Abstract

A new adaptive optics (AO) system for controlling the mode profile of a diode-laser-pumped Nd:YAG solid laser has been set up in our laboratory. A 19-element piezoelectric deformable mirror (DM), which is used as the rear mirror of the solid-state laser, is controlled by a genetic algorithm (GA). To improve the system convergence rate, the GA optimizes the first 10 orders of Zernike mode coefficients rather than optimize 19 voltages on the DM. The transform matrix between the 19 voltages and the first 10 orders of Zernike mode coefficients is deduced. Comparative numerical results show that the convergence speed and the correction performance of the AO system based on optimizing Zernike mode coefficients is far better than that of optimizing voltages. Moreover, experimental results showed that this AO system could change TEM10, TEM11, and TEM20 transverse modes into a TEM00 mode successfully.

© 2007 Optical Society of America

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References

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  1. W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10, 550-555 (2002).
    [PubMed]
  2. D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
    [CrossRef]
  3. P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).
  4. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, 1998).
  5. W. H. Jiang and H. G. Li, "Hartmann-Shack wave-front sensing and wave-front control algorithm," Proc. SPIE. 1271, 82-93 (1990).
    [CrossRef]
  6. P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
    [CrossRef]
  7. W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
    [CrossRef]
  8. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1st ed. (Addison-Wesley Publishing Company, Inc., Boston, 1989).
  9. O. Albert, L. Sherman, G. Mourou, and T. B. Norris, "Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy," Opt. Lett. 25, 52-54 (2000).
    [CrossRef]
  10. A. C. F. Gonté, A. Courteville, and R. Dändliker, "Optimization of single-mode fiber coupling efficiency with an adaptive membrane mirror," Opt. Eng. 41, 1073-1076 (2002).
    [CrossRef]
  11. P. N. Marsh, D. Burns, and J. M. Girikn, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express. 11, 1123-1130 (2003).
    [CrossRef] [PubMed]

2006

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

2005

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

2003

P. N. Marsh, D. Burns, and J. M. Girikn, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express. 11, 1123-1130 (2003).
[CrossRef] [PubMed]

2002

W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10, 550-555 (2002).
[PubMed]

D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
[CrossRef]

A. C. F. Gonté, A. Courteville, and R. Dändliker, "Optimization of single-mode fiber coupling efficiency with an adaptive membrane mirror," Opt. Eng. 41, 1073-1076 (2002).
[CrossRef]

2000

1996

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

1990

W. H. Jiang and H. G. Li, "Hartmann-Shack wave-front sensing and wave-front control algorithm," Proc. SPIE. 1271, 82-93 (1990).
[CrossRef]

Albert, O.

Bente, E.

W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10, 550-555 (2002).
[PubMed]

D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
[CrossRef]

Burns, D.

P. N. Marsh, D. Burns, and J. M. Girikn, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express. 11, 1123-1130 (2003).
[CrossRef] [PubMed]

W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10, 550-555 (2002).
[PubMed]

D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
[CrossRef]

Chen, S. Q.

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

Courteville, A.

A. C. F. Gonté, A. Courteville, and R. Dändliker, "Optimization of single-mode fiber coupling efficiency with an adaptive membrane mirror," Opt. Eng. 41, 1073-1076 (2002).
[CrossRef]

Dändliker, R.

A. C. F. Gonté, A. Courteville, and R. Dändliker, "Optimization of single-mode fiber coupling efficiency with an adaptive membrane mirror," Opt. Eng. 41, 1073-1076 (2002).
[CrossRef]

Ferguson, A. I.

D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
[CrossRef]

Girikn, J. M.

P. N. Marsh, D. Burns, and J. M. Girikn, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express. 11, 1123-1130 (2003).
[CrossRef] [PubMed]

Girkin, J.

Gong, Z. B.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Gonté, A. C. F.

A. C. F. Gonté, A. Courteville, and R. Dändliker, "Optimization of single-mode fiber coupling efficiency with an adaptive membrane mirror," Opt. Eng. 41, 1073-1076 (2002).
[CrossRef]

Guan, C. L.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Hu, S. J.

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

Jiang, L. T.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Jiang, S. F.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Jiang, W. H.

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

W. H. Jiang and H. G. Li, "Hartmann-Shack wave-front sensing and wave-front control algorithm," Proc. SPIE. 1271, 82-93 (1990).
[CrossRef]

Li, H. G.

W. H. Jiang and H. G. Li, "Hartmann-Shack wave-front sensing and wave-front control algorithm," Proc. SPIE. 1271, 82-93 (1990).
[CrossRef]

Ling, N.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Lubeigt, W.

D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
[CrossRef]

W. Lubeigt, G. Valentine, J. Girkin, E. Bente, and D. Burns, "Active transverse mode control and optimization of an all-solid-state laser using an intracavity adaptive-optic mirror," Opt. Express 10, 550-555 (2002).
[PubMed]

Marsh, P. N.

P. N. Marsh, D. Burns, and J. M. Girikn, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express. 11, 1123-1130 (2003).
[CrossRef] [PubMed]

Mourou, G.

Norris, T. B.

Rong, Z. J.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Sherman, L.

Valentine, G.

Valentine, G. J.

D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
[CrossRef]

Wang, C. H.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Wang, Y. J.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Wu, X. B.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Wu, Y.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Xian, H.

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

Xu, B.

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

Yang, P.

