Beam shaping for laser-based adaptive optics in astronomy

Clémentine Béchet; Andrés Guesalaga; Benoit Neichel; Vincent Fesquet; Héctor González-Núñez; Sebastián Zúñiga; Pedro Escarate; Dani Guzman

doi:10.1364/OE.22.012994

Beam shaping for laser-based adaptive optics in astronomy

Clémentine Béchet, Andrés Guesalaga, Benoit Neichel, Vincent Fesquet, Héctor González-Núñez, Sebastián Zúñiga, Pedro Escarate, and Dani Guzman

Optics Express
Vol. 22,
Issue 11,
pp. 12994-13013
(2014)
•https://doi.org/10.1364/OE.22.012994

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Clémentine Béchet, Andrés Guesalaga, Benoit Neichel, Vincent Fesquet, Héctor González-Núñez, Sebastián Zúñiga, Pedro Escarate, and Dani Guzman, "Beam shaping for laser-based adaptive optics in astronomy," Opt. Express 22, 12994-13013 (2014)

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Related Topics
Table of Contents Category
- Adaptive Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Inverse problems (100.3190)
- Phase retrieval (100.5070)
- Phase unwrapping (100.5088)
- Active or adaptive optics (110.1080)
- Laser beam shaping (140.3300)

About this Article
History
- Original Manuscript: March 27, 2014
- Revised Manuscript: May 12, 2014
- Manuscript Accepted: May 13, 2014
- Published: May 21, 2014

Accessible

Open Access

Abstract

The availability and performance of laser-based adaptive optics (AO) systems are strongly dependent on the power and quality of the laser beam before being projected to the sky. Frequent and time-consuming alignment procedures are usually required in the laser systems with free-space optics to optimize the beam. Despite these procedures, significant distortions of the laser beam have been observed during the first two years of operation of the Gemini South multi-conjugate adaptive optics system (GeMS). A beam shaping concept with two deformable mirrors is investigated in order to provide automated optimization of the laser quality for astronomical AO. This study aims at demonstrating the correction of quasi-static aberrations of the laser, in both amplitude and phase, testing a prototype of this two-deformable mirror concept on GeMS. The paper presents the results of the preparatory study before the experimental phase. An algorithm to control amplitude and phase correction, based on phase retrieval techniques, is presented with a novel unwrapping method. Its performance is assessed via numerical simulations, using aberrations measured at GeMS as reference. The results predict effective amplitude and phase correction of the laser distortions with about 120 actuators per mirror and a separation of 1.4 m between the mirrors. The spot size is estimated to be reduced by up to 15% thanks to the correction. In terms of AO noise level, this has the same benefit as increasing the photon flux by 40%.

