Abstract

An optimization-based correction method is developed to control simultaneously two deformable mirrors in a wavefront-sensor-less adaptive beam cleanup system, where the wave-front aberrations could not be compensated by a single deformable mirror. Stochastic parallel gradient decent algorithm is chosen as the optimization algorithm. In this control method, different aberrations are assigned to each deformable mirror according to their different correction quality. The method is proved to be effective by numerical simulations as well as experiments. Experimental results showed that the area containing 84% energy of the laser beam in the far-field can reach 3.0 times diffraction limited.

© 2012 OSA

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  1. W. Koechener, Solid-State Laser Engineering (Springer, 1999), Chap. 4.
  2. K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
    [CrossRef]
  3. X. Lei, B. Xu, P. Yang, L. Dong, W. Liu, and H. Yan, “Beam cleanup of a 532-nm pulsed solid-state laser using a bimorph mirror,” Chin. Opt. Lett. 10(2), 021401 (2012).
  4. P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010).
    [CrossRef] [PubMed]
  5. T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
    [CrossRef]
  6. S. Fourmaux, S. Payeur, A. Alexandrov, C. Serbanescu, F. Martin, T. Ozaki, A. Kudryashov, and J. C. Kieffer, “Laser beam wavefront correction for ultra high intensities with the 200 TW laser system at the Advanced Laser Light Source,” Opt. Express 16(16), 11987–11994 (2008).
    [CrossRef] [PubMed]
  7. 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(7), 517–521 (2008).
    [CrossRef]
  8. C. Li, N. Sredar, K. M. Ivers, H. Queener, and J. Porter, “A correction algorithm to simultaneously control dual deformable mirrors in a woofer-tweeter adaptive optics system,” Opt. Express 18(16), 16671–16684 (2010).
    [CrossRef] [PubMed]
  9. W. Zou, X. Qi, and S. A. Burns, “Woofer-tweeter adaptive optics scanning laser ophthalmoscopic imaging based on Lagrange-multiplier damped least-squares algorithm,” Biomed. Opt. Express 2(7), 1986–2004 (2011).
    [CrossRef] [PubMed]
  10. W. Zou and S. A. Burns, “Testing of Lagrange multiplier damped least-square control algorithm for woofer-tweeter adaptive optics,” Appl. Opt. 51(9), 1198–1208 (2012).
    [CrossRef]
  11. B. Cense, E. Koperda, J. M. Brown, O. P. Kocaoglu, W. Gao, R. S. Jonnal, and D. T. Miller, “Volumetric retinal imaging with ultrahigh-resolution spectral-domain optical coherence tomography and adaptive optics using two broadband light sources,” Opt. Express 17(5), 4095–4111 (2009).
    [CrossRef] [PubMed]
  12. D. C. Chen, S. M. Jones, D. A. Silva, and S. S. Olivier, “High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors,” J. Opt. Soc. Am. A 24(5), 1305–1312 (2007).
    [CrossRef] [PubMed]
  13. R. J. Zawadzki, S. S. Choi, S. M. Jones, S. S. Oliver, and J. S. Werner, “Adaptive optics-optical coherence tomography: optimizing visualization of microscopic retinal structures in three dimensions,” J. Opt. Soc. Am. A 24(5), 1373–1383 (2007).
    [CrossRef] [PubMed]
