Abstract

To provide complete compensation for turbulent distortions in the visible range at aperture dimensions typical for modern telescopes (6–10 m), one needs to develop adaptive systems with hundreds of control channels. More simple adaptive systems that provide complete compensation in the infrared range can give an essential advantage in angular resolution in the visible range too. In this case the image brightness characterized by the Strehl ratio remains much less than that in the diffraction-limited case, i.e., the system provides only partial compensation. We present the results of numerical calculations of the partially corrected point-spread function and discuss possible approaches to composing the adaptive system configuration.

© 1998 Optical Society of America

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References

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  17. B. M. Welsh, B. L. Ellenbroek, M. C. Roggermann, T. L. Pennington, “Fundamental performance comparison of a Hartmann and a shearing interferometer wave-front sensor,” Appl. Opt. 34, 4186–4195 (1995).
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1995 (1)

1991 (2)

M. C. Roggemann, “Limited degree of freedom adaptive optics and image reconstruction,” Appl. Opt. 30, 4227–4233 (1991).
[CrossRef] [PubMed]

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

1990 (3)

M. A. Ealey, J. F. Washeba, “Continuous facesheet low voltage deformable mirror,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

R. K. Tyson, “Adaptive optics system performance approximation for atmospheric turbulence correction,” Opt. Eng. 29, 1165–1173 (1990).
[CrossRef]

B. Hurlburd, D. Sandler, “Segmented mirrors for atmospheric compensation,” Opt. Eng. 29, 1186–1190 (1990).
[CrossRef]

1989 (2)

J. M. Beckers, F. Merkle, “Adaptive optics for large telescopes,” Astrophys. Space Sci. 160, 345–351 (1989).
[CrossRef]

R. C. Smithson, M. L. Peri, “Partial correction of astronomical images with active mirrors,” J. Opt. Soc. Am. A 6, 92–97 (1989).
[CrossRef]

1987 (1)

1983 (1)

1982 (1)

1978 (1)

1976 (1)

1971 (1)

R. B. Shack, B. C. Platt, “Production and use of lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 1586 (1971).

1965 (1)

D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1426–1435 (1965).
[CrossRef]

Barakat, R.

Beckers, J. M.

J. M. Beckers, F. Merkle, “Adaptive optics for large telescopes,” Astrophys. Space Sci. 160, 345–351 (1989).
[CrossRef]

Ealey, M. A.

M. A. Ealey, J. F. Washeba, “Continuous facesheet low voltage deformable mirror,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

M. A. Ealey, J. A. Wellman, “Deformable mirror: design fundamentals, key performance specification and parametric trades,” in Active and Adaptive Optical Components, M. A. Ealey, ed., Proc. SPIE1543, 36–51 (1991).
[CrossRef]

Ellenbroek, B. L.

Fortes, B. V.

B. V. Fortes, V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” in Atmospheric Propagation and Remote Sensing, A. Kohnle, W. Miller, eds., Proc. SPIE1668, 477–488 (1992).
[CrossRef]

Fried, D. L.

D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1426–1435 (1965).
[CrossRef]

Graves, J. E.

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Hurlburd, B.

B. Hurlburd, D. Sandler, “Segmented mirrors for atmospheric compensation,” Opt. Eng. 29, 1186–1190 (1990).
[CrossRef]

Lukin, V. P.

B. V. Fortes, V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” in Atmospheric Propagation and Remote Sensing, A. Kohnle, W. Miller, eds., Proc. SPIE1668, 477–488 (1992).
[CrossRef]

Markey, J. K.

Merkle, F.

J. M. Beckers, F. Merkle, “Adaptive optics for large telescopes,” Astrophys. Space Sci. 160, 345–351 (1989).
[CrossRef]

Nisenson, P.

Noll, R. J.

Northcott, M.

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Pennington, T. L.

Peri, M. L.

Platt, B. C.

R. B. Shack, B. C. Platt, “Production and use of lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 1586 (1971).

Roddier, F.

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Roggemann, M. C.

Roggermann, M. C.

Sandler, D.

B. Hurlburd, D. Sandler, “Segmented mirrors for atmospheric compensation,” Opt. Eng. 29, 1186–1190 (1990).
[CrossRef]

Shack, R. B.

R. B. Shack, B. C. Platt, “Production and use of lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 1586 (1971).

Smithson, R. C.

