Abstract

Self-referenced speckle holography (SRSH) is a postdetection turbulence-compensation technique for obtaining diffraction-limited imagery from ground-based telescopes degraded by atmospheric turbulence. In SRSH, image-plane information is used together with wave-front distortion information to reconstruct an estimate of the object spectrum. The wave-front distortion information is obtained from a wave-front sensor in the pupil plane of the telescope. This information is used in a postprocessing environment to estimate the point spread function of the combined telescope and atmosphere. The point spread function is then used to obtain an estimate of the object intensity distribution by deconvolution. We present the results of a detailed performance analysis of SRSH. Performance is quantified in terms of a system function and a system point spread function. The results show how the performance of SRSH is transfer dependent on the sampling intervals and shot noise in the wave-front sensor. The results also indicate how the technique, for a given set of design parameters, responds to changing seeing conditions. For wave-front sensor sampling intervals of the order of a Fried coherence cell size r0 and adequate light levels, SRSH boosts the high spatial frequencies (those near the diffraction limit of the telescope) to nearly 0.6.

© 1993 Optical Society of America

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    [Crossref]
  2. A. Labeyrie, Astron. Astrophys. 6, 85 (1970).
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    [Crossref]
  4. G. Weigelt, “Speckle imaging and speckle spectroscopy,” in New Technologies for Astronomy, J. Swings, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1130, 148–151 (1989.
  5. G. R. Ayers, M. J. Northcott, J. C. Dainty, “Knox–Thompson and triple-correlation imaging through atmospheric turbulence,” J. Opt. Soc. Am. 5, 963–985 (1988).
    [Crossref]
  6. A. W. Lohmann, G. Weigelt, B. Wirnitzer, “Speckle masking in astronomy: triple correlation theory and applications,” Appl. Opt. 22, 4028–4037 (1983).
    [Crossref] [PubMed]
  7. T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245, 263–269 (1989).
    [Crossref] [PubMed]
  8. J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
    [Crossref]
  9. J. D. Gonglewski, D. G. Voelz, J. S. Fender, D. C. Dayton, B. K. Spielbusch, R. E. Pierson, “First astronomical application of postdetection turbulence compensation: images of α Aurigae, ν Ursae Majoris, and α Geminorum using self-referenced speckle holography,” Appl. Opt. 29, 4527–4529 (1990).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  20. R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, Mass., 1991). Chap. 7.
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    [Crossref]
  22. B. M. Welsh, C. S. Gardner, “Effects of turbulence induced anisoplanatism on the imaging performance of adaptive astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
    [Crossref]
  23. B. M. Welsh, “Imaging performance analysis of adaptive telescopes using laser guide stars,” Appl. Opt. 30, 5021–5030 (1991).
    [Crossref] [PubMed]
  24. T. J. Kane, B. M. Welsh, C. S. Gardner, L. A. Thompson, “Wave-front detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. V. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.114, 160–171 (1989).

1992 (1)

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

1991 (2)

1990 (2)

1989 (2)

1988 (1)

G. R. Ayers, M. J. Northcott, J. C. Dainty, “Knox–Thompson and triple-correlation imaging through atmospheric turbulence,” J. Opt. Soc. Am. 5, 963–985 (1988).
[Crossref]

1983 (2)

1978 (1)

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

1970 (1)

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

1966 (2)

Ayers, G. R.

G. R. Ayers, M. J. Northcott, J. C. Dainty, “Knox–Thompson and triple-correlation imaging through atmospheric turbulence,” J. Opt. Soc. Am. 5, 963–985 (1988).
[Crossref]

Cornwell, T. J.

T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245, 263–269 (1989).
[Crossref] [PubMed]

Dainty, J. C.

G. R. Ayers, M. J. Northcott, J. C. Dainty, “Knox–Thompson and triple-correlation imaging through atmospheric turbulence,” J. Opt. Soc. Am. 5, 963–985 (1988).
[Crossref]

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 255–280.
[Crossref]

Dayton, D. C.

Fender, J. S.

Fontanella, J. C.

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[Crossref]

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

J. C. Fontanella, “Wave-front sensing, adaptive optics and deconvolution,” presented at the CFHT Workshop on High-Resolution Imaging in Astronomy, Kamuela, Hawaii, 25–26 October 1984.

Fried, D. L.

D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
[Crossref]

D. L. Fried, “Postdetection wave-front compensation,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 127–133 (1987).

Fuensaldia, J.

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

Gardner, C. S.

Gonglewski, J. D.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 8.

Hardy, J. H.

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

Kane, T. J.

T. J. Kane, B. M. Welsh, C. S. Gardner, L. A. Thompson, “Wave-front detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. V. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.114, 160–171 (1989).

