Abstract

Deconvolution from wave-front sensing (DWFS) has been proposed as a method for achieving high-resolution images of astronomical objects from ground-based telescopes. The technique consists of the simultaneous measurement of a short-exposure focal-plane speckled image, as well as the wave front, by use of a Shack–Hartmann sensor placed at the pupil plane. In early studies it was suspected that some problems would occur in poor seeing conditions; however, it was usually assumed that the technique would work well as long as the wave-front sensor subaperture spacing was less than r 0 (L/ r 0 < 1). Atmosphere-induced phase errors in the pupil of a telescope imaging system produce both phase errors and magnitude errors in the effective short-exposure optical transfer function (OTF) of the system. Recently it has been shown that the commonly used estimator for this technique produces biased estimates of the magnitude errors. The significance of this bias problem is that one cannot properly estimate or correct for the frame-to-frame fluctuations in the magnitude of the OTF but can do so only for fluctuations in the phase. An auxiliary estimate must also be used to correct for the mean value of the magnitude error. The inability to compensate for the magnitude fluctuations results in a signal-to-noise ratio (SNR) that is less favorable for the technique than was previously thought. In some situations simpler techniques, such as the Knox-Thompson and bispectrum methods, which require only speckle gram data from the focal plane of the imaging system, can produce better results. We present experimental measurements based on observations of bright stars and the Jovian moon Ganymede that confirm previous theoretical predictions.

© 1997 Optical Society of America

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References

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  1. J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” JOSA A 7, 1589–1608 (1990).
    [CrossRef]
  2. B. M. Welsh, R. N. Niederhausern, “Performance analysis of the self-referenced speckle-holography image-reconstruction technique,” Appl. Opt. 32, 5071–5078 (1993).
    [CrossRef] [PubMed]
  3. 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,” Appl. Opt. 29, 4527–4529 (1990).
    [CrossRef] [PubMed]
  4. J. W. Goodman, Statictical Optics (Wiley, New York, 1985), pp. 361–459.
  5. M. C. Roggeman, B. M. Welsh, J. Devey, “Biased estimators and object-spectrum estimation in the method of deconvolution from wave-front sensing,” Appl. Opt. 33, 5754–5763 (1994).
    [CrossRef]
  6. M. C. Roggeman, B. M. Welsh, “Signal-to-noise ratio for astronomical imaging by deconvolution from wave-front sensing,” Appl. Opt. 33, 5400–5414 (1994).
    [CrossRef]
  7. K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
    [CrossRef]
  8. J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984), pp. 278–280.
  9. O. von der Luhe, “Signal transfer function of the Knox-Thompson speckle imaging technique,” JOSA A 5, 721–729 (1988).
    [CrossRef]
  10. P. Nisenson, C. Papaliolios, “Effects of photon noise on speckle image reconstruction with the Knox-Thompson algorithm,” Optics Commun. 47, 91–96 (1983).
    [CrossRef]

1994 (2)

1993 (1)

1990 (2)

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,” Appl. Opt. 29, 4527–4529 (1990).
[CrossRef] [PubMed]

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

1988 (1)

O. von der Luhe, “Signal transfer function of the Knox-Thompson speckle imaging technique,” JOSA A 5, 721–729 (1988).
[CrossRef]

1983 (1)

P. Nisenson, C. Papaliolios, “Effects of photon noise on speckle image reconstruction with the Knox-Thompson algorithm,” Optics Commun. 47, 91–96 (1983).
[CrossRef]

1974 (1)

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984), pp. 278–280.

Dayton, D. C.

Devey, J.

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,” JOSA A 7, 1589–1608 (1990).
[CrossRef]

Gonglewski, J. D.

Goodman, J. W.

J. W. Goodman, Statictical Optics (Wiley, New York, 1985), pp. 361–459.

Knox, K. T.

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

Niederhausern, R. N.

Nisenson, P.

