Abstract

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view. Space-variant effects are particularly severe in horizontal-path imaging, slant-path (air-to-ground or ground-to-air) geometries, and ground-based imaging of low-elevation satellites or astronomical objects. In these geometries, the isoplanatic angle can be comparable to or even smaller than the diffraction-limited resolution angle. We report on a postdetection correction method that seeks to correct for the effects of space-variant aberrations, with the goal of reconstructing near-diffraction-limited imagery. Our approach has been to generalize the method of phase-diverse speckle (PDS) by using a physically motivated distributed-phase-screen model. Simulation results are presented that demonstrate the reconstruction of near-diffraction-limited imagery under both matched and mismatched model assumptions. In addition, we present evidence that PDS could be used as a beaconless wavefront sensor in a multiconjugate adaptive optics system when imaging extended scenes.

© 2008 Optical Society of America

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2006 (2)

C. J. Carrano, “Mitigating atmospheric effects in high-resolution infrared surveillance imagery with bispectral speckle imaging,” Proc. SPIE 6316, 631602 (2006).
[CrossRef]

R. L. Kendrick, J.-N. Aubrun, R. Bell, “Wide-field Fizeau imaging telescope: experimental results,” Appl. Opt. 45, 4235-4240 (2006).
[CrossRef] [PubMed]

2005 (1)

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

2004 (2)

2003 (3)

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imagery,” Proc. SPIE 5001, 56-64 (2003).
[CrossRef]

C. J. Carrano, “Anisoplanatic performance of horizontal-path speckle imaging,” Proc. SPIE 5162, 14-27 (2003).
[CrossRef]

B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A 20, 1490-1504 (2003).
[CrossRef]

2002 (1)

C. J. Carrano, “Speckle imaging over horizontal paths,” Proc. SPIE 4825, 109-120 (2002).
[CrossRef]

2001 (1)

2000 (1)

J. H. Seldin, R. G. Paxman, V. G. Zarafis, L. Benson, and R. E. Stone, “Closed-loop wavefront sensing for a sparse-aperture multiple-telescope array using broadband phase diversity,” Proc. SPIE 4091, 48-63 (2000).
[CrossRef]

1999 (4)

1998 (2)

G. W. Carhart and M. A. Vorontsov, “Synthetic imaging: nonadaptive anisoplanatic image correction in atmospheric turbulence,” Opt. Lett. 23, 745-747 (1998).
[CrossRef]

J. R. Fienup, B. J. Thelen, R. G. Paxman, and D. A. Carrara, “Comparison of phase diversity and curvature wavefront sensing,” Proc. SPIE 3353, 930-940 (1998).
[CrossRef]

1997 (1)

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

1996 (1)

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 467, 1087-1099 (1996).
[CrossRef]

1995 (1)

1994 (8)

1993 (1)

1992 (1)

1990 (1)

1989 (1)

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503-528 (1989).
[CrossRef]

1988 (1)

1985 (1)

M. I. Miller, D. L. Snyder, and T. R. Miller, “Maximum-likelihood reconstruction for single photon emission computed tomography,” IEEE Trans. Nucl. Sci. 32, 769-778 (1985).
[CrossRef]

1983 (1)

1979 (1)

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32-39 (1979).

1966 (1)

Acton, D. S.

Aubrun, J.-N.

Bates, R. H. T.

Bell, R.

Benson, L.

J. H. Seldin, R. G. Paxman, V. G. Zarafis, L. Benson, and R. E. Stone, “Closed-loop wavefront sensing for a sparse-aperture multiple-telescope array using broadband phase diversity,” Proc. SPIE 4091, 48-63 (2000).
[CrossRef]

Bezuit, J.-L.

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

Blanc, A.

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

Bowers, C. W.

Carhart, G. W.

Carrano, C. J.

C. J. Carrano, “Mitigating atmospheric effects in high-resolution infrared surveillance imagery with bispectral speckle imaging,” Proc. SPIE 6316, 631602 (2006).
[CrossRef]

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imagery,” Proc. SPIE 5001, 56-64 (2003).
[CrossRef]

C. J. Carrano, “Anisoplanatic performance of horizontal-path speckle imaging,” Proc. SPIE 5162, 14-27 (2003).
[CrossRef]

C. J. Carrano, “Speckle imaging over horizontal paths,” Proc. SPIE 4825, 109-120 (2002).
[CrossRef]

Carrara, D. A.

Chidlaw, R.

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32-39 (1979).

Conan, J.-M.

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

Dainty, J. C.

J. C. Dainty, “Stellar speckle imaging,” in Topics in Applied Physics: Laser Speckle and Related Phenomena, 2nd ed., J.C.Dainty, ed. (Springer-Verlag, 1984), pp. 297-328.