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References

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Publication

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[Crossref]
J. W. Ogland, “Mirror system for uniform beam transformation in high-power annular lasers,” Appl. Opt. 17, 2917–2923 (1978).
[Crossref] [PubMed]
D. Shafer, “Gaussian to flat-top intensity distributing lens,” Optics & Laser Technology 14, 159–160 (1982).
[Crossref]
P. W. Rhodes and D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
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[Crossref]
K. L. Baker, E. A. Stappaerts, D. Gavel, S. C. Wilks, J. Tucker, D. A. Silva, J. Olsen, S. S. Olivier, P. E. Young, M. W. Kartz, L. M. Flath, P. Kruelevitch, J. Crawford, and O. Azucena, “High-speed horizontal-path atmospheric turbulence correction with a large-actuator-number microelectromechanical system spatial light modulator in an interferometric phase-conjugation engine,” Opt. Lett. 29(15), 1781–1783 (2004).
[Crossref] [PubMed]
M. C. Roggemann and D. J. Lee, “Two-Deformable-Mirror Concept for Correcting Scintillation Effects in Laser Beam Projection Through the Turbulent Atmosphere,” Appl. Opt. 37(21), 4577–4585 (1998).
[Crossref]
J. D. Barchers and D. L. Fried, “Optimal control of laser beams for propagation through a turbulent medium,” J. Opt. Soc. Am. A 19, 1779–1793 (2002).
[Crossref]
M. A. Vorontsov and V. Kolosov, “Target-in-the-loop beam control: basic considerations for analysis and wavefront sensing,” J. Opt. Soc. Am. A 22(1), 126–141 (2005).
[Crossref]
Z. Zhao, S. D. Lyke, and M. C. Roggemann, “Adaptive Optical Communication through Turbulent Atmospheric Channels,” in Proceedings of IEEE Conference on Communications, 2008. ICC ’08 (Institute of Electrical and Electronics Engineers, New York, 2008), 5432–5436.
R. Kizito, M. C. Roggemann, T. J. Schulz, and Y. Zhang, “Image sharpness metric-based deformable mirror control for beam projection systems operating in strong scintillation,” Proc. SPIE 5160, 406–416 (2004).
[Crossref]
M. C. Roggemann and S. Deng, “Scintillation compensation for laser beam projection using segmented deformable mirrors,” Proc. SPIE 3763, 29–40 (1999).
[Crossref]
M. C. Roggemann and A. C. Koivunen, “Wavefront sensing and deformable mirror control in strong scintillation,” J. Opt. Soc. Am. A 17, 911–919 (2000).
[Crossref]
J. D. Barchers and B. L. Ellerbroek, “Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase adjustments,” J. Opt. Soc. Am. A 18(2), 399–411 (2001).
[Crossref]
J. D. Barchers, “Evaluation of the impact of finite-resolution effects on scintillation compensation using two deformable mirrors,” J. Opt. Soc. Am. A 18, 3098–3109 (2001).
[Crossref]
J. D. Barchers, “Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations,” J. Opt. Soc. Am. A 19, 926–945 (2002).
[Crossref]
F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
[Crossref]
R. A. Gonsalves, “Compensation of scintillation with a phase-only adaptive optic,” Opt. Lett. 22, 588–590 (1997).
[Crossref] [PubMed]
O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379–387 (2003).
[Crossref]
L. Pueyo and N. Kasdin, “Polychromatic compensation of propagated aberrations for high-contrast imaging,” Astrophys. J. 666, 609–625 (2007).
[Crossref]
L. Pueyo, J. Kay, N. J. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
[Crossref] [PubMed]
D. Gavel, M. Ammons, B. Bauman, D. Dillon, E. Gates, B. Grigsby, J. Johnson, C. Lockwood, K. Morzinski, D. Palmer, M. Reinig, and S. Severson, “Visible light laser guidestar experimental system (Villages): on-sky tests of new technologies for visible wavelength all-sky coverage adaptive optics systems,” Proc. SPIE 7015, 70150G (2008).
[Crossref]
A. P. Norton, D. Gavel, M. Helmbrecht, C. J. Kempf, E. L. Gates, K. Chloros, D. Redel, and D. Dillon, “Laser guidestar uplink correction using a MEMS deformable mirror: on-sky test results and implications for future AO systems,” accepted for Proc. SPIE (2014).
X. Lei, S. Wang, H. Yan, W. Liu, L. Dong, P. Yang, and B. Xu, “Double-deformable-mirror adaptive optics system for laser beam cleanup using blind optimization,” Opt. Express 20, 22143–22157 (2012).
[Crossref] [PubMed]
V. Fesquet, C. Araujo, V. Garrel, A. Serio, F. Vidal, G. Arriagada, M. Boccas, F. Collao, S. Diggs, J. Donahue, C. D’Orgeville, G. Gausachs, C. Marchant, V. Montes, C. Moreno, B. Neichel, R. Oram, P. Pessev, W. Rambold, C. Urrutia, and T. Vucina, “Review of Gemini South Laser Guide Star Facility performance and upgrades,” in Proceedings of the Third AO4ELT Conference, S. Esposito and L. Fini, eds. (INAF - Osservatorio Astrofisico di Arcetri, Firenze, Italy, 2013), 16120.
J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref] [PubMed]
R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
R. A. Gonsalves, “Phase retrieval from modulus data,” J. Opt. Soc. Am. 66, 961–964 (1976).
[Crossref]
J. R. Fienup, “Reconstruction of an object from the modulus of its fourier transform,” Opt. Lett. 3, 27–29 (1978).
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[Crossref] [PubMed]
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[Crossref]
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C. C. Beckner and D. W. Oesch, “Implementation of a projection-on-constraints algorithm for beam intensity redistribution,” Proc. SPIE 6711, 67110L (2007)

2014 (1)