Tyson, R. K.

R. K. Tyson, “Adaptive optics system performance approximation for atmospheric turbulence correction,” Opt. Eng. 29, 1165–1173 (1990).
[CrossRef]

Wallner, E. P.

Wang, J. Y.

Washeba, J. F.

M. A. Ealey, J. F. Washeba, “Continuous facesheet low voltage deformable mirror,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

Wellman, J. A.

M. A. Ealey, J. A. Wellman, “Deformable mirror: design fundamentals, key performance specification and parametric trades,” in Active and Adaptive Optical Components, M. A. Ealey, ed., Proc. SPIE1543, 36–51 (1991).
[CrossRef]

Welsh, B. M.

Winocur, J.

Appl. Opt. (3)

Astrophys. Space Sci. (1)

J. M. Beckers, F. Merkle, “Adaptive optics for large telescopes,” Astrophys. Space Sci. 160, 345–351 (1989).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (2)

Opt. Eng. (3)

M. A. Ealey, J. F. Washeba, “Continuous facesheet low voltage deformable mirror,” Opt. Eng. 29, 1191–1198 (1990).
[CrossRef]

R. K. Tyson, “Adaptive optics system performance approximation for atmospheric turbulence correction,” Opt. Eng. 29, 1165–1173 (1990).
[CrossRef]

B. Hurlburd, D. Sandler, “Segmented mirrors for atmospheric compensation,” Opt. Eng. 29, 1186–1190 (1990).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

F. Roddier, M. Northcott, J. E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Other (2)

B. V. Fortes, V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” in Atmospheric Propagation and Remote Sensing, A. Kohnle, W. Miller, eds., Proc. SPIE1668, 477–488 (1992).
[CrossRef]

M. A. Ealey, J. A. Wellman, “Deformable mirror: design fundamentals, key performance specification and parametric trades,” in Active and Adaptive Optical Components, M. A. Ealey, ed., Proc. SPIE1543, 36–51 (1991).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Two-dimensional intensity distribution of PSF’s for modal compensation. The value of the aperture normalized diameter is D/ r 0 = 20.

Fig. 2
Fig. 2

PSF’s when a modal corrector is used. Parameter N corresponds to the number of Zernike polynomials. The PSF is normalized to the axial value. S is the Strehl ratio.

Fig. 3
Fig. 3

Dependence of the contrast on the Strehl ratio for modal correction for D/ r 0 = 10, 20, 30.

Fig. 4
Fig. 4

PSF when the segmented adaptive mirror with 84 elements in a hexagonal form is used. Every segment is controlled by the position and slopes. The PSF is normalized by (a) its axial value, (b) the diffraction maximum.

Fig. 5
Fig. 5

PSF when a flexible adaptive mirror with the Gaussian reference function is used. Parameter N corresponds to the number of the control points at the aperture diameter. The PSF is normalized by its axial value.

Fig. 6
Fig. 6

Results of the simulation of an adaptive telescope with the Shack–Hartmann sensor. The normalized diameter of the aperture is D/ r 0 = 10. The dimension of the sensor lens diaphragm is 10 × 10. An estimation of the wave-front aberrations was performed with the modal algorithm (28 Zernike polynomials). Parameter N corresponds to the average statistical number of photons at the subaperture during one exposure.

Fig. 7
Fig. 7

PSF’s of the 10-m telescope at different wavelengths for adaptation with a LGS. The upper plots are for the sodium LGS (H = 100 km), and the lower plots are for the Rayleigh LGS (H = 10 km). In the left-hand plots the PSF is normalized to the diffraction maximum, and in the right-hand plots the PSF is normalized to its axial value. The wavelength λ is given in micrometers.

Tables (3)

Tables Icon

Table 1 Values of the CN Coefficients

Tables Icon

Table 2 Dependence of the Number of Modes N on the Normalized Aperture Diameter

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Table 3 Estimations of the Number of Corrector Elements N

Equations (7)

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

σ N 2 = C N D / r 0 5 / 3 ,
C N 0.2944   N -   3 / 2 .
N = 0.244 D / r 0 1.92 .
S = exp - σ N 2 = 1 / e 0.37 .
σ 2 = C d / r 0 5 / 3 ,
N = D d 2 = D / r 0 2 C / σ 2 6 / 5 .
OTF = OTF 1 + OTF 2 .

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