Abstract

The annular laser beam (ALB) has been widely used in many fields for its unique intensity distribution. Especially, in the materials processing, the power and the beam quality of the large-aperture thin-wall ALB are of vital. However, limited by the aperture, the actuators’ spacing or the damage threshold, the existing deformable mirrors (DMs) are not suitable for the correction of the ALB. Considering the stretching effect of the oblique incidence, in this paper, by using the tubular DM (TDM), a novel adaptive optics (AO) configuration is promoted to increase the number of the effective actuators covered by the input ALB. The coordinate transformation equations and correction principle of the novel AO configuration are derived based on the ray tracing. A typical TDM prototype is designed based on the coordinate transformation equations. The influence function characteristics of the TDM is analyzed using the finite element method, and the correction ability of the novel AO configuration based on the TDM is verified. Simulation results show that the TDM could perfectly compensate the wavefront distortions described by the 2th to 15th order Zernike annular aberrations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

L. Sun, Y. Guo, C. Shao, Y. Li, Y. Zheng, C. Sun, X. Wang, and L. Huang, “10.8 kW, 2.6 times diffraction limited laser based on a continuous wave Nd:YAG oscillator and an extra-cavity adaptive optics system,” Opt. Lett. 43(17), 4160–4163 (2018).
[Crossref] [PubMed]

2015 (2)

A. R. Bayanna, R. E. Louis, S. Chatterjee, S. K. Mathew, and P. Venkatakrisnan, “Membrane-based deformable mirror: intrinsic aberrations and alignment issues,” Appl. Opt. 54(7), 1727–1736 (2015).
[Crossref]

L. Burger, I. Litvin, S. Ngcobo, and A. Forbes, “Implementation of a spatial light modulator for intracavity beam shaping,” J. Opt. 17(1), 015604 (2015).
[Crossref]

2014 (1)

K. Yao, J. Wang, X. Liu, and W. Liu, “Closed-loop adaptive optics system with a single liquid crystal spatial light modulator,” Opt. Express 22(14), 17216–17226 (2014).
[Crossref] [PubMed]

2013 (1)

X. Ma, L. Huang, M. Gong, Q. Xue, Z. Feng, P. Yan, and Q. Liu, “Orientation dependent wavefront correction system under grazing incidence,” Opt. Express 21(18), 20497–20505 (2013).
[Crossref] [PubMed]

2012 (3)

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).
[Crossref]

M. A. Helmbrecht, M. He, and C. J. Kempf, “Development of high-order segmented MEMS deformable mirrors,” Proc. SPIE 825, 82530 (2012).

2010 (3)

D. Guzmán, F. J. D. C. Juez, R. Myers, A. Guesalaga, and F. S. Lasheras, “Modeling a MEMS deformable mirror using non-parametric estimation techniques,” Opt. Express 18(20), 21356–21369 (2010).
[Crossref] [PubMed]

S. Verpoort and U. Wittrock, “Actuator patterns for unimorph and bimorph deformable mirrors,” Appl. Opt. 49(31), G37–G46 (2010).
[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]

2009 (2)

B. Fernández and J. Kubby, “Initial Performance Results for High-Aspect Ratio Gold MEMS Deformable Mirrors,” Proc. SPIE 7209, 72090O (2009).

S. A. Cornelissen, P. A. Bierden, T. G. Bifano, and C. V. Lam, “4096-element continuous face-sheet MEMS deformable mirror for high-contrast imaging,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031308 (2009).
[Crossref]

2008 (1)

G. J. Xu, A. Tsuboi, T. Ogawa, T. Ikeda, and M. Kutsuna, “Super-short times laser welding of thermoplastic resins using a ring beam optics,” J. Laser Appl. 20(2), 116–121 (2008).
[Crossref]

2007 (2)

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

G. M. Dai and V. N. Mahajan, “Zernike annular polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 24(1), 139–155 (2007).
[Crossref] [PubMed]

2006 (3)

B. P. Wallace, P. J. Hampton, C. H. Bradley, and R. Conan, “Evaluation of a MEMS deformable mirror for an adaptive optics test bench,” Opt. Express 14(22), 10132–10138 (2006).
[Crossref] [PubMed]

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264(1), 25–34 (2006).
[Crossref]

W. P. Latham, “Shaping of annular laser intensity profiles and their thermal effects for optical trepanning,” Opt. Eng. 45(1), 014301 (2006).
[Crossref]

2004 (2)