F. Rigaut, B. Neichel, M. Boccas, C. d’Orgeville, F. Vidal, M. A. van Dam, G. Arriagada, V. Fesquet, R. L. Galvez, G. Gausachs, C. Cavedoni, A. W. Ebbers, S. Karewicz, E. James, J. Lührs, V. Montes, G. Perez, W. N. Rambold, R. Rojas, S. Walker, M. Bec, G. Trancho, M. Sheehan, B. Irarrazaval, C. Boyer, B. L. Ellerbroek, R. Flicker, D. Gratadour, A. Garcia-Rissmann, and F. Daruich, “Gemini multiconjugate adaptive optics system review - I. Design, trade-offs and integration,” Mon. Not. R. Astron. Soc. 437, 2361–2375 (2014).
[Crossref]

2012 (3)

C. d’Orgeville, S. Diggs, V. Fesquet, B. Neichel, W. Rambold, F. Rigaut, A. Serio, C. Araya, G. Arriagada, R. Balladares, M. Bec, M. Boccas, C. Duran, A. Ebbers, A. Lopez, C. Marchant, E. Marin, V. Montes, C. Moreno, E. Petit Vega, C. Segura, G. Trancho, C. Trujillo, C. Urrutia, P. Veliz, and T. Vucina, “Gemini South multi-conjugate adaptive optics (GeMS) laser guide star facility on-sky performance results,” Proc. SPIE 8447, 84471Q (2012).
[Crossref]

A. Guesalaga, B. Neichel, M. Boccas, C. d’Orgeville, F. Rigaut, D. Guzman, and J. Anguita, “Improving stability, robustness, and performance of laser systems,” Proc. SPIE 8447, 84474M (2012).
[Crossref]

X. Lei, S. Wang, H. Yan, W. Liu, L. Dong, P. Yang, and B. Xu, “Double-deformable-mirror adaptive optics system for laser beam cleanup using blind optimization,” Opt. Express 20, 22143–22157 (2012).
[Crossref] [PubMed]

2009 (2)

L. Pueyo, J. Kay, N. J. Kasdin, T. Groff, M. McElwain, A. Give’on, and R. Belikov, “Optimal dark hole generation via two deformable mirrors with stroke minimization,” Appl. Opt. 48, 6296–6312 (2009).
[Crossref] [PubMed]

Y. Feng, L. R. Taylor, and D. B. Calia, “25 W Raman-fiber-amplifier-based 589 nm laser for laser guide star,” Opt. Express 17(21), 19021–19026 (2009).
[Crossref]

2008 (4)

C. d’Orgeville, F. Daruich, G. Arriagada, M. Bec, M. Boccas, S. Bombino, C. Carter, C. Cavedoni, F. Collao, P. Collins, E. James, S. Karewicz, M. Lazo, D. Maltes, R. Mouser, G. Perez, F. Rigaut, R. Rojas, M. Sheehan, G. Trancho, V. Vergara, and T. Vucina, “The Gemini South MCAO laser guide star facility: getting ready for first light,” Proc. SPIE 7015, 70152P (2008).
[Crossref]

R. Holzlöhner, D. Bonaccini Calia, and W. Hackenberg, “Physical optics modeling and optimization of laser guide star propagation,” Proc. SPIE 7015, 701521 (2008).
[Crossref]

D. Gavel, M. Ammons, B. Bauman, D. Dillon, E. Gates, B. Grigsby, J. Johnson, C. Lockwood, K. Morzinski, D. Palmer, M. Reinig, and S. Severson, “Visible light laser guidestar experimental system (Villages): on-sky tests of new technologies for visible wavelength all-sky coverage adaptive optics systems,” Proc. SPIE 7015, 70150G (2008).
[Crossref]

T. M. Venema and J. D. Schmidt, “Optical phase unwrapping in the presence of branch points,” Opt. Express 16, 6985–6998 (2008).
[Crossref] [PubMed]

2007 (2)

L. Pueyo and N. Kasdin, “Polychromatic compensation of propagated aberrations for high-contrast imaging,” Astrophys. J. 666, 609–625 (2007).
[Crossref]

C. C. Beckner and D. W. Oesch, “Implementation of a projection-on-constraints algorithm for beam intensity redistribution,” Proc. SPIE 6711, 67110L (2007)

2005 (1)

