Abstract

A modified hill-climbing algorithm based on Zernike modes is used for laser beam correction. The algorithm adopts the Zernike mode coefficients, instead of the deformable mirror actuators’ voltages in a traditional hill-climbing algorithm, as the adjustable variables to optimize the object function. The effect of the mismatches between the laser beam and the deformable mirror both in the aperture size and the center position was analyzed numerically and experimentally to test the robustness of the algorithm. Both simulation and experimental results show that the mismatches have almost no influence on the laser beam correction, unless the laser beam exceeds the effective aperture of the deformable mirror, which indicates the good robustness of the algorithm.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. H. Rao, L. Zhu, X. J. Rao, C. L. Guan, D. H. Chen, S. Q. Chen, J. Lin, and Z. Z. Liu, “Performance of the 37-element solar adaptive optics for the 26  cm solar fine structure telescope at Yunnan Astronomical Observatory,” Appl. Opt. 49, G129–G135 (2010).
    [Crossref]
  2. A. Guesalaga, B. Neichel, J. O’Neal, and D. Guzman, “Mitigation of vibrations in adaptive optics by minimization of closed-loop residuals,” Opt. Express 21, 10676–10796 (2013).
    [Crossref]
  3. D. W. Arathorn, Q. Yang, C. R. Vogel, Y. H. Zhang, P. Tiruveedhula, and A. Roorda, “Retinally stabilized cone-targeted stimulus delivery,” Opt. Express 15, 13731–13744 (2007).
    [Crossref]
  4. N. Doble and D. R. Williams, “The application of MEMS technology for adaptive optics in vision science,” IEEE J. Sel. Top. Quantum Electron. 10, 629–635 (2004).
    [Crossref]
  5. O. Azucena, J. Crest, S. Kotadia, W. Sullivan, X. D. Tao, M. Reinig, D. Gavel, S. Olivier, and J. Kubby, “Adaptive optics wide-field microscopy using direct wavefront sensing,” Opt. Lett. 36, 825–827 (2011).
    [Crossref]
  6. M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. USA 99, 5788–5792 (2002).
    [Crossref]
  7. T. A. Planchon, J. P. Rousseau, F. Burgy, and G. Cheriaux, “Adaptive wavefront correction on a 100  TW/10  Hz chirped pulse amplification laser and effect of residual wavefront on beam propagation,” Opt. Commun. 252, 222–228 (2005).
    [Crossref]
  8. M. L. Gong, Y. T. Qiu, L. Huang, Q. Liu, P. Yan, and H. T. Zhang, “Beam quality improvement by joint compensation of amplitude and phase,” Opt. Lett. 38, 1101–1103 (2013).
    [Crossref]
  9. P. Yang, W. Yang, Y. Liu, S. J. Hu, M. W. Ao, B. Xu, and W. H. Jiang, “19-element sensor-less adaptive optical system based on modified hill-climbing and genetic algorithms,” Proc. SPIE 6723, 31–37 (2007).
  10. T. Planchon, W. Amir, J. J. Field, C. G. Durfee, and J. A. Squier, “Adaptive correction of a tightly focused, high-intensity laser beam by use of a third-harmonic signal generated at an interface,” Opt. Lett. 31, 2214–2216 (2006).
    [Crossref]
  11. S. P. Poland, A. J. Wright, and J. M. Girkin, “Evaluation of fitness parameters used in an iterative approach to aberration correction in optical sectioning microscopy,” Appl. Opt. 47, 731–736 (2008).
    [Crossref]
  12. H. T. Ma, Q. Zhou, X. J. Xu, S. J. Du, and Z. J. Liu, “Full-field unsymmetrical beam shaping for decreasing and homogenizing the thermal deformation of optical element in a beam control system,” Opt. Express 19, A1037–A1050 (2011).
    [Crossref]
  13. P. Piatrou and M. Roggemann, “Beaconless stochastic parallel gradient descent laser beam control: numerical experiments,” Appl. Opt. 46, 6831–6842 (2007).
    [Crossref]
  14. S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, “Simulated annealing in ocular adaptive optics,” Opt. Lett. 31, 939–941 (2006).
    [Crossref]
  15. 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]
  16. 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]
  17. Y. Liu, J. Q. Ma, B. Q. Li, and J. R. Chu, “Hill-climbing algorithm based on Zernike modes for wavefront sensor-less adaptive optics,” Opt. Eng. 52, 016601 (2013).
    [Crossref]
  18. M. J. Booth, “Wavefront sensorless adaptive optics for large aberrations,” Opt. Lett. 32, 5–7 (2007).
    [Crossref]
  19. S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
    [Crossref]
  20. J. Q. Ma, Y. Liu, T. He, B. Q. Li, and J. R. Chu, “Double drive modes unimorph deformable mirror for low-cost adaptive optics,” Appl. Opt. 50, 5647–5654 (2011).
    [Crossref]
  21. P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Z. Dong, H. Yan, W. J. Liu, W. H. Jiang, L. Liu, C. Wang, X. B. Liang, and X. Tang, “Enhancement of the beam quality of nonuniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18, 7121–7130 (2010).
    [Crossref]
  22. T. G. Bifano, P. Bierden, and S. A. Cornelissen, “MEMS deformable mirrors for space and defense applications,” Proc. SPIE 6959, 695914 (2008).
    [Crossref]
  23. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1983).

