Abstract

This paper proposes a method for lens system design. It consists of two main steps called Glass-Selection Step and Further-Optimization Step. We modify coordinate-wise algorithm to obtain the glass combination in Glass-Selection Step. In Further-Optimization Step, we use modified coordinate-wise algorithm combined with modified evolutionary algorithm to find out the optimal solution. We succeed in obtaining high quality design with the proposed method.

© 2010 OSA

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  1. J. A. Dobrowolski, F. C. Ho, A. Belkind, and V. A. Koss, “Merit function for more effective thin film calculations,” Appl. Opt. 28(14), 2824–2831 (1989).
    [CrossRef] [PubMed]
  2. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
  3. J. M. Geary, Introduction to Lens Design: with Practical ZEMAX, (Willmann-Bell, 2002).
  4. M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
    [CrossRef]
  5. J. Beaulieu, C. Gagne, and M. Parizeau, “Lens system design and re-engineering with evolutionary algorithm,” Proc.GECCO, 155–162 (2002).
  6. A. Håkansson, J. Sanchez-Dehesa, and L. Sanchis, “Acoustic lens design by genetic algorithms,” Phys. Rev. B 70(21), 214302 (2004).
    [CrossRef]
  7. S. Banerjee and L. Hazra, “Experiments with a genetic algorithm, for structural design of cemented doublets with prespecified aberration targets,” Appl. Opt. 24, 1864–1877 (1985).
  8. I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithm using UNDX,” Comput. Methods Appl. Mech. Eng. 186(2-4), 483–497 (2000).
    [CrossRef]
  9. C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008).
    [CrossRef]
  10. L. N. Hazra and S. Chatterjee, “A prophylactic strategy for global synthesis in lens design,” Opt. Rev. 12(3), 247–254 (2005).
    [CrossRef]
  11. SCHOTT, http://www.schott.com/optocs_devices/english/download/ .
  12. V. Franc, V. Hlavac, and M. Navara, “Sequential coordinate-wise algorithm for the non-negative least squares problem,” Lect. Notes Comput. Sci. 3691, 407–414 (2005).
    [CrossRef]
  13. W. T. Welford, Aberrations of the symmetrical optical system, (Academic Press, New York, 1974).
  14. E. Glatzel and R. Wilson, “Adaptive automatic correction in optical design,” Appl. Opt. 7(2), 265–276 (1968).
    [CrossRef] [PubMed]
  15. T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l (1993).
    [CrossRef]

2008 (1)

C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008).
[CrossRef]

2005 (2)

L. N. Hazra and S. Chatterjee, “A prophylactic strategy for global synthesis in lens design,” Opt. Rev. 12(3), 247–254 (2005).
[CrossRef]

V. Franc, V. Hlavac, and M. Navara, “Sequential coordinate-wise algorithm for the non-negative least squares problem,” Lect. Notes Comput. Sci. 3691, 407–414 (2005).
[CrossRef]

2004 (1)

A. Håkansson, J. Sanchez-Dehesa, and L. Sanchis, “Acoustic lens design by genetic algorithms,” Phys. Rev. B 70(21), 214302 (2004).
[CrossRef]

2000 (1)

I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithm using UNDX,” Comput. Methods Appl. Mech. Eng. 186(2-4), 483–497 (2000).
[CrossRef]

1995 (1)

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
[CrossRef]

1993 (1)

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l (1993).
[CrossRef]

1989 (1)

1985 (1)

1968 (1)

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Bäck, T.

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l (1993).
[CrossRef]

Banerjee, S.

Beaulieu, J.

C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008).
[CrossRef]

Belkind, A.

Chatterjee, S.

L. N. Hazra and S. Chatterjee, “A prophylactic strategy for global synthesis in lens design,” Opt. Rev. 12(3), 247–254 (2005).
[CrossRef]

Dobrowolski, J. A.

Franc, V.

