Abstract

We investigate the changes in the shape of a deformable mirror used at the National Ignition Facility caused by differences in temperature between the working environment and the mounting temperature of the mirror. In general, the temperature-induced profile change of the mirror is dominated by a few low-order aberrations, which mainly result in defocus. However, after these low-order distortions are corrected, there remain special, higher-order, surface distortions caused by the particular arrangement, construction, and mounting of the mirror actuators. This work analyzes these special aberrations, and their dependence on the particular actuator design, using the finite element method. Experiments are carried out to verify the computational results, and finally, design considerations to help minimize the temperature-induced high-order aberrations are suggested.

© 2013 Optical Society of America

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  1. R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).
  2. R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).
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    [CrossRef]
  12. N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
    [CrossRef]
  13. S. Olivier, V. Laude, and J.-P. Huignard, “Liquid-crystal Hartmann wave-front scanner,” Appl. Opt. 39, 3838–3846(2000).
    [CrossRef]
  14. S. E. Winters, J. H. Chung, and S. A. Velinsky, “Modeling and control of a deformable mirror,” J. Dyn. Syst. Meas. Control 124, 297–302 (2002).
    [CrossRef]

2012

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screen printed actuator,” Proc. SPIE 8253, 82530D (2012).
[CrossRef]

2011

2009

N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
[CrossRef]

2008

2006

2002

S. E. Winters, J. H. Chung, and S. A. Velinsky, “Modeling and control of a deformable mirror,” J. Dyn. Syst. Meas. Control 124, 297–302 (2002).
[CrossRef]

2001

2000

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

S. Olivier, V. Laude, and J.-P. Huignard, “Liquid-crystal Hartmann wave-front scanner,” Appl. Opt. 39, 3838–3846(2000).
[CrossRef]

1999

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

1970

1967

Appelfelder, M.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screen printed actuator,” Proc. SPIE 8253, 82530D (2012).
[CrossRef]

Astrath, N. G. C.

Baesso, M. L.

Beckert, E.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screen printed actuator,” Proc. SPIE 8253, 82530D (2012).
[CrossRef]

Belancon, M. P.

Bliss, E.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Boley, B. A.

Bruchmann, C.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screen printed actuator,” Proc. SPIE 8253, 82530D (2012).
[CrossRef]

Chang-Hui, R.

N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
[CrossRef]

Cheng, Z.

Chung, J. H.

S. E. Winters, J. H. Chung, and S. A. Velinsky, “Modeling and control of a deformable mirror,” J. Dyn. Syst. Meas. Control 124, 297–302 (2002).
[CrossRef]

Cremonese, G.

Da Deppo, V.

Debei, S.

Eberhardt, R.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screen printed actuator,” Proc. SPIE 8253, 82530D (2012).
[CrossRef]

Feldman, M.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Fixler, J.

Flamini, E.

Grey, A.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Hao, Y.

N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
[CrossRef]

Henesian, M.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Hong, Z.

N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
[CrossRef]

Huignard, J.-P.

Jacinto, C.

Koch, J.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Laude, V.

Lawson, J.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Lee, J. H.

Malacarne, L. C.

Malvick, A. J.

McHugh, S. L.

Mendes, R. S.

Morse, K. A.

Naletto, G.

Olivier, S.

Peng, Y.

Qiu, J.

Sacks, R.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Salmon, T.

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Segato, E.

Spitzer, L.

Stolz, C.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

Toeppen, J.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Tünnermann, A.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screen printed actuator,” Proc. SPIE 8253, 82530D (2012).
[CrossRef]

Van Atta, L.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Velinsky, S. A.

S. E. Winters, J. H. Chung, and S. A. Velinsky, “Modeling and control of a deformable mirror,” J. Dyn. Syst. Meas. Control 124, 297–302 (2002).
[CrossRef]

Wen-Han, J.

N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
[CrossRef]

Winters, S.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Winters, S. E.

S. E. Winters, J. H. Chung, and S. A. Velinsky, “Modeling and control of a deformable mirror,” J. Dyn. Syst. Meas. Control 124, 297–302 (2002).
[CrossRef]

Woods, B.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Yu, N.

N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
[CrossRef]

Zacharias, R.

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Zanuto, V. S.

Zhang, Y.

Appl. Opt.