Dean, B. H.

Duncan, A. L.

Ellerbroek, B. L.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783-805 (1994).
[CrossRef]

J. H. Seldin, R. G. Paxman, and B. L. Ellerbroek, “Post-detection correction of compensated imagery using phase-diverse speckle,” in Adaptive Optics, Vol. 23 of OSA Technical Digest Series (Optical Society of America, 1995), pp. 471-476.

J. H. Seldin, R. G. Paxman, B. L. Ellerbroek, and D. C. Johnston, “Phase-diverse speckle restorations of artificial satellites imaged with adaptive-optics compensation,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (addendum) (Optical Society of America, 1996).

Faisal, M.

Fienup, J. R.

J. R. Fienup, B. J. Thelen, R. G. Paxman, and D. A. Carrara, “Comparison of phase diversity and curvature wavefront sensing,” Proc. SPIE 3353, 930-940 (1998).
[CrossRef]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072-1085 (1992).
[CrossRef]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of OSA Technical Digest Series 1992 (Optical Society of American, 1992).

Flatte, S. M.

Fontanella, J. C.

Frank, Z. A.

R. A. Shine, A. M. Title, T. D. Tarbell, K. Smith, and Z. A. Frank, “High-resolution observations of the Evershed effect in sunspots,” Astrophys. J. 430, 413-424 (1994).
[CrossRef]

Fraser, D.

Fried, D. L.

Fright, W. R.

Fusco, T.

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, “Nonisoplanatic imaging by phase diversity,” Opt. Lett. 19, 493-495 (1994).
[CrossRef] [PubMed]

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32-39 (1979).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

Helstrom, C. W.

Hunt, B. R.

Johnston, D. C.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394-408 (1994).
[CrossRef]

J. H. Seldin, R. G. Paxman, B. L. Ellerbroek, and D. C. Johnston, “Phase-diverse speckle restorations of artificial satellites imaged with adaptive-optics compensation,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (addendum) (Optical Society of America, 1996).

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

Keller, C. U.

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 467, 1087-1099 (1996).
[CrossRef]

R. G. Paxman, J. H. Seldin, and C. U. Keller, “Phase-diversity data sets and processing strategies,” in High Resolution Solar Physics: Theory, Observations, and Techniques, T.R.Rimmele, K.S.Balasubramaniam, and R.R.Raddick, eds., Astron. Soc. Pac. Conf. Ser. 13, 311-329 (1999).

Kendrick, R. L.

Lambert, A.

Lanterman, A. D.

Lee, D. J.

Liu, D. C.

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503-528 (1989).
[CrossRef]

Löfdahl, M.

M. Löfdahl and G. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243 (1994).

Löfdahl, M. G.

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 467, 1087-1099 (1996).
[CrossRef]

Martin, J. M.

Michau, V.

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

Miller, J. J.

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2-10 (1999).
[CrossRef]

Miller, M. I.

M. I. Miller, D. L. Snyder, and T. R. Miller, “Maximum-likelihood reconstruction for single photon emission computed tomography,” IEEE Trans. Nucl. Sci. 32, 769-778 (1985).
[CrossRef]

Miller, T. R.

M. I. Miller, D. L. Snyder, and T. R. Miller, “Maximum-likelihood reconstruction for single photon emission computed tomography,” IEEE Trans. Nucl. Sci. 32, 769-778 (1985).
[CrossRef]

Nicolle, M. N.

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

Nocedal, J.

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503-528 (1989).
[CrossRef]

Paxman, R. G.

J. H. Seldin, R. G. Paxman, V. G. Zarafis, L. Benson, and R. E. Stone, “Closed-loop wavefront sensing for a sparse-aperture multiple-telescope array using broadband phase diversity,” Proc. SPIE 4091, 48-63 (2000).
[CrossRef]

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2-10 (1999).
[CrossRef]

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Maximum a posteriori estimation of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data,” J. Opt. Soc. Am. A 16, 1016-1025 (1999).
[CrossRef]

J. R. Fienup, B. J. Thelen, R. G. Paxman, and D. A. Carrara, “Comparison of phase diversity and curvature wavefront sensing,” Proc. SPIE 3353, 930-940 (1998).
[CrossRef]

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 467, 1087-1099 (1996).
[CrossRef]

J. H. Seldin and R. G. Paxman, “Phase-diverse speckle reconstruction of solar data,” Proc. SPIE 2302, 268-280 (1994).
[CrossRef]

R. G. Paxman, B. J. Thelen, and J. H. Seldin, “Phase-diversity correction of space-variant turbulence-induced blur,” Opt. Lett. 19, 1231-1233 (1994).
[CrossRef] [PubMed]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072-1085 (1992).
[CrossRef]

R. G. Paxman and J. H. Seldin, “Fine-resolution imaging of solar features using phase-diverse speckle imaging,” in Proceedings of the 13th Sacramento Peak Summer Workshop, Real Time and Post-Facto Solar Image Correction, R.R.Raddick, ed. (National Solar Observatory, 1994), pp. 112-118.