2013 (3)

2011 (3)

2010 (2)

2008 (2)

2007 (5)

2006 (2)

2005 (2)

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]

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

2004 (1)

N. Doble and D. R. Williams, “The application of MEMS technology for adaptive optics in vision science,” IEEE J. Sel. Top. Quantum Electron. 10, 629–635 (2004).
[Crossref]

2003 (1)

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

2002 (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

Adler, J.

Aka, G. P.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Amir, W.

Ao, M. W.

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, W. Yang, Y. Liu, S. J. Hu, M. W. Ao, B. Xu, and W. H. Jiang, “19-element sensor-less adaptive optical system based on modified hill-climbing and genetic algorithms,” Proc. SPIE 6723, 31–37 (2007).

Arathorn, D. W.

Azucena, O.

Balembois, F.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Bierden, P.

T. G. Bifano, P. Bierden, and S. A. Cornelissen, “MEMS deformable mirrors for space and defense applications,” Proc. SPIE 6959, 695914 (2008).
[Crossref]

Bifano, T. G.

T. G. Bifano, P. Bierden, and S. A. Cornelissen, “MEMS deformable mirrors for space and defense applications,” Proc. SPIE 6959, 695914 (2008).
[Crossref]

Booth, M. J.

M. J. Booth, “Wavefront sensorless adaptive optics for large aberrations,” Opt. Lett. 32, 5–7 (2007).
[Crossref]

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1983).

Bulte, H.

Burgy, F.

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

Chen, D. H.

Chen, S. Q.

Chénais, S.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Cheriaux, G.

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

Chu, J. R.

Y. Liu, J. Q. Ma, B. Q. Li, and J. R. Chu, “Hill-climbing algorithm based on Zernike modes for wavefront sensor-less adaptive optics,” Opt. Eng. 52, 016601 (2013).
[Crossref]

J. Q. Ma, Y. Liu, T. He, B. Q. Li, and J. R. Chu, “Double drive modes unimorph deformable mirror for low-cost adaptive optics,” Appl. Opt. 50, 5647–5654 (2011).
[Crossref]

Cornelissen, S. A.

T. G. Bifano, P. Bierden, and S. A. Cornelissen, “MEMS deformable mirrors for space and defense applications,” Proc. SPIE 6959, 695914 (2008).
[Crossref]

Crest, J.

Doble, N.

N. Doble and D. R. Williams, “The application of MEMS technology for adaptive optics in vision science,” IEEE J. Sel. Top. Quantum Electron. 10, 629–635 (2004).
[Crossref]

Dong, L. Z.

Druon, F.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Du, S. J.

Durfee, C. G.