Chin. Phys. B

N. Yu, Z. Hong, Y. Hao, R. Chang-Hui, and J. Wen-Han, “Thermal stability test and analysis of a 20-actuator bimorph deformable mirror,” Chin. Phys. B 18, 1089–1095 (2009).
[CrossRef]

J. Dyn. Syst. Meas. Control

S. E. Winters, J. H. Chung, and S. A. Velinsky, “Modeling and control of a deformable mirror,” J. Dyn. Syst. Meas. Control 124, 297–302 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Opt. Soc. Korea

Proc. SPIE

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screen printed actuator,” Proc. SPIE 8253, 82530D (2012).
[CrossRef]

R. Zacharias, E. Bliss, S. Winters, R. Sacks, M. Feldman, A. Grey, J. Koch, C. Stolz, J. Toeppen, L. Van Atta, and B. Woods, “Wavefront control of high-power laser beams in the National Ignition Facility (NIF),” Proc. SPIE 3889, 332–343 (2000).

R. Zacharias, E. Bliss, M. Feldman, A. Grey, M. Henesian, J. Koch, J. Lawson, R. Sacks, T. Salmon, J. Toeppen, L. Van Atta, S. Winters, and B. Woods, “The National Ignition Facility (NIF) wavefront control system,” Proc. SPIE 3492, 678–692 (1999).

Other

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Figures (15)

Fig. 1.
Fig. 1.

Detailed schematic of the deformable mirror structure.

Fig. 2.
Fig. 2.

(a) Overall surface shape (mm) (PV, 5.63 μm; RMS, 1.13 μm) and (b) the amplitude of the first 36 orders Legendre polynomials.

Fig. 3.
Fig. 3.

(a) After the first 36 orders Legendre low-pass-filtering (mm) (PV, 5.29 μm; RMS, 1.13 μm) and (b) after the high-pass-filtering (mm) (PV, 0.716 μm; RMS, 0.0993 μm).

Fig. 4.
Fig. 4.

(a) Fitting residual (mm) (PV, 0.709 μm; RMS, 0.119 μm) and (b) the local surface shapes of 20 * 20 mm areas on top of 39 actuators.

Fig. 5.
Fig. 5.

Residual shape in lines (mm).

Fig. 6.
Fig. 6.

Residual shape in columns (mm).

Fig. 7.
Fig. 7.

(a) Overall shape and (b) fitting residual with different temperature (the mounting temperature is 20 deg).

Fig. 8.
Fig. 8.

(a) Overall shape and (b) fitting residual with different thickness of mirror.

Fig. 9.
Fig. 9.

(a) Overall shape and (b) fitting residual with different thickness of base.

Fig. 10.
Fig. 10.

(a) Overall shape of square layout 36 actuators ( mm ) (PV, 5.92 μm; RMS, 1.06 μm) and (b) the fitting residual (mm) (PV, 1.10 μm; RMS, 0.131 μm).

Fig. 11.
Fig. 11.

(a) After the first 36 orders Legendre low-pass-filtering (mm) (PV, 5.76 μm; RMS, 1.05 μm) and (b) after the high-pass-filtering (mm) (PV, 0.442 μm; RMS, 0.0845 μm).

Fig. 12.
Fig. 12.

Surface shape of aluminum base deformable mirror at mounting temperature (19 deg) (PV, 0.37 μm; RMS, 0.063 μm).

Fig. 13.
Fig. 13.

(a) Fitting residual at 19.7 deg (PV, 0.63 μm; RMS, 0.095 μm) and (b) at 17.5 deg (PV, 1.33 μm; RMS, 0.23 μm).

Fig. 14.
Fig. 14.

(a) Fitting residual PV and (b) RMS of aluminum base deformable mirror in simulation and experiment.

Fig. 15.
Fig. 15.

(a) Fitting residual PV and (b) RMS of steel base deformable mirror in simulation and experiment.

Tables (3)

Tables Icon

Table 1. Parameters in Finite Element Simulation

Tables Icon

Table 2. Surface Shape of Different Actuator Layouts

Tables Icon

Table 3. Parameters of Deformable Mirrors in Experiment

Equations (9)

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

F i = σ i ( x , y ) d x d y ,
M x i = x σ i ( x , y ) d x d y ,
M y i = y σ i ( x , y ) d x d y .
i = 1 39 F i = i = 1 39 σ i ( x , y ) d x d y = 0 ,
i = 1 39 M x i = i = 1 39 x σ i ( x , y ) d x d y = 0 ,
i = 1 39 M y i = i = 1 39 y σ i ( x , y ) d x d y = 0.
σ i ( x , y ) d x d y = 0 ,
i = 1 39 M x i = i = 1 39 x σ i ( x , y ) d x d y = 0 ,
i = 1 39 M y i = i = 1 39 y σ i ( x , y ) d x d y = 0.

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