V. Franc, V. Hlavac, and M. Navara, “Sequential coordinate-wise algorithm for the non-negative least squares problem,” Lect. Notes Comput. Sci. 3691, 407–414 (2005).
[CrossRef]

Gagné, C.

C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008).
[CrossRef]

Glatzel, E.

Håkansson, A.

A. Håkansson, J. Sanchez-Dehesa, and L. Sanchis, “Acoustic lens design by genetic algorithms,” Phys. Rev. B 70(21), 214302 (2004).
[CrossRef]

Hazra, L.

Hazra, L. N.

L. N. Hazra and S. Chatterjee, “A prophylactic strategy for global synthesis in lens design,” Opt. Rev. 12(3), 247–254 (2005).
[CrossRef]

Hiraga, K.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
[CrossRef]

Hlavac, V.

V. Franc, V. Hlavac, and M. Navara, “Sequential coordinate-wise algorithm for the non-negative least squares problem,” Lect. Notes Comput. Sci. 3691, 407–414 (2005).
[CrossRef]

Ho, F. C.

Ishikawa, J.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
[CrossRef]

Isshiki, M.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
[CrossRef]

Kobayashi, S.

I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithm using UNDX,” Comput. Methods Appl. Mech. Eng. 186(2-4), 483–497 (2000).
[CrossRef]

Koss, V. A.

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Nakadate, S.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
[CrossRef]

Navara, M.

V. Franc, V. Hlavac, and M. Navara, “Sequential coordinate-wise algorithm for the non-negative least squares problem,” Lect. Notes Comput. Sci. 3691, 407–414 (2005).
[CrossRef]

Ono, H.

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
[CrossRef]

Ono, I.

I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithm using UNDX,” Comput. Methods Appl. Mech. Eng. 186(2-4), 483–497 (2000).
[CrossRef]

Parizeau, M.

C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008).
[CrossRef]

Sanchez-Dehesa, J.

A. Håkansson, J. Sanchez-Dehesa, and L. Sanchis, “Acoustic lens design by genetic algorithms,” Phys. Rev. B 70(21), 214302 (2004).
[CrossRef]

Sanchis, L.

A. Håkansson, J. Sanchez-Dehesa, and L. Sanchis, “Acoustic lens design by genetic algorithms,” Phys. Rev. B 70(21), 214302 (2004).
[CrossRef]

Schwefel, H. P.

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l (1993).
[CrossRef]

Thibault, S.

C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008).
[CrossRef]

Wilson, R.

Yoshida, K.

I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithm using UNDX,” Comput. Methods Appl. Mech. Eng. 186(2-4), 483–497 (2000).
[CrossRef]

Appl. Opt. (3)

Appl. Soft Comput. (1)

C. Gagné, J. Beaulieu, M. Parizeau, and S. Thibault, “Human-competitive lens system design with evolution strategies,” Appl. Soft Comput. 8(4), 1439–1452 (2008).
[CrossRef]

Comput. Methods Appl. Mech. Eng. (1)

I. Ono, S. Kobayashi, and K. Yoshida, “Optimal lens design by real-coded genetic algorithm using UNDX,” Comput. Methods Appl. Mech. Eng. 186(2-4), 483–497 (2000).
[CrossRef]

Evol. Comput. (1)

T. Bäck and H. P. Schwefel, “An overview of evolution algorithms for parameter optimization,” Evol. Comput. 1(1), l (1993).
[CrossRef]

Lect. Notes Comput. Sci. (1)

V. Franc, V. Hlavac, and M. Navara, “Sequential coordinate-wise algorithm for the non-negative least squares problem,” Lect. Notes Comput. Sci. 3691, 407–414 (2005).
[CrossRef]

Opt. Rev. (2)

L. N. Hazra and S. Chatterjee, “A prophylactic strategy for global synthesis in lens design,” Opt. Rev. 12(3), 247–254 (2005).
[CrossRef]