B. Wattellier, J. Fuchs, J. P. Zou, K. Abdeli, H. Pépin, and C. Haefner, “Repetition rate increase and diffraction-limited focal spots for a nonthermal-equilibrium 100-TW Nd:glass laser chain by use of adaptive optics,” Opt. Lett. 29(21), 2494–2496 (2004).
[Crossref] [PubMed]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12(26), 6403–6409 (2004).
[Crossref] [PubMed]

2000 (1)

N. V. Kamanina, N. A. Vasilenko, S. O. Kognovitsky, and N. M. Kozhevnikov, “LC SLM with Fullerene- Dye- Polyimide Photosensitive Layer,” Proc. SPIE 3951, 174–178 (2000).
[Crossref]

1999 (4)

J. L. Chaloupka and D. D. Meyerhofer, “Observation of Electron Trapping in an Intense Laser Beam,” Phys. Rev. Lett. 83(22), 4538–4541 (1999).
[Crossref]

K. T. Gahagan and G. A. Swartzlander, “Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap,” J. Opt. Soc. Am. B 16(4), 533–537 (1999).
[Crossref]

A. Lapucci and M. Ciofini, “Extraction of high-quality beams from narrow annular laser sources,” Appl. Opt. 38(21), 4552–4557 (1999).
[Crossref] [PubMed]

L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
[Crossref] [PubMed]

1994 (1)

W. Swantner and W. W. Chow, “Gram-Schmidt orthonormalization of Zernike polynomials for general aperture shapes,” Appl. Opt. 33(10), 1832–1837 (1994).
[Crossref] [PubMed]

1992 (1)

M. A. Ealey and J. A. Wellman, “Deformable Mirrors: Design Fundamentals, Key Performance Specifications, and Parametric Trades,” Proc. SPIE 1543, 36–52 (1992).
[Crossref]

1991 (1)

U. Wittrock, H. Weber, and B. Eppich, “Inside-pumped Nd:YAG tube laser,” Opt. Lett. 16(14), 1092–1094 (1991).
[Crossref] [PubMed]

1989 (1)

L. J. Hornbeck, “Deformable mirror spatial light modulators,” Proc. SPIE 1150, 1150 (1989).

Abdeli, K.

B. Wattellier, J. Fuchs, J. P. Zou, K. Abdeli, H. Pépin, and C. Haefner, “Repetition rate increase and diffraction-limited focal spots for a nonthermal-equilibrium 100-TW Nd:glass laser chain by use of adaptive optics,” Opt. Lett. 29(21), 2494–2496 (2004).
[Crossref] [PubMed]

Altay, S.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264(1), 25–34 (2006).
[Crossref]

Ao, M. W.

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Bartsch, D. U.

L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
[Crossref] [PubMed]

Bayanna, A. R.

A. R. Bayanna, R. E. Louis, S. Chatterjee, S. K. Mathew, and P. Venkatakrisnan, “Membrane-based deformable mirror: intrinsic aberrations and alignment issues,” Appl. Opt. 54(7), 1727–1736 (2015).
[Crossref]

Baykal, Y.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264(1), 25–34 (2006).
[Crossref]

Bierden, P.

A. Diouf, M. Gingras, J. B. Stewart, T. G. Bifano, S. Cornelissen, and P. Bierden, “Fabrication of single crystalline MEMS DM using anodic wafer bonding,” Proc. SPIE, 68880U (2008).

Bierden, P. A.

S. A. Cornelissen, P. A. Bierden, T. G. Bifano, and C. V. Lam, “4096-element continuous face-sheet MEMS deformable mirror for high-contrast imaging,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031308 (2009).
[Crossref]

Bifano, T. G.

S. A. Cornelissen, P. A. Bierden, T. G. Bifano, and C. V. Lam, “4096-element continuous face-sheet MEMS deformable mirror for high-contrast imaging,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031308 (2009).
[Crossref]

A. Diouf, M. Gingras, J. B. Stewart, T. G. Bifano, S. Cornelissen, and P. Bierden, “Fabrication of single crystalline MEMS DM using anodic wafer bonding,” Proc. SPIE, 68880U (2008).

Bradley, C. H.

B. P. Wallace, P. J. Hampton, C. H. Bradley, and R. Conan, “Evaluation of a MEMS deformable mirror for an adaptive optics test bench,” Opt. Express 14(22), 10132–10138 (2006).
[Crossref] [PubMed]

Burger, L.

L. Burger, I. Litvin, S. Ngcobo, and A. Forbes, “Implementation of a spatial light modulator for intracavity beam shaping,” J. Opt. 17(1), 015604 (2015).
[Crossref]

Cao, Z.