Labeyrie, A.

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Laurent, J.

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

Lohmann, A. W.

Marais, T.

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

McGlamery, B. L.

Michau, V.

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

Northcott, M. J.

G. R. Ayers, M. J. Northcott, J. C. Dainty, “Knox–Thompson and triple-correlation imaging through atmospheric turbulence,” J. Opt. Soc. Am. 5, 963–985 (1988).
[Crossref]

Papoulis, A.

A. Papoulis, “Linear mean-square estimation,” in Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 11.

Pierson, R. E.

Primot, J.

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[Crossref]

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

Roggemann, M. C.

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

Rousset, G.

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[Crossref]

Spielbusch, B. K.

Tallon, M.

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

Thompson, L. A.

T. J. Kane, B. M. Welsh, C. S. Gardner, L. A. Thompson, “Wave-front detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. V. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.114, 160–171 (1989).

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, Mass., 1991). Chap. 7.

Voelz, D. G.

VonNiederhausern, R. N.

R. N. VonNiederhausern, “Performance analysis of the speckle holography image reconstruction technique,” M.S. thesis (School of Engineering, U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1991).

Wallner, E. P.

Weigelt, G.

A. W. Lohmann, G. Weigelt, B. Wirnitzer, “Speckle masking in astronomy: triple correlation theory and applications,” Appl. Opt. 22, 4028–4037 (1983).
[Crossref] [PubMed]

G. Weigelt, “Speckle imaging and speckle spectroscopy,” in New Technologies for Astronomy, J. Swings, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1130, 148–151 (1989.

Welsh, B. M.

Wirnitzer, B.

Appl. Opt. (3)

Astron. Astrophys. (1)

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Comput. Electr. Eng. (1)

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

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

Proc. IEEE (1)

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

Science (1)

T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245, 263–269 (1989).
[Crossref] [PubMed]

Other (10)

V. Michau, T. Marais, J. Laurent, J. Primot, J. C. Fontanella, M. Tallon, J. Fuensaldia, “High-resolution astronomical observations using deconvolution from wave-front sensing,” in Propagation Engineering: Fourth in a Series, L. R. Bissonnette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. End.1487, 64–71 (1991).

R. N. VonNiederhausern, “Performance analysis of the speckle holography image reconstruction technique,” M.S. thesis (School of Engineering, U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1991).

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, New York, 1975), pp. 255–280.
[Crossref]

G. Weigelt, “Speckle imaging and speckle spectroscopy,” in New Technologies for Astronomy, J. Swings, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1130, 148–151 (1989.

J. C. Fontanella, “Wave-front sensing, adaptive optics and deconvolution,” presented at the CFHT Workshop on High-Resolution Imaging in Astronomy, Kamuela, Hawaii, 25–26 October 1984.

D. L. Fried, “Postdetection wave-front compensation,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 127–133 (1987).

A. Papoulis, “Linear mean-square estimation,” in Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965), Chap. 11.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 8.

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, Mass., 1991). Chap. 7.

T. J. Kane, B. M. Welsh, C. S. Gardner, L. A. Thompson, “Wave-front detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. V. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.114, 160–171 (1989).

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Figures (6)

Fig. 1
Fig. 1

Block diagram of the image-reconstruction algorithm.8

Fig. 2
Fig. 2

Telescope aperture and wave-front sensor geometry.

Fig. 3
Fig. 3

System transfer function (STF) for the aperture and WFS geometry shown in Fig. 2 and d/r0 = 1.

Fig. 4
Fig. 4

System transfer function (STF) for the aperture and WFS geometry shown in Fig. 2 and N = 50.

Fig. 5
Fig. 5

System line spread function (SLSF) for the aperture and WFS geometry shown in Fig. 2 and d/r0 = 1.

Fig. 6
Fig. 6

System line spread function (SLSF) for the aperture and WFS geometry shown in Fig. 2 and N = 50.

Equations (36)

