Abstract

We propose an efficient evolutionary approach for the thin-film synthesis of inhomogeneous optical coatings. The proposed approach consists of global and local strategies by integration of decreasing-based mutations and self-adaptive mutations by means of family competition and adaptive rules. Numerical results indicate that the proposed approach performs robustly and is competitive with other approaches. Our approach, although somewhat slower, is flexible and can easily be adopted to other application domains. Our approach is also able to generate homogeneous solutions with two materials available.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1986).
    [CrossRef]
  2. J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 42, pp. 2824–2831.
  3. J. A. Aguilera, J. Aguilera, P. Baumeister, A. Bloom, D. Coursen, J. A. Dobrowolski, F. T. Goldstein, D. E. Gustafson, R. A. Kemp, “Antireflection coatings for germanium IR optics: a comparison of numerical design methods,” Appl. Opt. 27, 2832–2840 (1988).
    [CrossRef] [PubMed]
  4. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [CrossRef] [PubMed]
  5. L. Li, J. A. Dobrowolski, “Computation speeds of different optical thin-film synthesis methods,” Appl. Opt. 31, 3790–3799 (1992).
    [CrossRef] [PubMed]
  6. A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993).
    [CrossRef] [PubMed]
  7. B. G. Bovard, “Derivation of a matrix describing a rugate dielectric thin film,” Appl. Opt. 27, 1998–2005 (1988).
    [CrossRef] [PubMed]
  8. S. Martin, J. Rivory, M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt. 34, 2247–2254 (1995).
    [CrossRef] [PubMed]
  9. H. Greiner, “Robust optical coating design with evolutionary strategies,” Appl. Opt. 36, 5477–5482 (1996).
    [CrossRef]
  10. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
  11. T. Bäck, F. Hoffmeister, H.-P. Schwefel, “A survey of evolution strategies,” in Proceedings of the Fourth International Conference on Genetic Algorithms (Michigan State University, East Lansing, Mich., 1991), pp. 2–9.
  12. D. B. Fogel, Evolutionary Computation: Toward a New Philosophy of Machine Intelligence (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995).
  13. T. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evol. Comput. 1, 3–17 (1997).
    [CrossRef]
  14. J.-M. Yang, C.-Y. Kao, “An evolutionary algorithm for synthesizing optical thin-film designs,” in Parallel Probling Solving in Nature—PPSN V, in Vol. 1498 of Lecture Notes in Computer Science Series (Springer-Verlag, Berlin, 1998), pp. 947–958.
    [CrossRef]
  15. J.-M. Yang, C.-Y. Kao, “Integrating adaptive mutations and family competition into genetic algorithms as function optimizer,” Soft Comput. 4, 89–102 (2000).
    [CrossRef]
  16. J.-M. Yang, C.-Y. Kao, “Flexible ligand docking using a robust evolutionary algorithm,” J. Comput. Chem. 21, 988–998 (2000).
    [CrossRef]
  17. B. T. Sullivan, J. A. Dobrowolski, “Implementation of a numerical needle method for thin-film design,” Appl. Opt. 35, 5484–5492 (1996).
    [CrossRef] [PubMed]
  18. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef] [PubMed]
  19. H.-P. Schwefel, Numerical Optimization of Computer Models (Wiley, Chichester, N.Y., 1981).
  20. X. Yao, Y. Liu, “Fast evolution strategies,” 151–161 (1997).
  21. A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
    [CrossRef] [PubMed]

2000

J.-M. Yang, C.-Y. Kao, “Integrating adaptive mutations and family competition into genetic algorithms as function optimizer,” Soft Comput. 4, 89–102 (2000).
[CrossRef]

J.-M. Yang, C.-Y. Kao, “Flexible ligand docking using a robust evolutionary algorithm,” J. Comput. Chem. 21, 988–998 (2000).
[CrossRef]

1997

T. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evol. Comput. 1, 3–17 (1997).
[CrossRef]

1996

1995

1993

1992

1990

1988

1985

Aguilera, J.

Aguilera, J. A.

Bäck, T.

T. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evol. Comput. 1, 3–17 (1997).
[CrossRef]

T. Bäck, F. Hoffmeister, H.-P. Schwefel, “A survey of evolution strategies,” in Proceedings of the Fourth International Conference on Genetic Algorithms (Michigan State University, East Lansing, Mich., 1991), pp. 2–9.

Baumeister, P.

Bloom, A.

Bovard, B. G.

Coursen, D.

DeBell, G. W.

Dobrowolski, J. A.

Fogel, D. B.

D. B. Fogel, Evolutionary Computation: Toward a New Philosophy of Machine Intelligence (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995).

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Goldstein, F. T.

Greiner, H.

H. Greiner, “Robust optical coating design with evolutionary strategies,” Appl. Opt. 36, 5477–5482 (1996).
[CrossRef]

Gustafson, D. E.