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of OSA Technical Digest Series 1992 (Optical Society of American, 1992).

J. H. Seldin, R. G. Paxman, and B. L. Ellerbroek, “Post-detection correction of compensated imagery using phase-diverse speckle,” in Adaptive Optics, Vol. 23 of OSA Technical Digest Series (Optical Society of America, 1995), pp. 471-476.

J. H. Seldin, R. G. Paxman, B. L. Ellerbroek, and D. C. Johnston, “Phase-diverse speckle restorations of artificial satellites imaged with adaptive-optics compensation,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (addendum) (Optical Society of America, 1996).

R. G. Paxman, J. H. Seldin, and C. U. Keller, “Phase-diversity data sets and processing strategies,” in High Resolution Solar Physics: Theory, Observations, and Techniques, T.R.Rimmele, K.S.Balasubramaniam, and R.R.Raddick, eds., Astron. Soc. Pac. Conf. Ser. 13, 311-329 (1999).

Prasad, S.

Primot, J.

Reiley, M. F.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

Roggemann, M. C.

Rousset, G.

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598-1608 (1990).
[CrossRef]

Scharmer, G.

M. Löfdahl and G. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243 (1994).

Scharmer, G. B.

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 467, 1087-1099 (1996).
[CrossRef]

Schulz, T. J.

T. J. Schulz, “Multi-frame blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064-1073 (1993).
[CrossRef]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072-1085 (1992).
[CrossRef]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of OSA Technical Digest Series 1992 (Optical Society of American, 1992).

Seldin, J. H.

J. H. Seldin, R. G. Paxman, V. G. Zarafis, L. Benson, and R. E. Stone, “Closed-loop wavefront sensing for a sparse-aperture multiple-telescope array using broadband phase diversity,” Proc. SPIE 4091, 48-63 (2000).
[CrossRef]

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Maximum a posteriori estimation of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data,” J. Opt. Soc. Am. A 16, 1016-1025 (1999).
[CrossRef]

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 467, 1087-1099 (1996).
[CrossRef]

J. H. Seldin and R. G. Paxman, “Phase-diverse speckle reconstruction of solar data,” Proc. SPIE 2302, 268-280 (1994).
[CrossRef]

R. G. Paxman, B. J. Thelen, and J. H. Seldin, “Phase-diversity correction of space-variant turbulence-induced blur,” Opt. Lett. 19, 1231-1233 (1994).
[CrossRef] [PubMed]

R. G. Paxman and J. H. Seldin, “Fine-resolution imaging of solar features using phase-diverse speckle imaging,” in Proceedings of the 13th Sacramento Peak Summer Workshop, Real Time and Post-Facto Solar Image Correction, R.R.Raddick, ed. (National Solar Observatory, 1994), pp. 112-118.

J. H. Seldin, R. G. Paxman, and B. L. Ellerbroek, “Post-detection correction of compensated imagery using phase-diverse speckle,” in Adaptive Optics, Vol. 23 of OSA Technical Digest Series (Optical Society of America, 1995), pp. 471-476.

J. H. Seldin, R. G. Paxman, B. L. Ellerbroek, and D. C. Johnston, “Phase-diverse speckle restorations of artificial satellites imaged with adaptive-optics compensation,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (addendum) (Optical Society of America, 1996).

R. G. Paxman, J. H. Seldin, and C. U. Keller, “Phase-diversity data sets and processing strategies,” in High Resolution Solar Physics: Theory, Observations, and Techniques, T.R.Rimmele, K.S.Balasubramaniam, and R.R.Raddick, eds., Astron. Soc. Pac. Conf. Ser. 13, 311-329 (1999).

Shine, R. A.

R. A. Shine, A. M. Title, T. D. Tarbell, K. Smith, and Z. A. Frank, “High-resolution observations of the Evershed effect in sunspots,” Astrophys. J. 430, 413-424 (1994).
[CrossRef]

Smith, K.

R. A. Shine, A. M. Title, T. D. Tarbell, K. Smith, and Z. A. Frank, “High-resolution observations of the Evershed effect in sunspots,” Astrophys. J. 430, 413-424 (1994).
[CrossRef]

Snyder, D. L.

D. L. Snyder, C. W. Helstrom, A. D. Lanterman, M. Faisal, and R. L. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, 272-283 (1995).
[CrossRef]

M. I. Miller, D. L. Snyder, and T. R. Miller, “Maximum-likelihood reconstruction for single photon emission computed tomography,” IEEE Trans. Nucl. Sci. 32, 769-778 (1985).
[CrossRef]

Stone, R. E.

