Abstract

We investigate numerically the feasibility of phase aberration correction in a wavefront sensorless adaptive optical system, based on the imperialist competitive algorithm (ICA). Considering a 61-element deformable mirror (DM) and the Strehl ratio as the cost function of ICA, this algorithm is employed to search the optimum surface profile of DM for correcting the phase aberrations in a solid-state laser system. The correction results show that ICA is a powerful correction algorithm for static or slowly changing phase aberrations in optical systems, such as solid-state lasers. The correction capability and the convergence speed of this algorithm are compared with those of the genetic algorithm (GA) and stochastic parallel gradient descent (SPGD) algorithm. The results indicate that these algorithms have almost the same correction capability. Also, ICA and GA are almost the same in convergence speed and SPGD is the fastest of these algorithms.

© 2013 Optical Society of America

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  1. H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953).
    [CrossRef]
  2. J. Porter, H. Queener, J. Lin, K. E. Thorn, and A. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).
  3. R. Tyson, J. Tharp, and D. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results,” Opt. Eng. 44, 096002 (2005).
    [CrossRef]
  4. M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
    [CrossRef]
  5. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
    [CrossRef]
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    [CrossRef]
  8. P. Yang, M. W. Ao, Y. Liu, B. Xu, and W. H. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15, 17051–17062 (2007).
    [CrossRef]
  9. H. Z. Yang and X. Y. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43, 630–635 (2011).
    [CrossRef]
  10. R. El-Agmy, H. Bulte, A. H. Greenaway, and D. T. Reid, “Adaptive beam profile control using a simulated annealing algorithm,” Opt. Express 13, 6085–6091 (2005).
    [CrossRef]
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    [CrossRef]
  14. W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, “Active transverse mode control and optimisation of an all-solid-state laser using an intracavity adaptive-optic mirror,” Opt. Express 10, 550–555 (2002).
    [CrossRef]
  15. E. Atashpaz-Gargari and C. Lucas, “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition,” in Congress on Evolutionary Computation (IEEE, 2007), pp. 4661–4667.
  16. E. Atashpaz-Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355 (2008).
  17. J. Alikhani-Koupaei and M. Abdechiri, “An optimization problem for evaluation of image segmentation methods,” Int. J. Comput. Netw. Secur. 2, 142–150 (2010).
  18. E. Shokrollahpour, M. Zandieh, and B. Dorri, “A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem,” Int. J. Prod. Res. 49, 3087–3103 (2011).
    [CrossRef]
  19. P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
    [CrossRef]
  20. W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
    [CrossRef]
  21. M. Born and E. Wolf, Principles of Optics (Cambridge University, 2003), pp. 768.

2011

H. Z. Yang and X. Y. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43, 630–635 (2011).
[CrossRef]

E. Shokrollahpour, M. Zandieh, and B. Dorri, “A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem,” Int. J. Prod. Res. 49, 3087–3103 (2011).
[CrossRef]

2010

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

J. Alikhani-Koupaei and M. Abdechiri, “An optimization problem for evaluation of image segmentation methods,” Int. J. Comput. Netw. Secur. 2, 142–150 (2010).

2009

L. Dong, P. Yang, and B. Xu, “Adaptive aberration correction based on ant colony algorithm for solid-state lasers: numerical simulations,” Appl. Phys. B 96, 527–533 (2009).
[CrossRef]

2008

E. Atashpaz-Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355 (2008).

P. Yang, Y. Liu, M. Ao, S. Hu, and B. Xu, “A wavefront sensor-less adaptive optical system for a solid-state laser,” Opt. Lasers Eng. 46, 517–521 (2008).
[CrossRef]

2007

2005

R. Tyson, J. Tharp, and D. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results,” Opt. Eng. 44, 096002 (2005).
[CrossRef]

R. El-Agmy, H. Bulte, A. H. Greenaway, and D. T. Reid, “Adaptive beam profile control using a simulated annealing algorithm,” Opt. Express 13, 6085–6091 (2005).
[CrossRef]

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

2002

1998

1997

1991

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

1974

1953

H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Abdechiri, M.

J. Alikhani-Koupaei and M. Abdechiri, “An optimization problem for evaluation of image segmentation methods,” Int. J. Comput. Netw. Secur. 2, 142–150 (2010).

Alikhani-Koupaei, J.

J. Alikhani-Koupaei and M. Abdechiri, “An optimization problem for evaluation of image segmentation methods,” Int. J. Comput. Netw. Secur. 2, 142–150 (2010).

Ao, M.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

P. Yang, Y. Liu, M. Ao, S. Hu, and B. Xu, “A wavefront sensor-less adaptive optical system for a solid-state laser,” Opt. Lasers Eng. 46, 517–521 (2008).
[CrossRef]

Ao, M. W.

Atashpaz-Gargari, E.

E. Atashpaz-Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355 (2008).

E. Atashpaz-Gargari and C. Lucas, “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition,” in Congress on Evolutionary Computation (IEEE, 2007), pp. 4661–4667.

Awwal, A.