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12(26), 6403–6409 (2004).
[Crossref] [PubMed]

Chaloupka, J. L.

J. L. Chaloupka and D. D. Meyerhofer, “Observation of Electron Trapping in an Intense Laser Beam,” Phys. Rev. Lett. 83(22), 4538–4541 (1999).
[Crossref]

Chatterjee, S.

A. R. Bayanna, R. E. Louis, S. Chatterjee, S. K. Mathew, and P. Venkatakrisnan, “Membrane-based deformable mirror: intrinsic aberrations and alignment issues,” Appl. Opt. 54(7), 1727–1736 (2015).
[Crossref]

Chow, W. W.

W. Swantner and W. W. Chow, “Gram-Schmidt orthonormalization of Zernike polynomials for general aperture shapes,” Appl. Opt. 33(10), 1832–1837 (1994).
[Crossref] [PubMed]

Ciofini, M.

A. Lapucci and M. Ciofini, “Extraction of high-quality beams from narrow annular laser sources,” Appl. Opt. 38(21), 4552–4557 (1999).
[Crossref] [PubMed]

Conan, R.

B. P. Wallace, P. J. Hampton, C. H. Bradley, and R. Conan, “Evaluation of a MEMS deformable mirror for an adaptive optics test bench,” Opt. Express 14(22), 10132–10138 (2006).
[Crossref] [PubMed]

Cornelissen, S.

A. Diouf, M. Gingras, J. B. Stewart, T. G. Bifano, S. Cornelissen, and P. Bierden, “Fabrication of single crystalline MEMS DM using anodic wafer bonding,” Proc. SPIE, 68880U (2008).

Cornelissen, S. A.

S. A. Cornelissen, P. A. Bierden, T. G. Bifano, and C. V. Lam, “4096-element continuous face-sheet MEMS deformable mirror for high-contrast imaging,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031308 (2009).
[Crossref]

Dai, G. M.

G. M. Dai and V. N. Mahajan, “Zernike annular polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 24(1), 139–155 (2007).
[Crossref] [PubMed]

Diouf, A.

A. Diouf, M. Gingras, J. B. Stewart, T. G. Bifano, S. Cornelissen, and P. Bierden, “Fabrication of single crystalline MEMS DM using anodic wafer bonding,” Proc. SPIE, 68880U (2008).

Dong, L.

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]

Duocastella, M.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012).
[Crossref]

Ealey, M.

M. Ealey, “High Density Deformable Mirrors to Enable Coronagraphic Planet Detection,” Proc. SPIE, 5166 (2004).

Ealey, M. A.

M. A. Ealey and J. A. Wellman, “Deformable Mirrors: Design Fundamentals, Key Performance Specifications, and Parametric Trades,” Proc. SPIE 1543, 36–52 (1992).
[Crossref]

Eppich, B.

U. Wittrock, H. Weber, and B. Eppich, “Inside-pumped Nd:YAG tube laser,” Opt. Lett. 16(14), 1092–1094 (1991).
[Crossref] [PubMed]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, S. Altay, and Y. Baykal, “Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence,” Opt. Commun. 264(1), 25–34 (2006).
[Crossref]

Fainman, Y.

L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
[Crossref] [PubMed]

Feng, Z.

X. Ma, L. Huang, M. Gong, Q. Xue, Z. Feng, P. Yan, and Q. Liu, “Orientation dependent wavefront correction system under grazing incidence,” Opt. Express 21(18), 20497–20505 (2013).
[Crossref] [PubMed]

Fernández, B.

B. Fernández and J. Kubby, “Initial Performance Results for High-Aspect Ratio Gold MEMS Deformable Mirrors,” Proc. SPIE 7209, 72090O (2009).

Forbes, A.

L. Burger, I. Litvin, S. Ngcobo, and A. Forbes, “Implementation of a spatial light modulator for intracavity beam shaping,” J. Opt. 17(1), 015604 (2015).
[Crossref]

Freeman, W. R.

L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
[Crossref] [PubMed]

Fuchs, J.

B. Wattellier, J. Fuchs, J. P. Zou, K. Abdeli, H. Pépin, and C. Haefner, “Repetition rate increase and diffraction-limited focal spots for a nonthermal-equilibrium 100-TW Nd:glass laser chain by use of adaptive optics,” Opt. Lett. 29(21), 2494–2496 (2004).
[Crossref] [PubMed]

Gahagan, K. T.