El-Agmy, R.

Fichot, Y.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Field, J. J.

Gaumé, R.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Gavel, D.

Georges, P.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Girkin, J. M.

Gong, M. L.

Greenaway, A. H.

Guan, C. L.

Guesalaga, A.

Guzman, D.

He, T.

Hu, S. J.

P. Yang, W. Yang, Y. Liu, S. J. Hu, M. W. Ao, B. Xu, and W. H. Jiang, “19-element sensor-less adaptive optical system based on modified hill-climbing and genetic algorithms,” Proc. SPIE 6723, 31–37 (2007).

Huang, L.

Jiang, W. H.

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

Kotadia, S.

Kubby, J.

Lei, X.

Li, B. Q.

Y. Liu, J. Q. Ma, B. Q. Li, and J. R. Chu, “Hill-climbing algorithm based on Zernike modes for wavefront sensor-less adaptive optics,” Opt. Eng. 52, 016601 (2013).
[Crossref]

J. Q. Ma, Y. Liu, T. He, B. Q. Li, and J. R. Chu, “Double drive modes unimorph deformable mirror for low-cost adaptive optics,” Appl. Opt. 50, 5647–5654 (2011).
[Crossref]

Li, X.

Liang, X. B.

Lin, J.

Lipson, S. G.

Liu, L.

Liu, Q.

Liu, W. J.

Liu, Y.

Y. Liu, J. Q. Ma, B. Q. Li, and J. R. Chu, “Hill-climbing algorithm based on Zernike modes for wavefront sensor-less adaptive optics,” Opt. Eng. 52, 016601 (2013).
[Crossref]

J. Q. Ma, Y. Liu, T. He, B. Q. Li, and J. R. Chu, “Double drive modes unimorph deformable mirror for low-cost adaptive optics,” Appl. Opt. 50, 5647–5654 (2011).
[Crossref]

P. Yang, W. Yang, Y. Liu, S. J. Hu, M. W. Ao, B. Xu, and W. H. Jiang, “19-element sensor-less adaptive optical system based on modified hill-climbing and genetic algorithms,” Proc. SPIE 6723, 31–37 (2007).

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]

Liu, Z. J.

Liu, Z. Z.

Lucas-Leclin, G.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Ma, H. T.

Ma, J. Q.

Y. Liu, J. Q. Ma, B. Q. Li, and J. R. Chu, “Hill-climbing algorithm based on Zernike modes for wavefront sensor-less adaptive optics,” Opt. Eng. 52, 016601 (2013).
[Crossref]

J. Q. Ma, Y. Liu, T. He, B. Q. Li, and J. R. Chu, “Double drive modes unimorph deformable mirror for low-cost adaptive optics,” Appl. Opt. 50, 5647–5654 (2011).
[Crossref]

Neichel, B.

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

Ning, Y.

O’Neal, J.

Olivier, S.

Piatrou, P.

Planchon, T.

Planchon, T. A.

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

Poland, S. P.

Qiu, Y. T.

Rao, C. H.

Rao, X. J.

Reid, D. T.

Reinig, M.

Ribak, E. N.

Roggemann, M.

Roorda, A.

Rousseau, J. P.

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

Squier, J. A.

Sullivan, W.

Tang, X.

Tao, X. D.

Tiruveedhula, P.

Viana, B.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Vivien, D.

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Vogel, C. R.

Wang, C.

Williams, D. R.

N. Doble and D. R. Williams, “The application of MEMS technology for adaptive optics in vision science,” IEEE J. Sel. Top. Quantum Electron. 10, 629–635 (2004).
[Crossref]

Wilson, T.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1983).

Wright, A. J.

Xu, B.

Xu, X. J.

Yan, H.

Yan, P.

Yang, P.

Yang, Q.

Yang, W.

P. Yang, W. Yang, Y. Liu, S. J. Hu, M. W. Ao, B. Xu, and W. H. Jiang, “19-element sensor-less adaptive optical system based on modified hill-climbing and genetic algorithms,” Proc. SPIE 6723, 31–37 (2007).