M. A. Vorontsov and V. Kolosov, “Target-in-the-loop beam control: basic considerations for analysis and wavefront sensing,” J. Opt. Soc. Am. A 22(1), 126–141 (2005).
[Crossref]

2004 (2)

R. Kizito, M. C. Roggemann, T. J. Schulz, and Y. Zhang, “Image sharpness metric-based deformable mirror control for beam projection systems operating in strong scintillation,” Proc. SPIE 5160, 406–416 (2004).
[Crossref]

K. L. Baker, E. A. Stappaerts, D. Gavel, S. C. Wilks, J. Tucker, D. A. Silva, J. Olsen, S. S. Olivier, P. E. Young, M. W. Kartz, L. M. Flath, P. Kruelevitch, J. Crawford, and O. Azucena, “High-speed horizontal-path atmospheric turbulence correction with a large-actuator-number microelectromechanical system spatial light modulator in an interferometric phase-conjugation engine,” Opt. Lett. 29(15), 1781–1783 (2004).
[Crossref] [PubMed]

2003 (1)

O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379–387 (2003).
[Crossref]

1999 (1)

M. C. Roggemann and S. Deng, “Scintillation compensation for laser beam projection using segmented deformable mirrors,” Proc. SPIE 3763, 29–40 (1999).
[Crossref]

1998 (2)

M. C. Roggemann and D. J. Lee, “Two-Deformable-Mirror Concept for Correcting Scintillation Effects in Laser Beam Projection Through the Turbulent Atmosphere,” Appl. Opt. 37(21), 4577–4585 (1998).
[Crossref]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).
[Crossref]

1997 (1)

R. A. Gonsalves, “Compensation of scintillation with a phase-only adaptive optic,” Opt. Lett. 22, 588–590 (1997).
[Crossref] [PubMed]

1996 (1)

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

1991 (1)

F. Y. Kanev and V. P. Lukin, “Amplitude phase beam control with the help of a two-mirror adaptive system,” Atmos. Opt. 4, 878–881 (1991).

1990 (1)

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[Crossref]

1989 (1)

M. T. Eismann, A. M. Tai, and J. N. Cederquist, “Iterative design of a holographic beamformer,” Appl. Opt. 28, 2641–2650 (1989).
[Crossref]

1982 (2)

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Optics & Laser Technology 14, 159–160 (1982).
[Crossref]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref] [PubMed]

1980 (1)

P. W. Rhodes and D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
[Crossref] [PubMed]

1978 (2)

J. W. Ogland, “Mirror system for uniform beam transformation in high-power annular lasers,” Appl. Opt. 17, 2917–2923 (1978).
[Crossref] [PubMed]

J. R. Fienup, “Reconstruction of an object from the modulus of its fourier transform,” Opt. Lett. 3, 27–29 (1978).
[Crossref] [PubMed]

1976 (1)

R. A. Gonsalves, “Phase retrieval from modulus data,” J. Opt. Soc. Am. 66, 961–964 (1976).
[Crossref]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1965 (1)

B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4, 1400–1403 (1965).
[Crossref]

Alford, W. J.

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

Ammons, M.

Anguita, J.

Araujo, C.

V. Fesquet, C. Araujo, V. Garrel, A. Serio, F. Vidal, G. Arriagada, M. Boccas, F. Collao, S. Diggs, J. Donahue, C. D’Orgeville, G. Gausachs, C. Marchant, V. Montes, C. Moreno, B. Neichel, R. Oram, P. Pessev, W. Rambold, C. Urrutia, and T. Vucina, “Review of Gemini South Laser Guide Star Facility performance and upgrades,” in Proceedings of the Third AO4ELT Conference, S. Esposito and L. Fini, eds. (INAF - Osservatorio Astrofisico di Arcetri, Firenze, Italy, 2013), 16120.

Araya, C.

Arriagada, G.

B. Neichel, F. Rigaut, F. Vidal, M. A. van Dam, V. Garrel, E. Rodrigo Carrasco, P. Pessev, C. Winge, M. Boccas, C. d’Orgeville, G. Arriagada, A. Serio, V. Fesquet, W. N. Rambold, J. Lührs, C. Moreno, G. Gausachs, R. L. Galvez, V. Montes, T. B. Vucina, E. Marin, C. Urrutia, A. Lopez, S. J. Diggs, C. Marchant, A. W. Ebbers, C. Trujillo, M. Bec, G. Trancho, P. McGregor, P. J. Young, F. Colazo, and M. L. Edwards, “Gemini multi-conjugate adaptive optics system review II: Commissioning, operation and overall performance,” Mon. Not. R. Astron. Soc., in press (2014).
[Crossref]

Azucena, O.

