Abstract

Damped least square method is one of the popular methods for automatic lens design. Various improvements in this automatic optical design are mainly due to the optimization of the damping factor and the weight factor. Especially in the four stages of lens design, designers pay more attention to the “correction” stage, and recognized the importance of human experience in “correction”. The introduction of computer brought the feeling of indescribable about the balance aberration of computer. In fact, the function of computer has not gone beyond the range of balance aberration. In this paper, we discussed how to make the whole process of lens design completely automatic by computer, including the selection, correction and evaluation of the system. To achieve this process, the key step is how to make the computer think like a designer and select the type of lens. The success of lens design depends largely on the type selection. Designers who have a profound understanding of optical design theory and rich practical experience can select the simplest and most suitable one from a wide range of types, therefore, this method can also express a new global search method for optical design. Least squares is added to Particle Swarm Optimization (PSO) algorithm to optimize glass selection in optical system. After comparing and analysing the optimized design solutions, the system performance is well achieved. This method can be conveniently implemented and expands the solution space of the optical system.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Damped Least-Squares Method for Automatic Lens Design

Joseph Meiron
J. Opt. Soc. Am. 55(9) 1105-1109 (1965)

Automatically retrieving an initial design of a double-sided telecentric zoom lens based on a particle swarm optimization

Zichao Fan, Shili Wei, Zhengbo Zhu, Yan Mo, Yiming Yan, and Donglin Ma
Appl. Opt. 58(27) 7379-7386 (2019)

Automatic Lens Design by the Least Squares Method

Joseph Meiron
J. Opt. Soc. Am. 49(3) 293-298 (1959)

References

  • View by:
  • |
  • |
  • |

  1. C. G. Wynne, “Lens designing by electronic digital computer,” Proc. Phys. Soc. 73(5), 777–787 (1959).
    [Crossref]
  2. J. Meiron, “Automatic lens design by the least squares method,” J. Opt. Soc. Am. 49(3), 293–298 (1959).
    [Crossref]
  3. C. G. Wynne and P. M. J. H. Wormell, “Lens design by computer,” Appl. Opt. 2(12), 1233–1238 (1963).
    [Crossref]
  4. R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
    [Crossref]
  5. B. F. de Albuquerque, J. Sasian, F. L. de Sousa, and A. S. Montes, “Method of glass selection for color correction in optical system design,” Opt. Express 20(13), 13592–13611 (2012).
    [Crossref] [PubMed]
  6. J. Kennedy and R. C. Eberhart, “Particle swarm optimization” Neural Networks, Proceedings., IEEE International Conference, 1942–1948 (1995).
  7. R. C. Eberhart and J. Kennedy, A New Optimizer Using Particle Swarm Theory, Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, (Academic, 1995), 39–43 (1995).
    [Crossref]
  8. S. Yuhui and R. C. Eberhart, “Parameter selection in particle swarm optimization,” International Conference on Evolutionary Programming , 1447 (1998).
  9. Y. Shi and R. C. Eberhart, “Empirical study of particle swarm optimization” Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress. 1, 320–324 (1999).
  10. R. C. Eberhart, “Comparing inertia weights and constriction factors in particle swarm optimization.” Proceedings of the 2000 IEEE Congress on Evolutionary Computation, La Jolla, CA IEEE, (2000).
    [Crossref]
  11. H. Qin, “Aberration correction of a single aspheric lens with particle swarm algorithm,” Opt. Commun. 285(13–14), 2996–3000 (2012).
  12. H. Qin, “Particle swarm optimization applied to automatic lens design,” Opt. Commun. 284(12), 2763–2766 (2011).
    [Crossref]
  13. M. Clerc and J. Kennedy, “The particle swarm explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
    [Crossref]
  14. H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).
  15. Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
    [Crossref]
  16. C. Yue, Z Qin, Y. Lang, and Q Liu, “Determination of thin metal film’s thickness and optical constants based on SPR phase detection by simulated annealing particle swarm optimization,” Opt. Commun. 430, 238–245 (2018).

2018 (2)

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

C. Yue, Z Qin, Y. Lang, and Q Liu, “Determination of thin metal film’s thickness and optical constants based on SPR phase detection by simulated annealing particle swarm optimization,” Opt. Commun. 430, 238–245 (2018).

