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  1. J. W. Hardy, “Adaptive Optics: a New Technology for the Control of Light,” Proc. IEEE 66, 651 (1978).
    [CrossRef]
  2. E. Steinhaus, S. G. Lipson, “Bimorph Piezoelectric Flexible Mirror,” J. Opt. Soc. Am. 69, 478 (1979).
    [CrossRef]
  3. S. A. Kokorowski, “Analysis of Adaptive Optical Elements Made from Piezoelectric Bimorphs,” J. Opt. Soc. Am. 69, 181 (1979).
    [CrossRef]
  4. T. Sato, H. Ishida, O. Ikeda, “Adaptive PVDF Piezoelectric Deformable Mirror System,” Appl. Opt. 19, 1430 (1980).
    [CrossRef] [PubMed]
  5. P. Halevi, “Bimorph Piezoelectric Flexible Mirror: Graphical Solution and Comparison with Experiment,” J. Opt. Soc. Am. 73, 110 (1983).
    [CrossRef]
  6. M. Yellin, “Using Membrane Mirrors in Adaptive Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 97 (1976).
  7. R. P. Grosso, M. Yellin, “Membrane Mirror as an Adaptive Optical Element,” J. Opt. Soc. Am. 67, 399 (1977).
    [CrossRef]
  8. F. Merkle, K. Freischlad, H. L. Reischmann, “Deformable Mirror with Combined Piezoelectric and Electrostatic Actuators,” Proc. Soc. Photo-Opt. Instrum. Eng. 332, 260 (1982).
  9. E. S. Claflin, N. Bareket, “Configuring an Electrostatic Membrane Mirror by Least-Squares Fitting with Analytically Derived Influence Functions,” J. Opt. Soc. Am. A 3, 1833 (1986).
    [CrossRef]
  10. F. Roddier, “Curvature Sensing: a Diffraction Theory,” NOAO R&D Note 87-3 (1987).
  11. F. Roddier, F. Forbes, S. Shaklan, C. Pinches,“Curvature Sensing and Compensation,” inProceeedings, Workshop on Adaptive Optics in Solar Observations, held inFreiburg, F.R.Germany, Kiepenheur Institut (8, 9 Sept. 1987).
  12. F. Roddier, Distributions et transformation de Fourier (McGraw Hill, New York, 1982), in French.
  13. A. D. Fisher, C. Warde, “Technique for Real-Time High-Resolution Adaptive Phase Compensation,” Opt. Lett. 8, 353 (1983).
    [CrossRef] [PubMed]
  14. J. W. Hardy, J. E. Lefebvre, C. L. Koliopoulos, “Real-time Atmospheric Compensation,” J. Opt. Soc. Am. 67, 360 (1977).
    [CrossRef]
  15. R. H. Hudgin, “Wave-front Reconstruction for Compensated Imaging,” J. Opt. Soc. Am. 67, 375 (1977).
    [CrossRef]

1987 (1)

F. Roddier, “Curvature Sensing: a Diffraction Theory,” NOAO R&D Note 87-3 (1987).

1986 (1)

1983 (2)

1982 (1)

F. Merkle, K. Freischlad, H. L. Reischmann, “Deformable Mirror with Combined Piezoelectric and Electrostatic Actuators,” Proc. Soc. Photo-Opt. Instrum. Eng. 332, 260 (1982).

1980 (1)

1979 (2)

1978 (1)

J. W. Hardy, “Adaptive Optics: a New Technology for the Control of Light,” Proc. IEEE 66, 651 (1978).
[CrossRef]

1977 (3)

1976 (1)

M. Yellin, “Using Membrane Mirrors in Adaptive Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 97 (1976).

Bareket, N.

Claflin, E. S.

Fisher, A. D.

Forbes, F.

F. Roddier, F. Forbes, S. Shaklan, C. Pinches,“Curvature Sensing and Compensation,” inProceeedings, Workshop on Adaptive Optics in Solar Observations, held inFreiburg, F.R.Germany, Kiepenheur Institut (8, 9 Sept. 1987).

Freischlad, K.

F. Merkle, K. Freischlad, H. L. Reischmann, “Deformable Mirror with Combined Piezoelectric and Electrostatic Actuators,” Proc. Soc. Photo-Opt. Instrum. Eng. 332, 260 (1982).

Grosso, R. P.

Halevi, P.

Hardy, J. W.

J. W. Hardy, “Adaptive Optics: a New Technology for the Control of Light,” Proc. IEEE 66, 651 (1978).
[CrossRef]

J. W. Hardy, J. E. Lefebvre, C. L. Koliopoulos, “Real-time Atmospheric Compensation,” J. Opt. Soc. Am. 67, 360 (1977).
[CrossRef]

Hudgin, R. H.