Hammel, U.

T. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evol. Comput. 1, 3–17 (1997).
[CrossRef]

Hoffmeister, F.

T. Bäck, F. Hoffmeister, H.-P. Schwefel, “A survey of evolution strategies,” in Proceedings of the Fourth International Conference on Genetic Algorithms (Michigan State University, East Lansing, Mich., 1991), pp. 2–9.

Kao, C.-Y.

J.-M. Yang, C.-Y. Kao, “Integrating adaptive mutations and family competition into genetic algorithms as function optimizer,” Soft Comput. 4, 89–102 (2000).
[CrossRef]

J.-M. Yang, C.-Y. Kao, “Flexible ligand docking using a robust evolutionary algorithm,” J. Comput. Chem. 21, 988–998 (2000).
[CrossRef]

J.-M. Yang, C.-Y. Kao, “An evolutionary algorithm for synthesizing optical thin-film designs,” in Parallel Probling Solving in Nature—PPSN V, in Vol. 1498 of Lecture Notes in Computer Science Series (Springer-Verlag, Berlin, 1998), pp. 947–958.
[CrossRef]

Kemp, R. A.

Li, L.

Liu, Y.

X. Yao, Y. Liu, “Fast evolution strategies,” 151–161 (1997).

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1986).
[CrossRef]

Martin, S.

Rivory, J.

Schoenauer, M.

Schwefel, H.-P.

T. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evol. Comput. 1, 3–17 (1997).
[CrossRef]

T. Bäck, F. Hoffmeister, H.-P. Schwefel, “A survey of evolution strategies,” in Proceedings of the Fourth International Conference on Genetic Algorithms (Michigan State University, East Lansing, Mich., 1991), pp. 2–9.

H.-P. Schwefel, Numerical Optimization of Computer Models (Wiley, Chichester, N.Y., 1981).

Southwell, W. H.

Sullivan, B. T.

Tikhonravov, A. V.

Trubetskov, M. K.

Yang, J.-M.

J.-M. Yang, C.-Y. Kao, “Flexible ligand docking using a robust evolutionary algorithm,” J. Comput. Chem. 21, 988–998 (2000).
[CrossRef]

J.-M. Yang, C.-Y. Kao, “Integrating adaptive mutations and family competition into genetic algorithms as function optimizer,” Soft Comput. 4, 89–102 (2000).
[CrossRef]

J.-M. Yang, C.-Y. Kao, “An evolutionary algorithm for synthesizing optical thin-film designs,” in Parallel Probling Solving in Nature—PPSN V, in Vol. 1498 of Lecture Notes in Computer Science Series (Springer-Verlag, Berlin, 1998), pp. 947–958.
[CrossRef]

Yao, X.

X. Yao, Y. Liu, “Fast evolution strategies,” 151–161 (1997).

Appl. Opt.

H. Greiner, “Robust optical coating design with evolutionary strategies,” Appl. Opt. 36, 5477–5482 (1996).
[CrossRef]

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[CrossRef] [PubMed]

B. G. Bovard, “Derivation of a matrix describing a rugate dielectric thin film,” Appl. Opt. 27, 1998–2005 (1988).
[CrossRef] [PubMed]

J. A. Aguilera, J. Aguilera, P. Baumeister, A. Bloom, D. Coursen, J. A. Dobrowolski, F. T. Goldstein, D. E. Gustafson, R. A. Kemp, “Antireflection coatings for germanium IR optics: a comparison of numerical design methods,” Appl. Opt. 27, 2832–2840 (1988).
[CrossRef] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[CrossRef] [PubMed]

L. Li, J. A. Dobrowolski, “Computation speeds of different optical thin-film synthesis methods,” Appl. Opt. 31, 3790–3799 (1992).
[CrossRef] [PubMed]

A. V. Tikhonravov, “Some theoretical aspects of thin-film optics and their applications,” Appl. Opt. 32, 5417–5426 (1993).
[CrossRef] [PubMed]

S. Martin, J. Rivory, M. Schoenauer, “Synthesis of optical multilayer systems using genetic algorithms,” Appl. Opt. 34, 2247–2254 (1995).
[CrossRef] [PubMed]

B. T. Sullivan, J. A. Dobrowolski, “Implementation of a numerical needle method for thin-film design,” Appl. Opt. 35, 5484–5492 (1996).
[CrossRef] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, G. W. DeBell, “Application of the needle optimization technique to design of optical coatings,” Appl. Opt. 35, 5493–5508 (1996).
[CrossRef] [PubMed]

IEEE Trans. Evol. Comput.

T. Bäck, U. Hammel, H.-P. Schwefel, “Evolutionary computation: comments on the history and current state,” IEEE Trans. Evol. Comput. 1, 3–17 (1997).
[CrossRef]

J. Comput. Chem.

J.-M. Yang, C.-Y. Kao, “Flexible ligand docking using a robust evolutionary algorithm,” J. Comput. Chem. 21, 988–998 (2000).
[CrossRef]

Soft Comput.