J. Porter, H. Queener, J. Lin, K. E. Thorn, and A. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Bente, E.

Booth, M. J.

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2003), pp. 768.

Buffington, A.

Bulte, H.

Burns, D.

Canning, D.

R. Tyson, J. Tharp, and D. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results,” Opt. Eng. 44, 096002 (2005).
[CrossRef]

Carhart, G. W.

Chen, S.

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

Dong, L.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

L. Dong, P. Yang, and B. Xu, “Adaptive aberration correction based on ant colony algorithm for solid-state lasers: numerical simulations,” Appl. Phys. B 96, 527–533 (2009).
[CrossRef]

Dorri, B.

E. Shokrollahpour, M. Zandieh, and B. Dorri, “A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem,” Int. J. Prod. Res. 49, 3087–3103 (2011).
[CrossRef]

El-Agmy, R.

Fried, D. L.

Girkin, J.

Greenaway, A. H.

Hashemzadeh, F.

E. Atashpaz-Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355 (2008).

Hu, S.

P. Yang, Y. Liu, M. Ao, S. Hu, and B. Xu, “A wavefront sensor-less adaptive optical system for a solid-state laser,” Opt. Lasers Eng. 46, 517–521 (2008).
[CrossRef]

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

Jiang, W. H.

Lei, X.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

Li, X. Y.

H. Z. Yang and X. Y. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43, 630–635 (2011).
[CrossRef]

Lin, J.

J. Porter, H. Queener, J. Lin, K. E. Thorn, and A. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).

Ling, N.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Liu, Y.

P. Yang, Y. Liu, M. Ao, S. Hu, and B. Xu, “A wavefront sensor-less adaptive optical system for a solid-state laser,” Opt. Lasers Eng. 46, 517–521 (2008).
[CrossRef]

P. Yang, M. W. Ao, Y. Liu, B. Xu, and W. H. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15, 17051–17062 (2007).
[CrossRef]

Lubeigt, W.

Lucas, C.

E. Atashpaz-Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355 (2008).

E. Atashpaz-Gargari and C. Lucas, “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition,” in Congress on Evolutionary Computation (IEEE, 2007), pp. 4661–4667.

Muller, R. A.

Porter, J.

J. Porter, H. Queener, J. Lin, K. E. Thorn, and A. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).

Queener, H.

J. Porter, H. Queener, J. Lin, K. E. Thorn, and A. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).

Rajabioun, R.

E. Atashpaz-Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355 (2008).

Rao, X. J.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Reid, D. T.

Ricklin, J. C.

Shi, F.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Shokrollahpour, E.

E. Shokrollahpour, M. Zandieh, and B. Dorri, “A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem,” Int. J. Prod. Res. 49, 3087–3103 (2011).
[CrossRef]

Tharp, J.

R. Tyson, J. Tharp, and D. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results,” Opt. Eng. 44, 096002 (2005).
[CrossRef]

Thorn, K. E.

J. Porter, H. Queener, J. Lin, K. E. Thorn, and A. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).

Tyson, R.

R. Tyson, J. Tharp, and D. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results,” Opt. Eng. 44, 096002 (2005).
[CrossRef]

Valentine, G.

Vorontsov, M. A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2003), pp. 768.

Xu, B.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

L. Dong, P. Yang, and B. Xu, “Adaptive aberration correction based on ant colony algorithm for solid-state lasers: numerical simulations,” Appl. Phys. B 96, 527–533 (2009).
[CrossRef]

P. Yang, Y. Liu, M. Ao, S. Hu, and B. Xu, “A wavefront sensor-less adaptive optical system for a solid-state laser,” Opt. Lasers Eng. 46, 517–521 (2008).
[CrossRef]

P. Yang, M. W. Ao, Y. Liu, B. Xu, and W. H. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15, 17051–17062 (2007).
[CrossRef]

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

Yang, H. Z.

H. Z. Yang and X. Y. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43, 630–635 (2011).
[CrossRef]

Yang, P.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

L. Dong, P. Yang, and B. Xu, “Adaptive aberration correction based on ant colony algorithm for solid-state lasers: numerical simulations,” Appl. Phys. B 96, 527–533 (2009).
[CrossRef]

P. Yang, Y. Liu, M. Ao, S. Hu, and B. Xu, “A wavefront sensor-less adaptive optical system for a solid-state laser,” Opt. Lasers Eng. 46, 517–521 (2008).
[CrossRef]

P. Yang, M. W. Ao, Y. Liu, B. Xu, and W. H. Jiang, “Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients,” Opt. Express 15, 17051–17062 (2007).
[CrossRef]

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

Yang, R.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

Yang, W.

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

Yang, X.

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

Zandieh, M.

E. Shokrollahpour, M. Zandieh, and B. Dorri, “A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem,” Int. J. Prod. Res. 49, 3087–3103 (2011).
[CrossRef]

Zhang, X.

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

Appl. Phys. B

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).