P. Nisenson, C. Papaliolios, “Effects of photon noise on speckle image reconstruction with the Knox-Thompson algorithm,” Optics Commun. 47, 91–96 (1983).
[CrossRef]

Papaliolios, C.

P. Nisenson, C. Papaliolios, “Effects of photon noise on speckle image reconstruction with the Knox-Thompson algorithm,” Optics Commun. 47, 91–96 (1983).
[CrossRef]

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,” JOSA A 7, 1589–1608 (1990).
[CrossRef]

Roggeman, M. C.

Rousset, G.

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

Spielbusch, B. K.

Thompson, B. J.

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

Voelz, D. G.

von der Luhe, O.

O. von der Luhe, “Signal transfer function of the Knox-Thompson speckle imaging technique,” JOSA A 5, 721–729 (1988).
[CrossRef]

Welsh, B. M.

Appl. Opt. (4)

Astrophys. J. (1)

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short-exposure photographs,” Astrophys. J. 193, L45–L48 (1974).
[CrossRef]

JOSA A (2)

O. von der Luhe, “Signal transfer function of the Knox-Thompson speckle imaging technique,” JOSA A 5, 721–729 (1988).
[CrossRef]

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

Optics Commun. (1)

P. Nisenson, C. Papaliolios, “Effects of photon noise on speckle image reconstruction with the Knox-Thompson algorithm,” Optics Commun. 47, 91–96 (1983).
[CrossRef]

Other (2)

J. W. Goodman, Statictical Optics (Wiley, New York, 1985), pp. 361–459.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984), pp. 278–280.

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Figures (9)

Fig. 1
Fig. 1

Synoptic sketch of the DWFS instrument.

Fig. 2
Fig. 2

Experimental DWFS estimator bias for (a) Psi Uma, (b) Arcturus, and (c) Antares.

Fig. 3
Fig. 3

Comparison of short-exposure focal-plane images and point-spread function estimates from wave-front sensor measurements.

Fig. 4
Fig. 4

Comparison of star reconstructions.

Fig. 5
Fig. 5

Modulo-2π reconstructed phase estimates.

Fig. 6
Fig. 6

Experimental SNR for the DWFS and power-spectrum estimators: (a) Psi Uma, (b) Arcturus, and (c) Antares.

Fig. 7
Fig. 7

Focal-plane data for the Jovian moon Ganymede.

Fig. 8
Fig. 8

Experimental SNR’s for the Ganymede observations.

Fig. 9
Fig. 9

Comparison of the Knox-Thompson and DWFS reconstructions of images of the Jovian moon Ganymede: (a) Knox-Thompson reconstruction, low-pass filtered and 40% of the diffraction limit. (b) Knox-Thompson reconstruction, low-pass filtered and 20% of the diffraction limit. (c) DWFS reconstruction, low-pass filtered and 40% of the diffraction limit.

Tables (1)

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Table 1 Seeing Parameters for the Observations

Equations (15)

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Ĥf=WfexpjϕˆfWfexp-jϕˆf.
Ôf=i=1NĤi*fIifi=1NĤi*fĤif.
Ôf=1Ni=1NĤi*f IifĤi*fĤif.
Iif=HifOf+noise.
Ôf=1Ni=1N Ĥi*fHifĤi*fĤifOf+noise terms.
SNRDWFSf=K¯OfHfĤ*fK¯Ĥf2+K¯2Of2varHfĤ*f1/2.
SNRpsf=K¯Of2Hf21+K¯Of2Hf2.
SNRDWFSf HfĤ*fvarHfĤ*f1/2,
SNRpsf1.
SNRDWFSfHf2Hf4-Hf221/2.
SNRDWFSf K¯OfHfĤ*fĤf21/2,
SNRpsf K¯Of2Hf2,
OTF=exp-3.44 λfr05/3T0,
SNRDWFSf=IfĤ*fIfĤ*f2-IfĤ*f21/2.
SNRpsf=I*fIf-KI*f If-K2-I*f If-K21/2.

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