Baker, K. L.

Balladares, R.

Barchers, J. D.

J. D. Barchers, “Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations,” J. Opt. Soc. Am. A 19, 926–945 (2002).
[Crossref]

J. D. Barchers and D. L. Fried, “Optimal control of laser beams for propagation through a turbulent medium,” J. Opt. Soc. Am. A 19, 1779–1793 (2002).
[Crossref]

J. D. Barchers, “Evaluation of the impact of finite-resolution effects on scintillation compensation using two deformable mirrors,” J. Opt. Soc. Am. A 18, 3098–3109 (2001).
[Crossref]

Bauman, B.

Bec, M.

Béchet, C.

C. Béchet, A. Guesalaga, B. Neichel, V. Fesquet, and D. Guzman, “A two deformable-mirror concept to improve the laser efficiency of Gemini South MCAO,”, in Proceedings of the Third AO4ELT Conference, S. Esposito and L. Fini, eds. (INAF - Osservatorio Astrofisico di Arcetri, Firenze, Italy, 2013), 13344.

Beckner, C. C.

C. C. Beckner and D. W. Oesch, “Implementation of a projection-on-constraints algorithm for beam intensity redistribution,” Proc. SPIE 6711, 67110L (2007)

Belikov, R.

Boccas, M.

Bombino, S.

Bonaccini Calia, D.

R. Holzlöhner, D. Bonaccini Calia, and W. Hackenberg, “Physical optics modeling and optimization of laser guide star propagation,” Proc. SPIE 7015, 701521 (2008).
[Crossref]

Boyer, C.

Calia, D. B.

Y. Feng, L. R. Taylor, and D. B. Calia, “25 W Raman-fiber-amplifier-based 589 nm laser for laser guide star,” Opt. Express 17(21), 19021–19026 (2009).
[Crossref]

Carter, C.

Cavedoni, C.

Cederquist, J. N.

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Appl. Opt. (7)

B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4, 1400–1403 (1965).
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J. W. Ogland, “Mirror system for uniform beam transformation in high-power annular lasers,” Appl. Opt. 17, 2917–2923 (1978).
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O. Guyon, “Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging,” Astron. Astrophys. 404, 379–387 (2003).
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Astrophys. J. (1)

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Atmos. Opt. (1)

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J. Opt. Soc. Am. (1)

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J. Opt. Soc. Am. A (7)

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15(10), 2759–2768 (1998).
[Crossref]

J. D. Barchers and D. L. Fried, “Optimal control of laser beams for propagation through a turbulent medium,” J. Opt. Soc. Am. A 19, 1779–1793 (2002).
[Crossref]

M. A. Vorontsov and V. Kolosov, “Target-in-the-loop beam control: basic considerations for analysis and wavefront sensing,” J. Opt. Soc. Am. A 22(1), 126–141 (2005).
[Crossref]

M. C. Roggemann and A. C. Koivunen, “Wavefront sensing and deformable mirror control in strong scintillation,” J. Opt. Soc. Am. A 17, 911–919 (2000).
[Crossref]

J. D. Barchers, “Evaluation of the impact of finite-resolution effects on scintillation compensation using two deformable mirrors,” J. Opt. Soc. Am. A 18, 3098–3109 (2001).
[Crossref]

J. D. Barchers, “Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations,” J. Opt. Soc. Am. A 19, 926–945 (2002).
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Mon. Not. R. Astron. Soc. (1)

Opt. Express (3)

Y. Feng, L. R. Taylor, and D. B. Calia, “25 W Raman-fiber-amplifier-based 589 nm laser for laser guide star,” Opt. Express 17(21), 19021–19026 (2009).
[Crossref]

T. M. Venema and J. D. Schmidt, “Optical phase unwrapping in the presence of branch points,” Opt. Express 16, 6985–6998 (2008).
[Crossref] [PubMed]

Opt. Lett. (3)