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

Yang, W.

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

Yang, X. D.

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

Zhang, X.

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

J. Phys: Conf. Series

P. Yang, S. J. Hu, S. Q. Chen, W. Yang, B. Xu, and W. H. Jiang, "Research on the phase aberration correction with a deformable mirror controlled by a genetic algorithm," J. Phys: Conf. Series 48, 1017-1024 (2006).
[CrossRef]

Opt. Eng.

A. C. F. Gonté, A. Courteville, and R. Dändliker, "Optimization of single-mode fiber coupling efficiency with an adaptive membrane mirror," Opt. Eng. 41, 1073-1076 (2002).
[CrossRef]

Opt. Express

Opt. Express.

P. N. Marsh, D. Burns, and J. M. Girikn, "Practical implementation of adaptive optics in multiphoton microscopy," Opt. Express. 11, 1123-1130 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Proc. SPIE

W. H. Jiang, N. Ling, X. B. Wu, C. H. Wang, H. Xian, S. F. Jiang, Z. J. Rong, C. L. Guan, L. T. Jiang, Z. B. Gong, Y. Wu, and Y. J. Wang, "37-element adaptive optics experimental system and turbulence compensation experiments," Proc. SPIE 2828, 312-321 (1996).
[CrossRef]

D. Burns, G. J. Valentine, W. Lubeigt, E. Bente, and A. I. Ferguson, "Development of high average power picosecond laser systems," Proc. SPIE 4629, 129-143 (2002).
[CrossRef]

Proc. SPIE.

W. H. Jiang and H. G. Li, "Hartmann-Shack wave-front sensing and wave-front control algorithm," Proc. SPIE. 1271, 82-93 (1990).
[CrossRef]

SPIE.

P. Yang, S. J. Hu, X. D. Yang, S. Q. 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.  6108182-191 (2005).

Other

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, 1998).

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1st ed. (Addison-Wesley Publishing Company, Inc., Boston, 1989).

Supplementary Material (2)

» Media 1: MOV (790 KB)     
» Media 2: MOV (909 KB)     

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Figures (13)

Fig. 1.
Fig. 1.

(a) Configuration of the 19-element DM. (b) Photograph of the DM.

Fig. 2.
Fig. 2.

Correction capability of the 19-element piezoelectric DM.

Fig. 3.
Fig. 3.

On the left is the wavefront generated by the first 10 orders of Zernike polynomial coefficients; in the center is the wavefront reconstructed by DM; on the right is the residual wavefront.

Fig. 4.
Fig. 4.

Flowchart of the genetic algorithm.

Fig. 5.
Fig. 5.

Fitness value based on two different bases; the four curves at the bottom are fitness values based on optimizing actuator voltages of DM, whereas the top four curves are fitness values based on optimizing the first 10 orders of Zernike mode coefficients.

Fig. 6.
Fig. 6.

(I) Near-field distribution before and after correction based on optimizing voltages (iterative number is 400). (II) Near-field distribution before and after correction based on optimizing the Zernike mode coefficients (iterative number is 200).

Fig. 7.
Fig. 7.

(I) Far-field distribution before and after correction based on optimizing voltages (iterative number is 400). (II) Far-field distribution before and after correction based on optimizing the Zernike mode coefficients (iterative number is 200).

Fig. 8.
Fig. 8.

Experimental schematic layout of the adaptive-mode control system.

Fig. 9.
Fig. 9.

(a) Far-field beam profiles distribution (TEM10) when AO system is off, whereas (b) is according to beam profiles distribution (TEM00) when AO system is on.

Fig. 10.
Fig. 10.

(621 KB) Video of TEM10 mode optimization before and after AO is on. [Media 1]

Fig. 11.
Fig. 11.

Far-field beam profiles from Nd:YAG laser recorded at various intervals during an optimization sequence (pump current is 50 A). The x-coordinate represents the optimization time; the y-coordinate represents relative power in a selective region of the CCD camera.

Fig. 12.
Fig. 12.

Far-field beam profiles from the Nd:YAG laser recorded at various intervals during another optimization sequence. The x-coordinate represents the optimization time; the ycoordinate represents relative power in a selective region of the CCD camera (pump current is 59 A).

Fig. 13.
Fig. 13.

(661KB) Video of TEM11 mode optimization before and after AO is on. [Media 2]

Equations (11)

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

φ ( x , y ) = j = 1 n v j V j ( x , y ) ,
V j ( x , y ) = exp [ ln ( w ) ( ( x x j ) 2 + ( y y j ) 2 d ) ) p ,
φ ( x , y ) = b 0 + k = 1 m b k Z k ( x , y ) ,
j = 1 n v j V j ( x , y ) = b 0 + k = 1 m b k Z k ( x , y ) .
j = 1 n v j V j ( x , y ) k = 1 m b k Z k ( x , y ) .
[ v 1 v 2 v n ] = [ u 11 , u 12 u 1 m u 21 , u 22 u 2 m ................. u n 1 , u n 2 u n m ] × [ b 1 b 2 b m ] .
V = U B .
V ( x , y ) 10000 × 19 u 19 × 1 ψ ( x , y ) 10000 × 1 .
Cond ( V ( x , y ) ) = δ max δ min ,
u 19 × 1 = V ( x , y ) 19 × 10000 + ψ ( x , y ) 10000 × 1 ,
U = [ u 1 , u 2 u i u 10 ] ,

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