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i ( x ) = o ( x ) * s ( x ) ,
I ( f ) = O ( f ) S ( f ) ,
O ^ ( f ) = I ( f ) S ^ * ( f ) S ^ ( f ) 2 + 2 ,
O ^ ( f ) = I ( f ) S ^ * ( f ) S ^ ( f ) 2 ,
S ( f ) = W A ( λ F f ) exp [ j ϕ ( λ F f ) ] W A ( λ F f ) exp [ j ϕ ( λ F f ) ] ,
g ( x ) f ( x ) = d 2 a g ( a ) f * ( a - x ) .
S ^ ( f ) = W A ( λ F f ) exp [ j ϕ ^ ( λ F f ) ] W A ( λ F f ) exp [ j ϕ ^ ( λ F f ) ] .
d 2 x W A ( x ) = 1 ,
ϕ ( x ) = ψ ( x ) - d 2 x W A ( x ) ψ ( x ) .
s n = d 2 x W n ( x ) [ ϕ ( x ) · d ^ n ] + α n ,
s n = - d 2 x W n s ( x ) ϕ ( x ) + α n ,
ϕ ^ ( x ) = j c j r j ( x ) ,
c j = n M j n s n ,
ϕ ^ ( x ) = j n s n M j n r j ( x ) .
2 ( x ) = [ ϕ ^ ( x ) - ϕ ( x ) ] 2 .
2 = d 2 x W A ( x ) 2 ( x ) = d 2 x W A ( x ) [ ϕ ^ ( x ) - ϕ ( x ) ] 2 .
M j n = j n R j j - 1 A j n S n n - 1 ,
R j j = d 2 x W A ( x ) r j ( x ) r j ( x ) ,
A j n = d 2 x W A ( x ) r j ( x ) s n ϕ ( x ) = - d 2 x d 2 x W A ( x ) r j ( x ) W n s ( x ) ϕ ( x ) ϕ ( x ) ,
S n n = s n s n = d 2 x d 2 x W n s ( x ) W n s ( x ) ϕ ( x ) ϕ ( x ) + α n α n .
STF ( f ) = S ( f ) S ^ * ( f ) S ^ ( f ) 2 .
STF ( f ) = d 2 x d 2 x W A ( x ) W A ( x - λ F f ) W A ( x ) W A ( x - λ F f ) exp { j [ ϕ ( x ) - ϕ ( x - λ F f ) - ϕ ^ ( x ) + ϕ ^ ( x - λ F f ) ] } d 2 x d 2 x W A ( x ) W A ( x - λ F f ) W A ( x ) W A ( x - λ F f ) exp { j [ ϕ ^ ( x ) - ϕ ^ ( x - λ F f ) - ϕ ^ ( x ) + ϕ ^ ( x - λ F f ) ] } .
STF ( f ) = d 2 x d 2 x W A ( x ) W A ( x - λ F f ) W A ( x ) W A ( x - λ F f ) exp { - 1 / 2 [ ϕ ( x ) - ϕ ( x - λ F f ) - ϕ ^ ( x ) + ϕ ^ ( x - λ F f ) ] 2 } d 2 x d 2 x W A ( x ) W A ( x - λ F f ) W A ( x ) W A ( x - λ F f ) exp { - 1 / 2 [ ϕ ^ ( x ) - ϕ ^ ( x - λ F f ) - ϕ ^ ( x ) + ϕ ^ ( x - λ F f ) ] 2 } .
ϕ ( x ) ϕ ( x ) = - ½ D ( x , x ) + g ( x ) + g ( x ) - a ,
ϕ ( x ) ϕ ^ ( x ) = 1 2 j n M j n r j ( x ) d 2 x W n s ( x ) × [ D ( x , x ) - 2 g ( x ) ] ,
ϕ ^ ( x ) ϕ ^ ( x ) = i j C i j r i ( x ) r j ( x ) ,
g ( x ) = 1 2 d 2 x W A ( x ) D ( x , x ) ,
a = 1 2 d 2 x d 2 x W A ( x ) W A ( x ) D ( x , x ) ,
C i j = n m M j n M i m S n m .
STF ( f ) = STF n u m STF d e n
STF num = exp [ - 1 2 D ( λ F f ) ] d 2 x d 2 x W A ( x ) W A ( x - λ F f ) × W A ( x ) W A ( x - λ F f ) exp { - 1 2 i j C i j × [ r i ( x ) - r i ( x - λ F f ) ] [ r j ( x ) - r j ( x - λ F f ) ] } × exp { - 1 2 j [ r j ( x ) - r j ( x - λ F f ) ] n d 2 x × W n s ( x ) [ D ( x - x ) - D ( x - λ F f - x ) ] } ,
STF den = d 2 x d 2 x W A ( x ) W A ( x - λ F f ) W A ( x ) W A ( x - λ F f ) × exp ( - 1 2 i j C i j { [ r i ( x ) - r i ( x - λ F f ) ] - [ r i ( x ) - r i ( x - λ F f ) ] } { [ r j ( x ) - r j ( x - λ F f ) ] - [ r j ( x ) - r j ( x - λ F f ) ] } ) .
SLSF ( u ) = d f x STF ( f x , 0 ) exp ( j 2 π f x u ) ,
σ α = { 0.86 π η N r 0             d > r 0 0.74 π η N d             d r 0 ,
r j ( x ) exp [ - ( x - x j ) 2 d a 2 ] ,
D ( x , x ) = 6.88 ( x - x r 0 ) 5 / 3 ,

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