R. A. Gonsalves, “Compensation of scintillation with a phase-only adaptive optic,” Opt. Lett. 22, 588–590 (1997).
[Crossref] [PubMed]

J. R. Fienup, “Reconstruction of an object from the modulus of its fourier transform,” Opt. Lett. 3, 27–29 (1978).
[Crossref] [PubMed]

Optics & Laser Technology (1)

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Optics & Laser Technology 14, 159–160 (1982).
[Crossref]

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. SPIE (10)

C. C. Beckner and D. W. Oesch, “Implementation of a projection-on-constraints algorithm for beam intensity redistribution,” Proc. SPIE 6711, 67110L (2007)

R. Holzlöhner, D. Bonaccini Calia, and W. Hackenberg, “Physical optics modeling and optimization of laser guide star propagation,” Proc. SPIE 7015, 701521 (2008).
[Crossref]

A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[Crossref]

D. R. Neal, W. J. Alford, J. K. Gruetzner, and M. E. Warren, “Amplitude and phase beam characterization using a two-dimensional wavefront sensor,” Proc. SPIE 2870, 72–82 (1996).
[Crossref]

M. C. Roggemann and S. Deng, “Scintillation compensation for laser beam projection using segmented deformable mirrors,” Proc. SPIE 3763, 29–40 (1999).
[Crossref]

Other (10)

F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
[Crossref]

G. Rousset, “Wave-front Sensors,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University, 1999), pp. 91–130.
[Crossref]

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with examples in MATLAB (SPIE Press, 2010).

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Fig. 1 Average irradiance map over 20 frames obtained from a 37 × 37 Shack-Hartmann sensor located at the output of the laser, during a run in April 2013 (top) and a run in October 2013 (bottom). Left: Irradiance map, with orthogonal lines of cuts through the maximum. Right: Cuts along x (dashed) and y-axis (solid) of the irradiance map above. The dotted horizontal line marks the half of the maximum.

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Fig. 2 Schematics of 2-DM correcting systems. (a): Mono-static system with DM2 in the far-field of DM1 [20]. The FTM box represents a Fourier transforming mirror. (b): 2-DM correcting system in the near-field proposed in this paper. DM1 is located in the near field of DM2, at a distance z. The configuration is named bistatic for having different receiving and projecting apertures.

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Fig. 3 Amplitudes of the output field at DM2, without correction ((a) and (b)) and with correction ((c) and (d)). Graphics (a) and (c) represent the 2D amplitude over the 1 cm aperture of DM2. Corresponding central cuts along x and y axis are presented as solid curves on the associated graphics on the right, (b) without correction and (d) with correction. The dotted curve in (b) stands for the Gaussian desired output amplitude. In (b) and (d), the vertical dashed lines stand for the diameter of DM2.

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Fig. 4 Estimated phase of the output field after DM2 with correction. Graphics (a) represents the 2D phase as estimated over the 1 cm aperture of DM2. The central cuts along x and y axis are shown with solid curves in (b). The dotted curve in (b) stands for the cuts of the desired output phase (defocus), which coincides with the achieved output in areas of non-negligible amplitude (see (d) in Fig. 3). The vertical dashed lines in (b) delimit diameter of DM2.

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Fig. 5 Convergence of the criteria

ε_{ampl}^{2}

(solid) and S (dashed) defined in Eqs. (16) and (17). The iteration counter in abscissae is presented in logarithmic scale from 1 to 400.

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Fig. 6 Phase corrections ϕ₁ (left) and ϕ₂ (right) to be applied to DM1 and DM2 respectively, after 400 iterations.

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Fig. 7 Central cut along y for the final wrapped (dotted curve) and unwrapped (solid curve) ϕ₁ estimate shown in Fig. 6. The horizontal dots represent the ] − π;π] interval of the wrapped phase estimation. The vertical dashed lines stand for the diameter of DM2.

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Fig. 8 Impact of the separation distance between the DMs on the M² factor of the output laser beam after 400 iterations. Solid line:

M_{x}^{2}

. Dashed line :

M_{y}^{2}

M_{x}^{2}

and

M_{y}^{2}

of the input laser beam are represented by the horizontal dotted lines (

M_{x}^{2}

: top;

M_{y}^{2}

: bottom).