Zhang, H. T.

Zhang, Y. H.

Zhou, Q.

Zhu, L.

Zommer, S.

Appl. Opt. (4)

IEEE J. Sel. Top. Quantum Electron. (1)

N. Doble and D. R. Williams, “The application of MEMS technology for adaptive optics in vision science,” IEEE J. Sel. Top. Quantum Electron. 10, 629–635 (2004).
[Crossref]

Opt. Commun. (1)

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

Opt. Eng. (1)

Y. Liu, J. Q. Ma, B. Q. Li, and J. R. Chu, “Hill-climbing algorithm based on Zernike modes for wavefront sensor-less adaptive optics,” Opt. Eng. 52, 016601 (2013).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Opt. Mater. (1)

S. Chénais, F. Druon, F. Balembois, G. Lucas-Leclin, Y. Fichot, P. Georges, R. Gaumé, B. Viana, G. P. Aka, and D. Vivien, “Thermal lensing measurements in diode-pumped Yb-doped GdCOB, YCOB, YSO, YAG and KGW,” Opt. Mater. 22, 129–137 (2003).
[Crossref]

Proc. Nat. Acad. Sci. USA (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Nat. Acad. Sci. USA 99, 5788–5792 (2002).
[Crossref]

Proc. SPIE (2)

P. Yang, W. Yang, Y. Liu, S. J. Hu, M. W. Ao, B. Xu, and W. H. Jiang, “19-element sensor-less adaptive optical system based on modified hill-climbing and genetic algorithms,” Proc. SPIE 6723, 31–37 (2007).

T. G. Bifano, P. Bierden, and S. A. Cornelissen, “MEMS deformable mirrors for space and defense applications,” Proc. SPIE 6959, 695914 (2008).
[Crossref]

Other (1)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1983).

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 (12)

Fig. 1.
Fig. 1.

Schematic illustration of (a) Case I: the aperture diameters do not match, (b) Case II: the two centers are not aligned, with the laser beam still in the DM effective aperture, and (c) Case III: the two centers are not aligned, with the laser beam exceeding the DM effective aperture.

Fig. 2.
Fig. 2.

Simulated normalized rms error for correction Zernike aberrations.

Fig. 3.
Fig. 3.

Zernike coefficients of the generated wavefront.

Fig. 4.
Fig. 4.

Correction results for mismatched apertures: the DM’s effective aperture was 10 mm and the laser beam aperture varied from 5 to 10 mm.

Fig. 5.
Fig. 5.

Correction results for different center offsets. (a) The laser beam aperture did not exceed the DM’s effective aperture. (b) The laser beam aperture exceeded the DM’s effective aperture.

Fig. 6.
Fig. 6.

Schematic illustration of the experimental setup for aberration correction.

Fig. 7.
Fig. 7.

Far field beam spots after correction with different apertures: (a) 5 mm, (b) 6 mm, (c) 7 mm, (d) 8 mm, (e) 9 mm, and (f) 10 mm.

Fig. 8.
Fig. 8.

Intensity concentration of the laser beam spots of different apertures.

Fig. 9.
Fig. 9.

Far field spots of 7 mm laser beam after correction with different offsets of the centers: (a) 0.5 mm, (b) 1 mm, and (c) 1.5 mm.

Fig. 10.
Fig. 10.

Intensity concentration of the spots with different center offsets, when the laser beam did not exceed the DM effective aperture.

Fig. 11.
Fig. 11.

Far field spots of 10 mm laser beam after correction with different offsets of the centers: (a) 0.5 mm, (b) 1 mm, (c) 1.5 mm, and (d) 2 mm.

Fig. 12.
Fig. 12.

Intensity concentration of the spots with different center offsets, when the laser beam exceeds the DM effective aperture.

Equations (4)

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

SR1σϕ2,
Φ(r,θ)=n=1NcnZn(r,θ).
σϕ2=n=1Ncn2.
II0(1n=1Ncn2),

Metrics