L. Dong, P. Yang, and B. Xu, “Adaptive aberration correction based on ant colony algorithm for solid-state lasers: numerical simulations,” Appl. Phys. B 96, 527–533 (2009).
[CrossRef]

Astron. Soc. Pac.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Int. J. Comput. Netw. Secur.

J. Alikhani-Koupaei and M. Abdechiri, “An optimization problem for evaluation of image segmentation methods,” Int. J. Comput. Netw. Secur. 2, 142–150 (2010).

Int. J. Intell. Comput. Cybern.

E. Atashpaz-Gargari, F. Hashemzadeh, R. Rajabioun, and C. Lucas, “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process,” Int. J. Intell. Comput. Cybern. 1, 337–355 (2008).

Int. J. Prod. Res.

E. Shokrollahpour, M. Zandieh, and B. Dorri, “A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem,” Int. J. Prod. Res. 49, 3087–3103 (2011).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

R. Tyson, J. Tharp, and D. Canning, “Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results,” Opt. Eng. 44, 096002 (2005).
[CrossRef]

Opt. Express

Opt. Laser Technol.

H. Z. Yang and X. Y. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43, 630–635 (2011).
[CrossRef]

Opt. Lasers Eng.

P. Yang, Y. Liu, M. Ao, S. Hu, and B. Xu, “A wavefront sensor-less adaptive optical system for a solid-state laser,” Opt. Lasers Eng. 46, 517–521 (2008).
[CrossRef]

Opt. Lett.

Phil. Trans. R. Soc. A

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A 365, 2829–2843 (2007).
[CrossRef]

Proc. SPIE

P. Yang, S. Hu, X. Yang, S. Chen, W. Yang, X. Zhang, and B. Xu, “Test and analysis of the time and space characteristics of phase aberration in a diode-side-pumped Nd:YAG laser,” Proc. SPIE 6018, 60180M (2005).
[CrossRef]

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2003), pp. 768.

J. Porter, H. Queener, J. Lin, K. E. Thorn, and A. Awwal, Adaptive Optics for Vision Science: Principles, Practices, Design and Applications (Wiley, 2006).

E. Atashpaz-Gargari and C. Lucas, “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition,” in Congress on Evolutionary Computation (IEEE, 2007), pp. 4661–4667.

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Figures (13)

Fig. 1.
Fig. 1.

Creating the initial empires. The imperialist with more colonies has bigger mark.

Fig. 2.
Fig. 2.

Assimilation. Moving colony toward its relevant imperialist.

Fig. 3.
Fig. 3.

Revolution. A sudden change in socio-political characteristics of a country.

Fig. 4.
Fig. 4.

(a) Exchanging the positions of a colony and the imperialist. (b) The entire empire after position exchange.

Fig. 5.
Fig. 5.

Imperialistic competition. The more powerful an empire is, the more likely it possesses the weakest colony of the weakest empire.

Fig. 6.
Fig. 6.

Eliminating the powerless empires. Empire 4, with no colonies, does not have the power for competition and so it is eliminated from other empires.

Fig. 7.
Fig. 7.

Schematic of wavefront sensorless AO system.

Fig. 8.
Fig. 8.

Actuator configuration of 61-element DM.

Fig. 9.
Fig. 9.

Wavefront distribution before and after defocus correction with ICA.

Fig. 10.
Fig. 10.

Wavefront distribution before and after astigmatism correction with ICA.

Fig. 11.
Fig. 11.

Wavefront distribution before and after aberration correction with ICA.

Fig. 12.
Fig. 12.

(a) Zernike coefficients of the input phase aberrations. (b) Zernike coefficients of residual phase aberrations, after correction with ICA. (c) Zernike coefficients attenuation, after correction with ICA. Zernike coefficients attenuation for the first 40 Zernike modes, after correction with (d) ICA, (e) GA, and (f) SPGD.

Fig. 13.
Fig. 13.

Strehl ratio (SRctr) during optimization process with (a) ICA, (b) GA, and (c) SPGD, averaged over 10 corrections for each algorithm.

Tables (2)

Tables Icon

Table 1. Comparison of Optimization Results of ICA, GA, and SPGD

Tables Icon

Table 2. Comparison of Convergence Speeds of ICA, GA, and SPGD

Equations (16)

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

country=C=[u1,u2,u3,,uN].
J=J(C)=J(u1,u2,u3,,uN).
Jn=Jnmin{Ji},
Pn=|Jni=1N*Ji|.
NCn=round{Pn·Ncol},
xiU(0,β×di),
TCn=Jn+ξ·mean{Jin},
NTCn=TCnmin{TCi},
ppn=|NTCni=1N*NTCi|.
P=[pp1,pp2,pp3,,ppN*].
R=[r1,r2,r3,,rN*].
D=PR=[D1,D2,D3,,DN*]=[pp1r1,pp2r2,pp3r3,,ppN*rN*].
φ(x,y)=j=161ujVj(x,y),
Vj(x,y)=exp[ln(ω)((xxj)2+(yyj)2/d)α],
country=C=[u1,u2,u3,,u61].
population=[country1country2...country50].

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