  14. S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu, and W. Jiang, “Double-deformable-mirror adaptive optics system for phase compensation,” Appl. Opt. 45(12), 2638–2642 (2006).
    [CrossRef] [PubMed]
  15. R. Conan, C. Bradley, P. Hampton, O. Keskin, A. Hilton, and C. Blain, “Distributed modal command for a two-deformable-mirror adaptive optics system,” Appl. Opt. 46(20), 4329–4340 (2007).
    [CrossRef] [PubMed]
  16. H. Y and X. Li, “The Control Method of Close-Loop Adaptive Optical System with Multi-Wavefront-Correctors,” Chin. J. Lasers 36(Suppl.), 67–72 (2009).
  17. H. Baumhacker, G. Pretzler, K. J. Witte, M. Hegelich, M. Kaluza, S. Karsch, A. Kudryashov, V. Samarkin, and A. Roukossouev, “Correction of strong phase and amplitude modulations by two deformable mirrors in a multistaged Ti:sapphire laser,” Opt. Lett. 27(17), 1570–1572 (2002).
    [CrossRef] [PubMed]
  18. J. D. Barchers, “Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations,” J. Opt. Soc. Am. A 19(5), 926–945 (2002).
    [CrossRef] [PubMed]
  19. J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront,” Proc. SPIE 6872, 68720B(2008).
    [CrossRef]
  20. C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
    [CrossRef] [PubMed]
  21. H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
    [CrossRef]
  22. H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
    [CrossRef]
  23. M. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wavefront phase-distortion correction,” J. Opt. Soc. Am. A 15(10), 2745–2758 (1998).
    [CrossRef]
  24. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17(8), 1440–1453 (2000).
    [CrossRef] [PubMed]
  25. P. Piatrou and M. Roggemann, “Beaconless stochastic parallel gradient descent laser beam control: numerical experiments,” Appl. Opt. 46(27), 6831–6842 (2007).
    [CrossRef] [PubMed]
  26. M. A. Vorontsov and G. W. Carhart, “Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters,” J. Opt. Soc. Am. A 23(10), 2613–2622 (2006).
    [CrossRef] [PubMed]
  27. T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. A. Hammer, M. Cohen, and G. Cauwenberghs, “Microscale adaptive optics: wave-front control with a μ-mirror array and a VLSI stochastic gradient descent controller,” Appl. Opt. 40(24), 4243–4253 (2001).
    [CrossRef] [PubMed]
  28. T. Weyrauch and M. A. Vorontsov, “Dynamic wave-front distortion compensation with a 134-control-channel submillisecond adaptive system,” Opt. Lett. 27(9), 751–753 (2002).
    [CrossRef] [PubMed]
  29. 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(2-3), 527–533 (2009).
    [CrossRef]
  30. Z. Yang, “Description of wave-front modes in square area and its application in ICF system,” Engineering Master Dissertation (University of Electronic Science and Technology of China, 2008) (in Chinese).
  31. X. Rao, N. Ling, and W. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. 15, 1446–1451 (1995) (in Chinese).
  32. A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1. http://www.opticsinfobase.org/abstract.cfm?URI=DLAI-1998-MQ1 .
  33. X. Li, X. Hao, C. Wang, and W. Jiang, “Relationship between beam quality factor β and wavefront error,” Chin. J. Lasers 32(6), 798–802 (2005) (in Chinese).

