9, pp. 709-720, 1972
2 J. R. Fineup, 'Phase-retrieval algorithm for a complicated optical system,' Applied Optics, vol. 32, no. 10, pp. 1737-1746, 1993   DOI
3 Z. Michalewicz, Genetic Algorithms+Data Structures = Evolution Programs, Berlin,1992
4 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
5 V. A. Soifer, V. V. Kotlyar, and L. L. Doskolovich, Iterative methods for diffractive optical elements computation(Taylor & Francis Publishers, London, 1997)
6 J. Goodman, Introduction to Fourier Optics, 2nd ed.(McGraw-Hill Book Co., New York, 1996)
7 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   DOI
8 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   DOI
9 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   DOI   ScienceOn
10 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   DOI   ScienceOn
11 S. Rudnaya, Analysis and Optimal Design of Diffractive Optical Elements, Ph. D. thesis, Univ. of Minnesota, 1999
12 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
13 H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems(Kluwer Academic Publishers, Dordrecht, Boston, London,1996)
14 A. M. Cohen and M. Woodring, Win32 Multithreaded Programming(O'Reilly & Associated Inc., Sebastopol, CA, 1998)
15 김휘, 양병춘, 박진홍, 이병호, '회절광학소자 설계를 위한 반복 푸리에 알고리즘의 최척활용에 대한 연구', 제8회 광전자 및 광통신 학술회의, FD2-2, pp. 357-358, 2001