Abstract

Correction by active mirror systems of image distortion due to atmospheric turbulence promises to improve the quality of ground-based astronomical observations. Although the ideal of fully correcting average-to-poor seeing to the diffraction limit of a large telescope cannot be easily realized with current technology, it has been demonstrated that partial correction of severe seeing disturbances can significantly improve image resolution. This paper describes a computer simulation of partial seeing correction by the Lockheed Active Mirror. Quantitative evaluation of the effects of partial correction on simulated wavefronts indicates that, even with a modest number of mirror actuators, one can achieve a diffraction-limited image superimposed on a background of scattered light.

© 1988 Optical Society of America

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References

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  1. R. H. Hudgin, “Wave-Front Compensation Error Due to Finite Corrector-Element Size,” J. Opt. Soc. Am. 67, 393 (1977).
    [CrossRef]
  2. R. C. Smithson, “Initial Solar Observations at Sacramento Peak Using the Lockheed Active Optics System,” Bull. Am. Astron. Soc. 18, 923 (1986).
  3. J. L. Walsh, P. B. Ulrich, “Thermal Blooming in the Atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978).
    [CrossRef]
  4. D. L. Fried, “Statistics of a Geometric Representation of Wave-front Distortion,” J. Opt. Soc. Am. 55, 1427 (1965).
    [CrossRef]
  5. R. J. Noll, “Zernike Polynomials and Atmospheric Turbulence,” J. Opt. Soc. Am. 66, 207 (1976).
    [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chaps. 3,4.
  7. T. D. Tarbell, R. C. Smithson, “A Simple Image Motion Compensation System for Solar Observations,” in Solar Instrumentation: What’s Next, R. B. Dunn, Ed. (Sacramento Peak National Observatory, Sunspot, NM, 1981).
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 462.

1986 (1)

R. C. Smithson, “Initial Solar Observations at Sacramento Peak Using the Lockheed Active Optics System,” Bull. Am. Astron. Soc. 18, 923 (1986).

1977 (1)

1976 (1)

1965 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 462.

Fried, D. L.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chaps. 3,4.

Hudgin, R. H.

Noll, R. J.

Smithson, R. C.

R. C. Smithson, “Initial Solar Observations at Sacramento Peak Using the Lockheed Active Optics System,” Bull. Am. Astron. Soc. 18, 923 (1986).

T. D. Tarbell, R. C. Smithson, “A Simple Image Motion Compensation System for Solar Observations,” in Solar Instrumentation: What’s Next, R. B. Dunn, Ed. (Sacramento Peak National Observatory, Sunspot, NM, 1981).

Tarbell, T. D.

T. D. Tarbell, R. C. Smithson, “A Simple Image Motion Compensation System for Solar Observations,” in Solar Instrumentation: What’s Next, R. B. Dunn, Ed. (Sacramento Peak National Observatory, Sunspot, NM, 1981).

Ulrich, P. B.

J. L. Walsh, P. B. Ulrich, “Thermal Blooming in the Atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978).
[CrossRef]

Walsh, J. L.

J. L. Walsh, P. B. Ulrich, “Thermal Blooming in the Atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 462.

Bull. Am. Astron. Soc. (1)

R. C. Smithson, “Initial Solar Observations at Sacramento Peak Using the Lockheed Active Optics System,” Bull. Am. Astron. Soc. 18, 923 (1986).

J. Opt. Soc. Am. (3)

Other (4)

J. L. Walsh, P. B. Ulrich, “Thermal Blooming in the Atmosphere,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chaps. 3,4.

T. D. Tarbell, R. C. Smithson, “A Simple Image Motion Compensation System for Solar Observations,” in Solar Instrumentation: What’s Next, R. B. Dunn, Ed. (Sacramento Peak National Observatory, Sunspot, NM, 1981).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 462.

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Figures (7)

Fig. 1
Fig. 1

Layout of the active mirror and 1.0-m telescope aperture and simulation grids. Wavefronts are simulated on a 200- × 200-point square grid representing 2.0 × 2.0 m. At the aperture plane wavefronts are cropped, retaining the central 1.0 m2, to define the 100- × 100-point calculation grid.

Fig. 2
Fig. 2

Simulated long-exposure point spread functions with r0 = 17.2 cm. (a)–(c) Various corrections; (d) perfect diffraction pattern for comparison. Rayleigh distance for the perfect spot is 1/8 sec of arc. Grid is 100 × 100 points covering 2.75 × 2.75 sec of arc. Intensity is plotted on a linear axis and scaled to unit height.

Fig. 3
Fig. 3

Simulated long-exposure point spread functions with r0 = 7.5 cm. (a)–(c) Various corrections; (d) perfect diffraction pattern for comparison. Grid size is 2.75 × 2.75 sec of arc. Intensity is plotted on a linear axis and scaled to unit height.

Fig. 4
Fig. 4

Simulated long-exposure point spread functions with r0 = 3.3 cm. (a)–(c) Various corrections; (d) perfect diffraction pattern for comparison. Grid size is 2.75 × 2.75 sec of arc. Intensity is plotted on a linear axis and scaled to unit height.

Fig. 5
Fig. 5

Instantaneous exposure point spread functions for four uncorrelated random wavefronts with r0 = 7.5 cm. (a)–(d) Uncorrected speckle pattern; (e)–(h) corresponding images after piston–tilt correction by the active mirror. Grid size is 2.75 × 2.75 sec of arc. Intensity is plotted on a linear axis and scaled to unit height.

Fig. 6
Fig. 6

Full width at half-maximum for (a) uncorrected and (b) active mirror corrected long-exposure images with varying amounts of wavefront deviation.

Fig. 7
Fig. 7

Radius of the contour encircling 50% of the incident energy for (a) uncorrected and (b) piston–tilt corrected long-exposure images with varying amounts of wavefront deviation.

Tables (4)

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Table I Average Residual rms Wavefront Error (Waves) on a 1.0-m Diam Circular Aperture

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Table II Intensity of Brightest Speckle in Short-Exposure Images Given as a Percentage of Peak Intensity

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Table III Strehl Ratio and Normalized Contrast of Various Corrections of Simulated Long-Exposure Images

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Table IV Radius (In Seconds of Arc) of Encircled Energy for 25%, 50%, and 75 % of Incident Energy

Equations (2)

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1 grid size f 1 2 Δ x = N / 2 grid size .
Δ 3 = 0 . 134 ( 2 π ) 2 ( D / r 0 ) 3 ,

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