K. T. Gahagan and G. A. Swartzlander, “Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap,” J. Opt. Soc. Am. B 16(4), 533–537 (1999).
[Crossref]

Gingras, M.

A. Diouf, M. Gingras, J. B. Stewart, T. G. Bifano, S. Cornelissen, and P. Bierden, “Fabrication of single crystalline MEMS DM using anodic wafer bonding,” Proc. SPIE, 68880U (2008).

Gong, M.

X. Ma, L. Huang, M. Gong, Q. Xue, Z. Feng, P. Yan, and Q. Liu, “Orientation dependent wavefront correction system under grazing incidence,” Opt. Express 21(18), 20497–20505 (2013).
[Crossref] [PubMed]

Guesalaga, A.

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L. Sun, Y. Guo, C. Shao, Y. Li, Y. Zheng, C. Sun, X. Wang, and L. Huang, “10.8 kW, 2.6 times diffraction limited laser based on a continuous wave Nd:YAG oscillator and an extra-cavity adaptive optics system,” Opt. Lett. 43(17), 4160–4163 (2018).
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M. A. Helmbrecht, M. He, and C. J. Kempf, “Development of high-order segmented MEMS deformable mirrors,” Proc. SPIE 825, 82530 (2012).

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N. V. Kamanina, N. A. Vasilenko, S. O. Kognovitsky, and N. M. Kozhevnikov, “LC SLM with Fullerene- Dye- Polyimide Photosensitive Layer,” Proc. SPIE 3951, 174–178 (2000).
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D. Guzmán, F. J. D. C. Juez, R. Myers, A. Guesalaga, and F. S. Lasheras, “Modeling a MEMS deformable mirror using non-parametric estimation techniques,” Opt. Express 18(20), 21356–21369 (2010).
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L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12(26), 6403–6409 (2004).
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M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
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L. Sun, Y. Guo, C. Shao, Y. Li, Y. Zheng, C. Sun, X. Wang, and L. Huang, “10.8 kW, 2.6 times diffraction limited laser based on a continuous wave Nd:YAG oscillator and an extra-cavity adaptive optics system,” Opt. Lett. 43(17), 4160–4163 (2018).
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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).
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X. Ma, L. Huang, M. Gong, Q. Xue, Z. Feng, P. Yan, and Q. Liu, “Orientation dependent wavefront correction system under grazing incidence,” Opt. Express 21(18), 20497–20505 (2013).
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K. Yao, J. Wang, X. Liu, and W. Liu, “Closed-loop adaptive optics system with a single liquid crystal spatial light modulator,” Opt. Express 22(14), 17216–17226 (2014).
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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).
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K. Yao, J. Wang, X. Liu, and W. Liu, “Closed-loop adaptive optics system with a single liquid crystal spatial light modulator,” Opt. Express 22(14), 17216–17226 (2014).
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L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12(26), 6403–6409 (2004).
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D. Guzmán, F. J. D. C. Juez, R. Myers, A. Guesalaga, and F. S. Lasheras, “Modeling a MEMS deformable mirror using non-parametric estimation techniques,” Opt. Express 18(20), 21356–21369 (2010).
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L. Burger, I. Litvin, S. Ngcobo, and A. Forbes, “Implementation of a spatial light modulator for intracavity beam shaping,” J. Opt. 17(1), 015604 (2015).
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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).
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G. J. Xu, A. Tsuboi, T. Ogawa, T. Ikeda, and M. Kutsuna, “Super-short times laser welding of thermoplastic resins using a ring beam optics,” J. Laser Appl. 20(2), 116–121 (2008).
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B. Wattellier, J. Fuchs, J. P. Zou, K. Abdeli, H. Pépin, and C. Haefner, “Repetition rate increase and diffraction-limited focal spots for a nonthermal-equilibrium 100-TW Nd:glass laser chain by use of adaptive optics,” Opt. Lett. 29(21), 2494–2496 (2004).
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M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
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J. S. Lu and G. D. J. Su, “Optical zoom lens module using MEMS deformable mirrors for portable device,” Proc. SPIE848, 84880D (2012).