2012 (2)

2011 (3)

W. Zou, X. Qi, and S. A. Burns, “Woofer-tweeter adaptive optics scanning laser ophthalmoscopic imaging based on Lagrange-multiplier damped least-squares algorithm,” Biomed. Opt. Express 2(7), 1986–2004 (2011).
[CrossRef] [PubMed]

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

2010 (2)

2009 (3)

B. Cense, E. Koperda, J. M. Brown, O. P. Kocaoglu, W. Gao, R. S. Jonnal, and D. T. Miller, “Volumetric retinal imaging with ultrahigh-resolution spectral-domain optical coherence tomography and adaptive optics using two broadband light sources,” Opt. Express 17(5), 4095–4111 (2009).
[CrossRef] [PubMed]

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(2-3), 527–533 (2009).
[CrossRef]

H. Y and X. Li, “The Control Method of Close-Loop Adaptive Optical System with Multi-Wavefront-Correctors,” Chin. J. Lasers 36(Suppl.), 67–72 (2009).

2008 (3)

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(7), 517–521 (2008).
[CrossRef]

J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront,” Proc. SPIE 6872, 68720B(2008).
[CrossRef]

S. Fourmaux, S. Payeur, A. Alexandrov, C. Serbanescu, F. Martin, T. Ozaki, A. Kudryashov, and J. C. Kieffer, “Laser beam wavefront correction for ultra high intensities with the 200 TW laser system at the Advanced Laser Light Source,” Opt. Express 16(16), 11987–11994 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (2)

2005 (2)

X. Li, X. Hao, C. Wang, and W. Jiang, “Relationship between beam quality factor β and wavefront error,” Chin. J. Lasers 32(6), 798–802 (2005) (in Chinese).

T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
[CrossRef]

2004 (1)

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

2002 (3)

2001 (1)

2000 (1)

1998 (1)

1995 (2)

C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34(12), 2081–2088 (1995).
[CrossRef] [PubMed]

X. Rao, N. Ling, and W. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. 15, 1446–1451 (1995) (in Chinese).

Alexandrov, A.

Ao, M.

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(7), 517–521 (2008).
[CrossRef]

Barchers, J. D.

Barclay, H. T.

Baumhacker, H.

Bifano, T. G.

Blain, C.

Bradley, C.

Brase, J. M.

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

Brown, J. M.

Burgy, F.

T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
[CrossRef]

Burns, S. A.

Carhart, G. W.

Cauwenberghs, G.

Cense, B.

Chambaret, J.-P.

T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
[CrossRef]

Chen, D. C.

Chériaux, G.

T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
[CrossRef]

Choi, S. S.

Cohen, M.

Conan, R.

Dane, C. B.

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

Dong, L.

Fochs, S. N.

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

Fourmaux, S.

Gao, W.

Hammer, J. A.

Hampton, P.

Hao, X.

X. Li, X. Hao, C. Wang, and W. Jiang, “Relationship between beam quality factor β and wavefront error,” Chin. J. Lasers 32(6), 798–802 (2005) (in Chinese).

Hegelich, M.

Herrmann, J.

Hilton, A.

Hou, J.

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(7), 517–521 (2008).
[CrossRef]

S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu, and W. Jiang, “Double-deformable-mirror adaptive optics system for phase compensation,” Appl. Opt. 45(12), 2638–2642 (2006).
[CrossRef] [PubMed]

Humphreys, R. A.

Hurd, R. L.

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

Ivers, K. M.

Jiang, W.

P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010).
[CrossRef] [PubMed]

S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu, and W. Jiang, “Double-deformable-mirror adaptive optics system for phase compensation,” Appl. Opt. 45(12), 2638–2642 (2006).
[CrossRef] [PubMed]

X. Li, X. Hao, C. Wang, and W. Jiang, “Relationship between beam quality factor β and wavefront error,” Chin. J. Lasers 32(6), 798–802 (2005) (in Chinese).

X. Rao, N. Ling, and W. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. 15, 1446–1451 (1995) (in Chinese).

Johansson, E. M.

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

Jones, S. M.

Jonnal, R. S.

Kaluza, M.

Karsch, S.

Keskin, O.

Kieffer, J. C.

Kocaoglu, O. P.

Koperda, E.

Kudryashov, A.

LaFortune, K. N.

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

Lei, X.

Li, C.

Li, X.

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010).
[CrossRef] [PubMed]

X. Li, X. Hao, C. Wang, and W. Jiang, “Relationship between beam quality factor β and wavefront error,” Chin. J. Lasers 32(6), 798–802 (2005) (in Chinese).

Liang, X.

Ling, N.

X. Rao, N. Ling, and W. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. 15, 1446–1451 (1995) (in Chinese).

Liu, L.

Liu, W.

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(7), 517–521 (2008).
[CrossRef]

Liu, Z.

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

Ma, H.

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

Ma, Y.

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

Martin, F.

Miller, D. T.

Ning, Y.

Oliver, S. S.

Olivier, S. S.

Ozaki, T.

Payeur, S.

Piatrou, P.

Planchon, T. A.

T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
[CrossRef]

Porter, J.

Pretzler, G.