J.-M. Yang, C.-Y. Kao, “Integrating adaptive mutations and family competition into genetic algorithms as function optimizer,” Soft Comput. 4, 89–102 (2000).
[CrossRef]

Other

J.-M. Yang, C.-Y. Kao, “An evolutionary algorithm for synthesizing optical thin-film designs,” in Parallel Probling Solving in Nature—PPSN V, in Vol. 1498 of Lecture Notes in Computer Science Series (Springer-Verlag, Berlin, 1998), pp. 947–958.
[CrossRef]

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1986).
[CrossRef]

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 42, pp. 2824–2831.

H.-P. Schwefel, Numerical Optimization of Computer Models (Wiley, Chichester, N.Y., 1981).

X. Yao, Y. Liu, “Fast evolution strategies,” 151–161 (1997).

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

T. Bäck, F. Hoffmeister, H.-P. Schwefel, “A survey of evolution strategies,” in Proceedings of the Fourth International Conference on Genetic Algorithms (Michigan State University, East Lansing, Mich., 1991), pp. 2–9.

D. B. Fogel, Evolutionary Computation: Toward a New Philosophy of Machine Intelligence (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Top, profiles of a target specification and a real coating system; bottom, construction parameters of a coating system.

Fig. 2
Fig. 2

Overview of our algorithm: (a) FCEA, (b) FC_adaptive procedure.

Fig. 3
Fig. 3

Different characteristics of FCEA mutation operators. (a) Density functions of Gaussian and Cauchy distributions. (b) Difference in search spaces between (i) self-adaptive and (ii) decreasing-based mutations.

Fig. 4
Fig. 4

Spectral reflectance and refractive-index profile of an 18-layer solution generated by the FCEA for the beam-splitter coating in the region of interest 0.4 ≤ λ ≤ 1.0 µm with refractive indices within the range 1.35 ≤ η ≤ 2.35.

Fig. 5
Fig. 5

Spectral reflectance and refractive-index profile of a 16-layer solution generated by the FCEA for the beam-splitter coating with refractive indices of η h = 2.35 and η l = 1.35.

Fig. 6
Fig. 6

Spectral reflectance and refractive-index profile of a 33-layer narrow-band reflection filter obtained by FCEA in the region of interest 0.5 ≤ λ ≤ 0.7 µm on a η s = 1.52 substrate.

Fig. 7
Fig. 7

Spectral reflectance and refractive-index profile of a 66-layer short-wave-pass nonpolarized filter obtained by the FCEA at a 45° angle of incidence on the region of interest 0.4 ≤ λ ≤ 1.2 µm. The available value of refractive index is continuous from 1.45 to 2.35.

Fig. 8
Fig. 8

Spectral reflectance and refractive-index profile of a 71-layer long-wave-pass filter for nonpolarized light at a 45° angle of incidence on the region of interest 0.4 ≤ λ ≤ 1.2 µm. The refractive index is continuous from 1.45 to 2.35.

Fig. 9
Fig. 9

Series of intermediate performances and the refractive-index profiles of our FCEA for the CIE λ filter for the tristimulus colorimeters in the region 380–780 nm.

Tables (5)

Tables Icon

Table 1 Parameters of FCEA and Notation Used in This Paper

Tables Icon

Table 2 Comparisons of FCEA with Refinement Methodsa

Tables Icon

Table 3 Comparison of the FCEA with the Needle Method on the Beam Splitter with Refractive Indices of η h = 2.35 and η l = 1.35 as well as 301 Equispaced Points in the Region of Interest 0.4 ≤ λ ≤ 1.0 µm

Tables Icon

Table 4 Construction Parameters of the Solutions Found by FCEA for the Narrow-Band Reflector, the Beam Splitter, and the CIE λ Filter in Both Inhomogeneous Coatings and Homogeneous Coatings

Tables Icon

Table 5 Comparison of FCEA with the Needle Method on the CIE λ Filter for the Tristimulus Colorimeters in the Region 380–780 nm

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

fη, d, λk=1Wk=1WRη, d, λk-Rˆλk2δRk1/2,
xjc=xjawith probability 0.8xjbwith probability 0.2.
xjc=xja+0.5xjb-xja,
wjc=wja+0.5wjb-wja,
xi=xi+wD(·),
vjc=vja expτN0, 1+τNj0, 1,
xjc=xja+vjcNj0, 1,
ψjc=ψja expτN0, 1+τNj0, 1,
xjc=xja+ψjcCjt.
σc=γσa,
xjc=xja+σcNj0, 1.
wja=0.95wja,
σc=maxσc, βvmeanc,

Metrics