Abstract

Previous analyses have predicted that improved power-spectrum estimation results from application of speckle-imaging postprocessing to compensated astronomical images. We report the first results, to our knowledge, of compensated-speckle-imaging experiments, conducted at a compensated telescope operated by the U.S. Air Force, that confirm these predictions. The power-spectrum signal-to-noise ratio is used as the metric for evaluating the performance. We report the results of power-spectrum estimation for a single star and three binary stars, and we reconstruct images of the binary stars using the bispectrum method to obtain the Fourier phase of the object. Compensated and uncompensated results are compared. A previously derived expression that expresses the power-spectrum signal-to-noise ratio in terms of the compensated optical transfer function statistics and object parameters is verified by experimental data.

© 1994 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. J. C. Dainty, A. H. Greenaway, “Estimation of power spectra in speckle interferometry,” J. Opt. Soc. Am. 69, 786–790 (1979).
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    [CrossRef]
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  15. D. Hoffleit, C. Jaschek, The Bright Star Catalogue, 4th ed. (Yale U. Press, New Haven, Conn.1982).
  16. D. L. Hench, “Improved speckle imaging using limited degree-of-freedom adaptive optics,” Rep. TR-908 (Optical Sciences Company, Placentia, Calif., 1988).
  17. C. E. Worley, W. D. Heintz, Fourth Catalog of Orbits of Visual Binary Stars (U.S. Government Printing Office, Washington, D.C., 1983).

1992

M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” Opt. Soc. Am. A 9, 1525–1535 (1992).
[CrossRef]

M. C. Roggemann, “Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors,” Comput. Electr. Eng. 18, 451–466 (1992).
[CrossRef]

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

1991

1989

1987

1983

1981

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Prog. Opt. 19, 283–376 (1981).

1979

1978

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

1977

1970

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Barakat, R.

Dainty, J. C.

Fitch, J. P.

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

Gardner, C. S.

Goodman, D. M.

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Greenaway, A. H.

Hardy, J. W.

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

Heintz, W. D.

C. E. Worley, W. D. Heintz, Fourth Catalog of Orbits of Visual Binary Stars (U.S. Government Printing Office, Washington, D.C., 1983).

Hench, D. L.

D. L. Hench, “Improved speckle imaging using limited degree-of-freedom adaptive optics,” Rep. TR-908 (Optical Sciences Company, Placentia, Calif., 1988).

Hoffleit, D.

D. Hoffleit, C. Jaschek, The Bright Star Catalogue, 4th ed. (Yale U. Press, New Haven, Conn.1982).

Jaschek, C.

D. Hoffleit, C. Jaschek, The Bright Star Catalogue, 4th ed. (Yale U. Press, New Haven, Conn.1982).

Johansson, E. M.

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Lawrence, T. W.

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

Lohman, A. W.

Massie, N. A.

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

Matson, C. L.

M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” Opt. Soc. Am. A 9, 1525–1535 (1992).
[CrossRef]

C. L. Matson, “Weighted least-squares phase reconstruction from the bispectrum,” J. Opt. Soc. Am. A 8, 1905–1913 (1991).
[CrossRef]

Miller, M. G.

Nisenson, P.

Roddier, F.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Prog. Opt. 19, 283–376 (1981).

Roggemann, M. C.

M. C. Roggemann, “Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors,” Comput. Electr. Eng. 18, 451–466 (1992).
[CrossRef]

M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” Opt. Soc. Am. A 9, 1525–1535 (1992).
[CrossRef]

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

Sherwood, R. J.

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

Weigelt, G.

Welsh, B. M.

Wirnitzer, B.

Worley, C. E.

C. E. Worley, W. D. Heintz, Fourth Catalog of Orbits of Visual Binary Stars (U.S. Government Printing Office, Washington, D.C., 1983).

Appl. Opt.

Astron. Astrophys.

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Comput. Electr. Eng.

M. C. Roggemann, “Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors,” Comput. Electr. Eng. 18, 451–466 (1992).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

T. W. Lawrence, J. P. Fitch, D. M. Goodman, N. A. Massie, R. J. Sherwood, E. M. Johansson, “Extended-image reconstruction through horizontal path turbulence using bispectral speckle interferometry,” Opt. Eng. 31, 627–636 (1992).
[CrossRef]

Opt. Soc. Am. A

M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” Opt. Soc. Am. A 9, 1525–1535 (1992).
[CrossRef]

Proc. IEEE

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

Prog. Opt.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Prog. Opt. 19, 283–376 (1981).

Other

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

D. Hoffleit, C. Jaschek, The Bright Star Catalogue, 4th ed. (Yale U. Press, New Haven, Conn.1982).

D. L. Hench, “Improved speckle imaging using limited degree-of-freedom adaptive optics,” Rep. TR-908 (Optical Sciences Company, Placentia, Calif., 1988).