Price, T. R.

Primmerman, C. A.

Qi, X.

Queener, H.

Rao, X.

X. Rao, N. Ling, and W. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. 15, 1446–1451 (1995) (in Chinese).

Roggemann, M.

Roukossouev, A.

Rousseau, J.-P.

T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
[CrossRef]

Samarkin, V.

J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront,” Proc. SPIE 6872, 68720B(2008).
[CrossRef]

H. Baumhacker, G. Pretzler, K. J. Witte, M. Hegelich, M. Kaluza, S. Karsch, A. Kudryashov, V. Samarkin, and A. Roukossouev, “Correction of strong phase and amplitude modulations by two deformable mirrors in a multistaged Ti:sapphire laser,” Opt. Lett. 27(17), 1570–1572 (2002).
[CrossRef] [PubMed]

Serbanescu, C.

Sheldakova, J.

J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront,” Proc. SPIE 6872, 68720B(2008).
[CrossRef]

Silva, D. A.

Sivokon, V. P.

Sredar, N.

Tang, X.

Vorontsov, M. A.

Wang, C.

Wang, X.

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

Werner, J. S.

Weyrauch, T.

Witte, K. J.

Wu, J.

Xu, B.

Xu, X.

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

Yan, H.

Yang, P.

X. Lei, B. Xu, P. Yang, L. Dong, W. Liu, and H. Yan, “Beam cleanup of a 532-nm pulsed solid-state laser using a bimorph mirror,” Chin. Opt. Lett. 10(2), 021401 (2012).

P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010).
[CrossRef] [PubMed]

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(2-3), 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(7), 517–521 (2008).
[CrossRef]

Zavalova, V.

J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront,” Proc. SPIE 6872, 68720B(2008).
[CrossRef]

Zawadzki, R. J.

Zhang, X.

Zhao, H.

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

Zhao, Y.

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

Zhou, P.

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

Zollars, B. G.

Zou, W.

Acta Opt. Sin. (1)

X. Rao, N. Ling, and W. Jiang, “Experimental of measuring influence function of deformable mirror using digital interferometer,” Acta Opt. Sin. 15, 1446–1451 (1995) (in Chinese).

Appl. Opt. (6)

Appl. Phys. B (1)

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(2-3), 527–533 (2009).
[CrossRef]

Biomed. Opt. Express (1)

Chin. J. Lasers (2)

H. Y and X. Li, “The Control Method of Close-Loop Adaptive Optical System with Multi-Wavefront-Correctors,” Chin. J. Lasers 36(Suppl.), 67–72 (2009).

X. Li, X. Hao, C. Wang, and W. Jiang, “Relationship between beam quality factor β and wavefront error,” Chin. J. Lasers 32(6), 798–802 (2005) (in Chinese).

Chin. Opt. Lett. (1)

J. Opt. (1)

H. Ma, Z. Liu, X. Xu, X. Wang, Y. Ma, and P. Zhou, “Adaptive generation of a near-diffraction-limited square flattop beam with dual phase only liquid crystal spatial light mudulators,” J. Opt. 13(1), 015707 (2011).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Commun. (2)

T. A. Planchon, J.-P. Rousseau, F. Burgy, G. Chériaux, and J.-P. Chambaret, “Adaptive wavefront correction on a 100-TW/10-Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252(4-6), 222–228 (2005).
[CrossRef]

H. Zhao, H. Ma, P. Zhou, X. Wang, Y. Ma, X. Li, X. Xu, and Y. Zhao, “Muitimode fiber laser beam cleanup based on stochastic parallel gradient descent algorithm,” Opt. Commun. 284(2), 613–615 (2011).
[CrossRef]

Opt. Express (4)

Opt. Lasers Eng. (1)

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(7), 517–521 (2008).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (2)

J. Sheldakova, A. Kudryashov, V. Samarkin, and V. Zavalova, “Problem of Shack-Hartmann wavefront sensor and Interferometer use while testing strongly distorted laser wavefront,” Proc. SPIE 6872, 68720B(2008).
[CrossRef]