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Fig. 9 Left: Evolution of

ε_{ampl}^{2}

along with the iterations, for various DMs separations z = 1, 1.5, 2, 3, 4 and 5 meters. The slowest convergence is for z = 1 m. Right: Central cut along y of the final ϕ₁ deformation to be applied for the same DMs separations z = 1, 1.5, 2, 3, 4 and 5 meters. The largest phase amplitude is required for z = 1 m and the smallest for z = 5 m.

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Fig. 10

ε_{ampl}^{2}

after 400 iterations as a function of the separation z between DMs, and for different number of samples n across the pupil diameter. Amplitude distortions of input are taken from available measurements on GeMS laser in April 2013 (left) and October 2013 (right). No phase distortions are assumed at input.

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Fig. 11 Same as in Fig. 10 but the error is presented as an absolute value, not relatively to

ε_{ampl}^{2} (0)

. The dashed lines represent

ε_{ampl}^{2} (0)

as a function of z.

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Fig. 12 Equivalent increase of photons corresponding to the laser spot size reduction when launching (i) a Gaussian beam, (ii) the beam corrected with 17 × 17 devices separated by 80 cm and (iii) the beam corrected with 11 × 11 devices separated by 1.4 m. The reference laser spot size is the one produced by the laser aberrations measured at GeMS: Left: aberrations of April 2013. Right: aberrations of October 2013.

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Equations (17)

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

σ_{meas} \propto \frac{θ_{image}}{\sqrt{N_{ph}}},

M_{x}^{2} = \frac{π D_{x} θ_{x}}{4^{3} λ}

U_{l} (x) = u_{l} (x) exp (j ϕ_{l} (x)),

U_{1} (x) = U_{l} (x) m_{1} (x) exp (j ϕ_{1} (x)),

U_{z} (x^{'}) = T_{z} [U_{1} (x)] = ℱ^{- 1} [ℱ (U_{1}) exp (- j π λ z {| f_{x} |}^{2}) exp (j 2 π z / λ)],

U_{2} (x^{'}) = U_{z} (x^{'}) m_{2} (x^{'}) exp (j ϕ_{2} (x^{'})),

U_{t} (x^{'}) = u_{t} (x^{'}) exp (j ϕ_{t} (x^{'})),

U_{z} (x^{'}) = T_{z} {u_{l} (x) m_{1} (x) exp [j (ϕ_{l} (x) + ϕ_{1} (x))]} .

ϕ_{2} (x^{'}) = - arg [U_{t}^{*} (x^{'}) U_{z} (x^{'}) m_{2} (x^{'})] .

α = \frac{E_{2}}{E_{t}} = \frac{\iint {| U_{z} (x^{'}) m_{2} (x^{'}) |}^{2} d x^{'}}{\iint {| U_{t} (x^{'}) m_{2} (x^{'}) |}^{2} d x^{'}} .

U_{z} (x^{'}) = \sqrt{α} U_{t} (x^{'}) m_{2} (x^{'}) exp (- j ϕ_{2} (x^{'})),

U_{1} (x) = T_{- z} [U_{z} (x^{'})] = T_{z}^{*} [U_{z}^{*} (x^{'})] .

ϕ_{1} (x) = arg [U_{l}^{*} (x) m_{1} (x) U_{1} (x)] .

(G^{T} W_{g} G + μ C^{T} C) \hat{ϕ} = G^{T} W_{g} 𝒫 𝒱 [G ϕ],

W_{g x} (i, j) = log (u (x_{i + 1}, y_{j}) u (x_{i}, y_{j}) + ε) - log (ε)

ε_{ampl}^{2} (i) = \frac{\iint {[| U_{t} (x^{'}) | - | U_{2}^{(i)} (x^{'}) |]}^{2} d x^{'}}{\iint {[| U_{t} (x^{'}) | - | U_{2}^{(0)} (x^{'}) |]}^{2} d x^{'}}

S (i) = \frac{{| \iint U_{t}^{*} (x^{'}) U_{2}^{(i)} (x^{'}) d x^{'} |}^{2}}{| \iint U_{t} (x^{'}) U_{t}^{*} (x^{'}) d x^{'} | | \iint U_{2}^{(i)} (x^{'}) U_{2}^{(i) *} (x^{'}) d x^{'} |},

Abstract

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