2016 (1)

Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
[Crossref]

2012 (2)

B. F. de Albuquerque, J. Sasian, F. L. de Sousa, and A. S. Montes, “Method of glass selection for color correction in optical system design,” Opt. Express 20(13), 13592–13611 (2012).
[Crossref] [PubMed]

H. Qin, “Aberration correction of a single aspheric lens with particle swarm algorithm,” Opt. Commun. 285(13–14), 2996–3000 (2012).

2011 (1)

H. Qin, “Particle swarm optimization applied to automatic lens design,” Opt. Commun. 284(12), 2763–2766 (2011).
[Crossref]

2004 (1)

R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
[Crossref]

2002 (1)

M. Clerc and J. Kennedy, “The particle swarm explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
[Crossref]

1963 (1)

1959 (2)

C. G. Wynne, “Lens designing by electronic digital computer,” Proc. Phys. Soc. 73(5), 777–787 (1959).
[Crossref]

J. Meiron, “Automatic lens design by the least squares method,” J. Opt. Soc. Am. 49(3), 293–298 (1959).
[Crossref]

Ajdad, H.

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

Al Mers, A.

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

Baba, F

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

Bouatem, A.

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

Boutammachte, N

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

Clerc, M.

M. Clerc and J. Kennedy, “The particle swarm explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
[Crossref]

de Albuquerque, B. F.

de Sousa, F. L.

Eberhart, R. C.

S. Yuhui and R. C. Eberhart, “Parameter selection in particle swarm optimization,” International Conference on Evolutionary Programming , 1447 (1998).

Fischer, R. E.

R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
[Crossref]

Fotheringham, U.

R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
[Crossref]

Grant, A. J.

R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
[Crossref]

Hartmann, P.

R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
[Crossref]

Kennedy, J.

M. Clerc and J. Kennedy, “The particle swarm explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
[Crossref]

Lang, Y.

C. Yue, Z Qin, Y. Lang, and Q Liu, “Determination of thin metal film’s thickness and optical constants based on SPR phase detection by simulated annealing particle swarm optimization,” Opt. Commun. 430, 238–245 (2018).

Liu, Q

C. Yue, Z Qin, Y. Lang, and Q Liu, “Determination of thin metal film’s thickness and optical constants based on SPR phase detection by simulated annealing particle swarm optimization,” Opt. Commun. 430, 238–245 (2018).

Meiron, J.

Merroun, O.

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

Montes, A. S.

Qin, H.

H. Qin, “Aberration correction of a single aspheric lens with particle swarm algorithm,” Opt. Commun. 285(13–14), 2996–3000 (2012).

H. Qin, “Particle swarm optimization applied to automatic lens design,” Opt. Commun. 284(12), 2763–2766 (2011).
[Crossref]

Qin, Z

C. Yue, Z Qin, Y. Lang, and Q Liu, “Determination of thin metal film’s thickness and optical constants based on SPR phase detection by simulated annealing particle swarm optimization,” Opt. Commun. 430, 238–245 (2018).

Reichel, S.

R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
[Crossref]

Ruan, Z. H.

Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
[Crossref]

Sasian, J.

Shuai, Y.

Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
[Crossref]

Tan, H.-P.

Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
[Crossref]

Wormell, P. M. J. H.

Wynne, C. G.

C. G. Wynne and P. M. J. H. Wormell, “Lens design by computer,” Appl. Opt. 2(12), 1233–1238 (1963).
[Crossref]

C. G. Wynne, “Lens designing by electronic digital computer,” Proc. Phys. Soc. 73(5), 777–787 (1959).
[Crossref]

Yuan, Y.

Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
[Crossref]

Yue, C.

C. Yue, Z Qin, Y. Lang, and Q Liu, “Determination of thin metal film’s thickness and optical constants based on SPR phase detection by simulated annealing particle swarm optimization,” Opt. Commun. 430, 238–245 (2018).

Yuhui, S.

S. Yuhui and R. C. Eberhart, “Parameter selection in particle swarm optimization,” International Conference on Evolutionary Programming , 1447 (1998).

Zhang, X.-X.

Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Evol. Comput. (1)

M. Clerc and J. Kennedy, “The particle swarm explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6(1), 58–73 (2002).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Commun. (3)

H. Qin, “Aberration correction of a single aspheric lens with particle swarm algorithm,” Opt. Commun. 285(13–14), 2996–3000 (2012).

H. Qin, “Particle swarm optimization applied to automatic lens design,” Opt. Commun. 284(12), 2763–2766 (2011).
[Crossref]

C. Yue, Z Qin, Y. Lang, and Q Liu, “Determination of thin metal film’s thickness and optical constants based on SPR phase detection by simulated annealing particle swarm optimization,” Opt. Commun. 430, 238–245 (2018).

Opt. Express (1)

Proc. Phys. Soc. (1)

C. G. Wynne, “Lens designing by electronic digital computer,” Proc. Phys. Soc. 73(5), 777–787 (1959).
[Crossref]

Proc. SPIE (1)

R. E. Fischer, A. J. Grant, U. Fotheringham, P. Hartmann, and S. Reichel, “Removing the mystique of glass selection,” Proc. SPIE 5524, 134–146 (2004).
[Crossref]

Renew. Energy (1)

H. Ajdad, F Baba, A. Al Mers, O. Merroun, A. Bouatem, and N Boutammachte, “Particle swarm optimization algorithm for Optical-geometric optimization of Linear Fresnel solar concentrators,” Renew. Energy 130, 992–1001 (2018).

Sol. Energy (1)

Z. H. Ruan, Y. Yuan, X.-X. Zhang, Y. Shuai, and H.-P. Tan, “Determination of optical properties and thickness of optical thin film using stochastic particle swarm optimization,” Sol. Energy 127, 147–158 (2016).
[Crossref]

Other (5)

J. Kennedy and R. C. Eberhart, “Particle swarm optimization” Neural Networks, Proceedings., IEEE International Conference, 1942–1948 (1995).

R. C. Eberhart and J. Kennedy, A New Optimizer Using Particle Swarm Theory, Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, (Academic, 1995), 39–43 (1995).
[Crossref]

S. Yuhui and R. C. Eberhart, “Parameter selection in particle swarm optimization,” International Conference on Evolutionary Programming , 1447 (1998).

Y. Shi and R. C. Eberhart, “Empirical study of particle swarm optimization” Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress. 1, 320–324 (1999).

R. C. Eberhart, “Comparing inertia weights and constriction factors in particle swarm optimization.” Proceedings of the 2000 IEEE Congress on Evolutionary Computation, La Jolla, CA IEEE, (2000).
[Crossref]

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 (19)

Fig. 1
Fig. 1 The flow chart of PSO
Fig. 2
Fig. 2 Relative relationship between particle position and solution space
Fig. 3
Fig. 3 Refractive index and Abbe number distribution of glass Storage
Fig. 4
Fig. 4 The flow chart of optimized PSO.
Fig. 5
Fig. 5 Specification of optical system. EFFL = 55mm, Paraxial Image H = 20.018.
Fig. 6
Fig. 6 Optical design system layout and parameters of the system 1
Fig. 7
Fig. 7 Optical design system 1 performance
Fig. 8
Fig. 8 Distortion of optical system 1
Fig. 9
Fig. 9 Optical design system layout and parameters of the system 2
Fig. 10
Fig. 10 Optical design system 2 performance
Fig. 11
Fig. 11 Distortion of optical system 2
Fig. 12
Fig. 12 Optical design system layout and parameters of the system 3
Fig. 13
Fig. 13 Optical design system 3 performance
Fig. 14
Fig. 14 Distortion of optical system 3
Fig. 15
Fig. 15 Optical design system layout and parameters of the system 4
Fig. 16
Fig. 16 Optical design system 4 performance
Fig. 17
Fig. 17 Distortion of optical system 4
Fig. 18
Fig. 18 Error function progress.
Fig. 19
Fig. 19 Error function value vs run time.

Tables (6)

Tables Icon

Table 1 The Characteristics and Material of Glass

Tables Icon

Table 2 Initial focus distribution of optical system

Tables Icon

Table 3 System 1 parameters obtained by PSO

Tables Icon

Table 4 System 2 parameters obtained by PSO

Tables Icon

Table 5 System 3 parameters obtained by PSO

Tables Icon

Table 6 System 4 parameters obtained by PSO

Metrics