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L. Sun, Y. Guo, C. Shao, Y. Li, Y. Zheng, C. Sun, X. Wang, and L. Huang, “10.8 kW, 2.6 times diffraction limited laser based on a continuous wave Nd:YAG oscillator and an extra-cavity adaptive optics system,” Opt. Lett. 43(17), 4160–4163 (2018).
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L. Sun, Y. Guo, C. Shao, Y. Li, Y. Zheng, C. Sun, X. Wang, and L. Huang, “10.8 kW, 2.6 times diffraction limited laser based on a continuous wave Nd:YAG oscillator and an extra-cavity adaptive optics system,” Opt. Lett. 43(17), 4160–4163 (2018).
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L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
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G. J. Xu, A. Tsuboi, T. Ogawa, T. Ikeda, and M. Kutsuna, “Super-short times laser welding of thermoplastic resins using a ring beam optics,” J. Laser Appl. 20(2), 116–121 (2008).
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N. V. Kamanina, N. A. Vasilenko, S. O. Kognovitsky, and N. M. Kozhevnikov, “LC SLM with Fullerene- Dye- Polyimide Photosensitive Layer,” Proc. SPIE 3951, 174–178 (2000).
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G. Vdovin, M. Loktev, and A. Simonov, “Low-cost deformable mirrors: technologies and goals,” Proc. SPIE58940B (2005).

A. Tokovinin, S. Thomas, and G. Vdovin, “Using 50-mm electrostatic membrane deformable mirror in astronomical adaptive optics,” Proc. SPIE, 580 (2004).

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A. R. Bayanna, R. E. Louis, S. Chatterjee, S. K. Mathew, and P. Venkatakrisnan, “Membrane-based deformable mirror: intrinsic aberrations and alignment issues,” Appl. Opt. 54(7), 1727–1736 (2015).
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S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).
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S. Verpoort and U. Wittrock, “Actuator patterns for unimorph and bimorph deformable mirrors,” Appl. Opt. 49(31), G37–G46 (2010).
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B. P. Wallace, P. J. Hampton, C. H. Bradley, and R. Conan, “Evaluation of a MEMS deformable mirror for an adaptive optics test bench,” Opt. Express 14(22), 10132–10138 (2006).
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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).
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L. Sun, Y. Guo, C. Shao, Y. Li, Y. Zheng, C. Sun, X. Wang, and L. Huang, “10.8 kW, 2.6 times diffraction limited laser based on a continuous wave Nd:YAG oscillator and an extra-cavity adaptive optics system,” Opt. Lett. 43(17), 4160–4163 (2018).
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S. Verpoort and U. Wittrock, “Actuator patterns for unimorph and bimorph deformable mirrors,” Appl. Opt. 49(31), G37–G46 (2010).
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[Crossref] [PubMed]

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G. J. Xu, A. Tsuboi, T. Ogawa, T. Ikeda, and M. Kutsuna, “Super-short times laser welding of thermoplastic resins using a ring beam optics,” J. Laser Appl. 20(2), 116–121 (2008).
[Crossref]

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L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12(26), 6403–6409 (2004).
[Crossref] [PubMed]

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X. Ma, L. Huang, M. Gong, Q. Xue, Z. Feng, P. Yan, and Q. Liu, “Orientation dependent wavefront correction system under grazing incidence,” Opt. Express 21(18), 20497–20505 (2013).
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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]

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X. Ma, L. Huang, M. Gong, Q. Xue, Z. Feng, P. Yan, and Q. Liu, “Orientation dependent wavefront correction system under grazing incidence,” Opt. Express 21(18), 20497–20505 (2013).
[Crossref] [PubMed]

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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]

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Yang, Z. P.

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Yao, K.

K. Yao, J. Wang, X. Liu, and W. Liu, “Closed-loop adaptive optics system with a single liquid crystal spatial light modulator,” Opt. Express 22(14), 17216–17226 (2014).
[Crossref] [PubMed]

Zheng, Y.

L. Sun, Y. Guo, C. Shao, Y. Li, Y. Zheng, C. Sun, X. Wang, and L. Huang, “10.8 kW, 2.6 times diffraction limited laser based on a continuous wave Nd:YAG oscillator and an extra-cavity adaptive optics system,” Opt. Lett. 43(17), 4160–4163 (2018).
[Crossref] [PubMed]

Zhu, L.

L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
[Crossref] [PubMed]

Zou, J. P.