C. E. Worley, W. D. Heintz, Fourth Catalog of Orbits of Visual Binary Stars (U.S. Government Printing Office, Washington, D.C., 1983).

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Figures (13)

Fig. 1
Fig. 1

Compensated and uncompensated single-frame expected-power spectrum SNR’s for a star of visual magnitude 8. The horizontal axis is normalized to the diffraction-limited cutoff frequency for this aperture.

Fig. 2
Fig. 2

Same as Fig. 1 but with fewer photons available to the wave-front sensor.

Fig. 3
Fig. 3

Schematic of the AMOS adaptive-optics and image-measurement system: FOV, field-of-view.

Fig. 4
Fig. 4

Surface plot of logarithm base 10 of the read-noise power spectrum for the CCD camera used.

Fig. 5
Fig. 5

Standard deviations of the real and the imaginary parts of the compensated OTF measured for star HR 3982.

Fig. 6
Fig. 6

Modulus of the average compensated OTF measured for star HR 3982.

Fig. 7
Fig. 7

Expected single-frame power-spectrum SNIR for star HR 3982. Both the measured power-spectrum SNR and the power-spectrum SNR predicted from the OTF statistics ar(shown.

Fig. 8
Fig. 8

Compensated and uncompensated expected single-frame power-spectrum SNR’s for star HR 3982.

Fig. 9
Fig. 9

Compensated and uncompensated power-spectrum SNR’s for binary stars (a) HR 3579, (b) HR 6378, and (c) HR 5849. The solid curve is the compensated power-spectrum SNR; the dashed curve is the uncompensated power-spectrum SNR.

Fig. 10
Fig. 10

(a) Uncompensated deconvolved power spectrum for binary star HR 6378; (b) the compensated deconvolved power spectrum for the same star.

Fig. 11
Fig. 11

Surface plots of normalized intensity for the uncompensated bispectrum reconstructions of the three binary stars examined: (a) HR 3579, (b) HR 6378, (c) HR 5849.

Fig. 12
Fig. 12

Same as Fig. 11 but for the compensated bispectrum reconstructions.

Fig. 13
Fig. 13

Surface intensity plots of the normalized intensities of (a) the uncompensated long-exposure image of HR 6378 and (b) the compensated long-exposure image of HR 6378.

Equations (22)

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d ( x ) = k = 1 K δ ( x - x k ) ,
D ( u ) = d ( x ) exp ( - j 2 π u x ) d 2 x = k = 1 K exp ( - j 2 π u x k ) .
ϕ ( u ) = D ( u ) 2 .
Q ( u ) = D ( u ) 2 - K .
SNR Q ( u ) = Q ( u ) { var [ Q ( u ) ] } 1 / 2 ,
Q ( u ) = ( K ¯ ) 2 O ^ ( u ) 2 H ( u ) 2 ,
var [ Q ( u ) ] = ( K ¯ ) 2 + ( K ¯ ) 2 O ^ ( 2 u ) 2 H ( 2 u ) 2 + 2 ( K ¯ ) 3 O ^ ( u ) 2 H ( u ) 2 + ( K ¯ ) 4 O ^ ( u ) 4 { H ( u ) 4 - [ H ( u ) 2 ] 2 } .
SNR Q ( u ) = K ¯ H ( u ) 2 O ^ ( u ) 2 1 + K ¯ H ( u ) 2 O ^ ( u ) 2 ,
H ( u ) 2 ( r 0 D 0 ) 2 H 0 ( u ) ,
SNR Q N ( u ) = N 1 / 2 SNR Q ( u ) ,
H c ( u ) 4 = 3 σ r 4 + 6 σ r 2 s 2 + s 4 + 2 ( σ r 2 + s 2 ) σ i 2 + 3 σ i 4 ,
Q 1 ( u ) = D ( u ) 2 - K - P σ r n 2 .
var [ Q 1 ( u ) ] = var [ Q ( u ) ] + ( P σ r n 2 ) 2 .
Q 1 n ( u ) = D n ( u ) - K n - P σ r n 2 ,
Q 1 N ( u ) = 1 N n = 1 N Q 1 n ( u ) .
Q 1 n N = 1 N n = 1 N Q 1 n ( u ) .
SNR Q 1 N ( u ) = Q 1 N ( u ) var [ Q 1 n ( u ) ] ,
var [ Q 1 n ( u ) ] = [ Q 1 n ( u ) ] 2 N - [ Q 1 n ( u ) N ] 2 .
m ( x ) = s ( x ) + n ( x ) .
G q ( u ) = F [ q ( x ) ] 2 ,
G m ( u ) = G s ( u ) + G n ( u ) ,
G o ( u ) = G i ( u ) G ˜ r ( u ) + ,

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