K. N. LaFortune, R. L. Hurd, E. M. Johansson, C. B. Dane, S. N. Fochs, and J. M. Brase, “Intracavity adaptive correction of a 10 kW, solid-state, heat-capacity laser,” Proc. SPIE 5333, 53–61 (2004).
[CrossRef]

Other (3)

W. Koechener, Solid-State Laser Engineering (Springer, 1999), Chap. 4.

Z. Yang, “Description of wave-front modes in square area and its application in ICF system,” Engineering Master Dissertation (University of Electronic Science and Technology of China, 2008) (in Chinese).

A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M. Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1. http://www.opticsinfobase.org/abstract.cfm?URI=DLAI-1998-MQ1 .

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Figures (16)

Fig. 1
Fig. 1

Schematic of actuator configuration of the rectangular DM.

Fig. 2
Fig. 2

Correction quality of a 39-element DM with the first 35 orders of Zernike polynomials in a unit square area.

Fig. 3
Fig. 3

(a) The wave-front aberration before correction. (b) The focal spot with normalized intensity before correction.

Fig. 4
Fig. 4

The residual wave-front after corrected directly by: (a) single limited stroke 39-actuator DM; (b) single ideal stroke 39-actuator DM.

Fig. 5
Fig. 5

(a) The surface shape generated by limited stroke DM 1. (b) The surface shape generated by limited stroke DM 2. (c) The residual wave-front after corrected by double limited stroke DMs system.

Fig. 6
Fig. 6

Comparison of focal spots whose wave-front aberrations are corrected by a single limited stroke 39-actuator DM, double limited stroke DMs and a single ideal stroke DM.

Fig. 7
Fig. 7

(a) The wave-front before correction. (b) The wave-front coefficients of orthogonal polynomials before correction.

Fig. 8
Fig. 8

Residual wave-fronts and the corresponding coefficients in 3 cases. (a) and (b): Residual wave-front and the corresponding coefficients, when the number of correction orders is larger than the number of real aberration orders. (c) and (d): Residual wave-front and the corresponding coefficients, when the number of correction orders is equal to the number of real aberration orders. (e) and (f): Residual wave-front and the corresponding coefficients, when the number of correction orders is smaller than the number of real aberration orders.

Fig. 9
Fig. 9

Strehl ratio changes with iteration number.

Fig. 10
Fig. 10

Schematic of a wavefront-sensor-less two-DM beam cleanup system.

Fig. 11
Fig. 11

Relation matrix of response functions and orthogonal polynomials. The first 15 orders of Zernike polynomials in square area are selected to calculate this matrix.

Fig. 12
Fig. 12

Iteration curve by this wavefront-sensor-less double-DM system

Fig. 13
Fig. 13

Long time exposure far-field spots: (a) the original far-field spot (before correction); (b) the far-field spot with DM1 on; (c) the far-field spot with DM1 and DM2 both on. (d) PIB curves, the X-coordinate represents the times of the diffraction-limited, the Y-coordinate represents the fraction of total energy.

Fig. 14
Fig. 14

Horizontal and vertical cut of the focal plane images: (a) horizontal; (b) vertical.

Fig. 15
Fig. 15

The comparison of the orthogonal polynomials’ coefficients decomposed from two DMs’ surface shape.

Fig. 16
Fig. 16

The voltages applied on DM 1. The voltages are limited from −450V to 450V.

Equations (5)

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Φ(x,y)= m=1 l a m δ m (x,y),
j=1 N u j n R j n (x,y) = δ m (x,y),
m=1 l a m ( u m n R n )= m=1 l a m δ m ,
Φ 1 + Φ 2 +...+ Φ n1 + m=t+1 l a m ( u m n R n )+ε= m=1 l a m δ m ,
f j (x,y)=exp [ln(ω) (x x j ) 2 + (y y j ) 2 /d) α ],

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