M. Isshiki, H. Ono, K. Hiraga, J. Ishikawa, and S. Nakadate, “Lens design: global optimization with escape function,” Opt. Rev. 2(6), 463–470 (1995).
[CrossRef]

Phys. Rev. B (1)

A. Håkansson, J. Sanchez-Dehesa, and L. Sanchis, “Acoustic lens design by genetic algorithms,” Phys. Rev. B 70(21), 214302 (2004).
[CrossRef]

Q. Appl. Math. (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Other (4)

J. M. Geary, Introduction to Lens Design: with Practical ZEMAX, (Willmann-Bell, 2002).

J. Beaulieu, C. Gagne, and M. Parizeau, “Lens system design and re-engineering with evolutionary algorithm,” Proc.GECCO, 155–162 (2002).

SCHOTT, http://www.schott.com/optocs_devices/english/download/ .

W. T. Welford, Aberrations of the symmetrical optical system, (Academic Press, New York, 1974).

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Figures (8)

Fig. 1
Fig. 1

Flow chart of Two-step method.

Fig. 2
Fig. 2

Flow chart of Further-Optimization Step.

Fig. 3
Fig. 3

MTF of the doublet lens.

Fig. 4
Fig. 4

Ray fan aberration of the doublet lens. (a) Field angle 0 Degree. (b) Field angle 0.7 Degree. (c) Field angle 1.0 Degree.

Fig. 5
Fig. 5

Optimization route of Further-Optimization Step for the doublet lens design. (a) Route of iterations between 0 and 1200. (b) Route of iterations between 500 and 750. (c) Route of iterations between 760 and 900. (d) Route of iterations between 850 and 880.

Fig. 6
Fig. 6

Best three lens system designs found with Two-step method. (a) Solution 1(with 75% encircled energy diameter of 10.41μm). (b) Solution 2 (with a 75% encircled energy diameter of 13.85μm). (c) Solution3 (with 75% encircled energy diameter of 12.19μm).

Fig. 7
Fig. 7

Encircled energy of the three lens system designs. (a) Solution 1. (b) Solution 2. (c) Solution 3.

Fig. 8
Fig. 8

Solution found with standard evolutionary algorithm. (a) The layout of lens system. (b) The encircled energy of the lens system.

Tables (13)

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Table 1 SCHOTT glass data based on ascending sort of the refractive index

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Table 2 Specification of doublet lens design

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Table 3 Parameters of initial design for the doublet design

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Table 4 The data of doublet design

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Table 5 Specification of ILS problem

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Table 6 Physical constraints for the ILS problem

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Table 7 Parameters of the initial design for the ILS problem

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Table 8 Parameters of Solution 1

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Table 9 Parameters of Solution 2

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Table 10 Parameters of Solution 3

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Table 11 Some parameters of the best three solutions found with Two-step method

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Table 12 Parameters of the solution found with standard evolutionary algorithm

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Table 13 Comparison of the best solutions found with Two-step method and the solution found with evolutionary algorithm

Equations (14)

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

F 1 = 1 M C 1 + C 2 .
J ' = J                         ( i f     F ' < F ) ,
J ' = J + 1                         ( i f     F ' > F ) ,
t i ' = t i + u i                       ( i f       J ' = 0 ) ,
t i ' = t i u i                         ( i f     J ' = 1 ) ,
u i = D u i ,
t i c = t i a                         ( w i t h       t h e       p r o b a b i l i t y       P c ) ,
t i c = t i b                         ( w i t h       t h e       p r o b a b i l i t y       1 P c ) ,
v i c = v i a { exp [ τ N ( 0 , 1 ) + τ N i ( 0 , 1 ) ] } n { Q N i ( 0 , 1 ) } n ,
t i c = t i a + v i c ,
τ = ( 2 N ) 1 ,
τ = ( 2 N ) 1 ,
F 2 = L 0 + K 0 + L F C ,
F 2 = P t t + P i m g + P m a g + P v i g n + max j = { 0 , 28 , 40 } ( D y o b j = j 0.01 ) ,

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