B. Wattellier, J. Fuchs, J. P. Zou, K. Abdeli, H. Pépin, and C. Haefner, “Repetition rate increase and diffraction-limited focal spots for a nonthermal-equilibrium 100-TW Nd:glass laser chain by use of adaptive optics,” Opt. Lett. 29(21), 2494–2496 (2004).
[Crossref] [PubMed]

Appl. Opt. (5)

A. Lapucci and M. Ciofini, “Extraction of high-quality beams from narrow annular laser sources,” Appl. Opt. 38(21), 4552–4557 (1999).
[Crossref] [PubMed]

A. R. Bayanna, R. E. Louis, S. Chatterjee, S. K. Mathew, and P. Venkatakrisnan, “Membrane-based deformable mirror: intrinsic aberrations and alignment issues,” Appl. Opt. 54(7), 1727–1736 (2015).
[Crossref]

L. Zhu, P. C. Sun, D. U. Bartsch, W. R. Freeman, and Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38(1), 168–176 (1999).
[Crossref] [PubMed]

S. Verpoort and U. Wittrock, “Actuator patterns for unimorph and bimorph deformable mirrors,” Appl. Opt. 49(31), G37–G46 (2010).
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Figures (12)

Fig. 1
Fig. 1 (a) Cross section of the ALB; (b) Very limited effective actuators are covered by the ALB.
Fig. 2
Fig. 2 (a) Diagram of the novel AO unit based on the TDM. (b) Cross section of the beam transformation and control system (TCS).
Fig. 3
Fig. 3 The XOY-section diagram (a) and the ρOZ-section diagram (b) of the ALB wavefront transformation from plane to inner cylindrical surface. (c) is the ray propagation process in the prism P1.
Fig. 4
Fig. 4 Simplified structure of the TDM. (a) is the 3D views; (b) and (d) are the circumferential and radial cross sections, respectively; (c) shows the partial enlarged drawing of the (b)/(d). (e) is the distribution of the actuators (in white) on the TDM.
Fig. 5
Fig. 5 (a) is unfolded view of the inner cylindrical surface of the TDM (in blue) and the inner cylindrical wavefront (in pink); (d) is the equivalent effective actuators on the ALB. (b) and (c) are the partial enlarged views of the red dash areas marked in (a) and (d), respectively.
Fig. 6
Fig. 6 (a)-(f) are the IF-ICS corresponding to the No.1-6 actuators in Fig. 5(e); (g) is the circumferential section of the IFs-ICS shown in (a)-(f); (h) and (i) are the partial enlarged views along the generatrix direction of (a) and (c), respectively.
Fig. 7
Fig. 7 (a)-(f) are the IFs-AW corresponding to the No.1-6 actuators in Fig. 6(c). The 2nd and 4th columns depict the partial enlarged views of the 1st and 3rd columns.
Fig. 8
Fig. 8 Zernike annular aberrations from Z2 to Z15
Fig. 9
Fig. 9 The compensation residues of the first-type Zernike annular aberrations.
Fig. 10
Fig. 10 The compensation residues of the second-type Zernike annular aberrations.
Fig. 11
Fig. 11 (a) is PV values of the correction residues. (b) and (c) are the normalized correction residues of the first type and the second type Zernike aberrations, respectively.
Fig. 12
Fig. 12 The influence of the angle β on (a) the angle α, (b) the radial magnification Γ r and (c) the circumferential magnification Γ c at r m = 23mm and d = 157mm.

Tables (3)

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Table 1 The parameters of the designed TDM prototype

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Table 2 Material parameters in the finite element simulation

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Table 3 The moderating effects of the α and the distance d

Equations (16)

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R D = r m +(d r m cotβ)tanα
α= θ 1 θ 2 =arcsin[ n 1 sin( π 2 β)]( π 2 β)
z A ' = r A /tanβ
d A =( R D r A )/tanα
z o = d A + z A ' = R D tanβ r A (tanβtanα) tanαtanβ
{ x A = r A cosγ, y A = r A sinγ x o = R D cosγ, y o = R D sinγ
{ x o = R D x A / x A 2 + y A 2 y o = R D y A / x A 2 + y A 2 z o = R D tanβ x A 2 + y A 2 (tanβtanα) tanαtanβ
{ r D = ( R D tanβ z o ' tanβtanα)/ (tanβtanα) x D = x o ' r D / R D y D = y o ' r D / R D
{ Γ c = C TDM / C ALB Γ r =L/Δr
{ Γ c =1+(d/ r m cotβ)tanα Γ r =cotαcotβ
L= Γ r Δr
{ r Di = R D tanβ(d+H/2 )tanαtanβ tanβtanα r Do = R D tanβ(dH/2 )tanαtanβ tanβtanα
h r =h/ Γ r
{ h ck = γ o r ck r ck = r i +(6k) h r
Δ ω ' =Δωcos(π/2 α)=Δωsin(α)
{ N r =1+L/h=1+ Γ r Δr/h1+Δrcotα/h N c =2π R D /h=2π Γ c r m /h2π( r m +dtanα)/h

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