Ikeda, O.

Ishida, H.

Kokorowski, S. A.

Koliopoulos, C. L.

Lefebvre, J. E.

Lipson, S. G.

Merkle, F.

F. Merkle, K. Freischlad, H. L. Reischmann, “Deformable Mirror with Combined Piezoelectric and Electrostatic Actuators,” Proc. Soc. Photo-Opt. Instrum. Eng. 332, 260 (1982).

Pinches, C.

F. Roddier, F. Forbes, S. Shaklan, C. Pinches,“Curvature Sensing and Compensation,” inProceeedings, Workshop on Adaptive Optics in Solar Observations, held inFreiburg, F.R.Germany, Kiepenheur Institut (8, 9 Sept. 1987).

Reischmann, H. L.

F. Merkle, K. Freischlad, H. L. Reischmann, “Deformable Mirror with Combined Piezoelectric and Electrostatic Actuators,” Proc. Soc. Photo-Opt. Instrum. Eng. 332, 260 (1982).

Roddier, F.

F. Roddier, “Curvature Sensing: a Diffraction Theory,” NOAO R&D Note 87-3 (1987).

F. Roddier, F. Forbes, S. Shaklan, C. Pinches,“Curvature Sensing and Compensation,” inProceeedings, Workshop on Adaptive Optics in Solar Observations, held inFreiburg, F.R.Germany, Kiepenheur Institut (8, 9 Sept. 1987).

F. Roddier, Distributions et transformation de Fourier (McGraw Hill, New York, 1982), in French.

Sato, T.

Shaklan, S.

F. Roddier, F. Forbes, S. Shaklan, C. Pinches,“Curvature Sensing and Compensation,” inProceeedings, Workshop on Adaptive Optics in Solar Observations, held inFreiburg, F.R.Germany, Kiepenheur Institut (8, 9 Sept. 1987).

Steinhaus, E.

Warde, C.

Yellin, M.

R. P. Grosso, M. Yellin, “Membrane Mirror as an Adaptive Optical Element,” J. Opt. Soc. Am. 67, 399 (1977).
[CrossRef]

M. Yellin, “Using Membrane Mirrors in Adaptive Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 97 (1976).

Appl. Opt. (1)

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (1)

NOAO R&D Note 87-3 (1)

F. Roddier, “Curvature Sensing: a Diffraction Theory,” NOAO R&D Note 87-3 (1987).

Opt. Lett. (1)

Proc. IEEE (1)

J. W. Hardy, “Adaptive Optics: a New Technology for the Control of Light,” Proc. IEEE 66, 651 (1978).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

F. Merkle, K. Freischlad, H. L. Reischmann, “Deformable Mirror with Combined Piezoelectric and Electrostatic Actuators,” Proc. Soc. Photo-Opt. Instrum. Eng. 332, 260 (1982).

M. Yellin, “Using Membrane Mirrors in Adaptive Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 75, 97 (1976).

Other (2)

F. Roddier, F. Forbes, S. Shaklan, C. Pinches,“Curvature Sensing and Compensation,” inProceeedings, Workshop on Adaptive Optics in Solar Observations, held inFreiburg, F.R.Germany, Kiepenheur Institut (8, 9 Sept. 1987).

F. Roddier, Distributions et transformation de Fourier (McGraw Hill, New York, 1982), in French.

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Figures (2)

Fig. 1
Fig. 1

Difference in illumination between planes P1 and P2 is a measure of the local curvature distribution in the incoming wavefront W. It also measures the wavefront radial tilt at the edge.

Fig. 2
Fig. 2

Examples of sensor signals (left) and of the associated pressure distribution on a stretched membrane (right): (a) wavefront tilt; (b) balanced astigmatism; (c) focus error.

Equations (9)

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ρ ( x , y ) = 2 z x 2 + 2 z y 2 = 2 z ,
2 z t 2 = A 4 z + B 2 V ,
2 z t 2 = A 2 z + B P ,
λ ( f l ) r 0 r 0 l f ,
I 2 ( r ) I 1 ( r ) I 2 ( r ) + I 1 ( r ) = f ( f l ) 2 l [ n z ( f r / l ) δ c + 2 z ( f r / l ) ] ,
2 z ( r ) P ( r ) .
2 z ( r ) = k [ n z ( r ) δ c + 2 z ( r ) ] inside the pupil = 0 outisde the pupil ,
2 z ( r ) = σ n δ c + { 2 z ( r ) } ,
z ( r ) = k z ( r )

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