J. H. Seldin, R. G. Paxman, V. G. Zarafis, L. Benson, and R. E. Stone, “Closed-loop wavefront sensing for a sparse-aperture multiple-telescope array using broadband phase diversity,” Proc. SPIE 4091, 48-63 (2000).
[CrossRef]

Stribling, B. E.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

Tarbell, T. D.

R. A. Shine, A. M. Title, T. D. Tarbell, K. Smith, and Z. A. Frank, “High-resolution observations of the Evershed effect in sunspots,” Astrophys. J. 430, 413-424 (1994).
[CrossRef]

Thelen, B. J.

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2-10 (1999).
[CrossRef]

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Maximum a posteriori estimation of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data,” J. Opt. Soc. Am. A 16, 1016-1025 (1999).
[CrossRef]

J. R. Fienup, B. J. Thelen, R. G. Paxman, and D. A. Carrara, “Comparison of phase diversity and curvature wavefront sensing,” Proc. SPIE 3353, 930-940 (1998).
[CrossRef]

R. G. Paxman, B. J. Thelen, and J. H. Seldin, “Phase-diversity correction of space-variant turbulence-induced blur,” Opt. Lett. 19, 1231-1233 (1994).
[CrossRef] [PubMed]

Thorpe, G.

Title, A. M.

R. A. Shine, A. M. Title, T. D. Tarbell, K. Smith, and Z. A. Frank, “High-resolution observations of the Evershed effect in sunspots,” Astrophys. J. 430, 413-424 (1994).
[CrossRef]

Vorontsov, M. A.

Welsh, B. M.

White, R. L.

Zarafis, V. G.

J. H. Seldin, R. G. Paxman, V. G. Zarafis, L. Benson, and R. E. Stone, “Closed-loop wavefront sensing for a sparse-aperture multiple-telescope array using broadband phase diversity,” Proc. SPIE 4091, 48-63 (2000).
[CrossRef]

Appl. Opt. (3)

Astron. Astrophys. Suppl. Ser. (1)

M. Löfdahl and G. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243 (1994).

Astrophys. J. (2)

R. G. Paxman, J. H. Seldin, M. G. Löfdahl, G. B. Scharmer, and C. U. Keller, “Evaluation of phase-diversity techniques for solar-image restoration,” Astrophys. J. 467, 1087-1099 (1996).
[CrossRef]

R. A. Shine, A. M. Title, T. D. Tarbell, K. Smith, and Z. A. Frank, “High-resolution observations of the Evershed effect in sunspots,” Astrophys. J. 430, 413-424 (1994).
[CrossRef]

C. R. Phys. (1)

T. Fusco, M. N. Nicolle, G. Rousset, V. Michau, A. Blanc, J.-L. Bezuit, and J.-M. Conan, “Problmatique de l'analyse de front d'onde en optique adaptative multiconjugue,” C. R. Phys. 6, 1049-4058 (2005).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

M. I. Miller, D. L. Snyder, and T. R. Miller, “Maximum-likelihood reconstruction for single photon emission computed tomography,” IEEE Trans. Nucl. Sci. 32, 769-778 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (12)

D. L. Snyder, C. W. Helstrom, A. D. Lanterman, M. Faisal, and R. L. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, 272-283 (1995).
[CrossRef]

J. Primot, G. Rousset, and J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598-1608 (1990).
[CrossRef]

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072-1085 (1992).
[CrossRef]

M. A. Vorontsov and G. W. Carhart, “Anisoplanatic imaging through turbulent media: image recovery by local information fusion from a set of short-exposure images,” J. Opt. Soc. Am. A 18, 1312-1324 (2001).
[CrossRef]

B. H. Dean and C. W. Bowers, “Diversity selection for phase-diverse phase retrieval,” J. Opt. Soc. Am. A 20, 1490-1504 (2003).
[CrossRef]

D. C. Johnston and B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394-408 (1994).
[CrossRef]

B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783-805 (1994).
[CrossRef]

D. J. Lee, M. C. Roggemann, and B. M. Welsh, “Cramer-Rao analysis of phase-diverse wave-front sensing,” J. Opt. Soc. Am. A 16, 1005-1015 (1999).
[CrossRef]

B. J. Thelen, R. G. Paxman, D. A. Carrara, and J. H. Seldin, “Maximum a posteriori estimation of fixed aberrations, dynamic aberrations, and the object from phase-diverse speckle data,” J. Opt. Soc. Am. A 16, 1016-1025 (1999).
[CrossRef]

D. Fraser, G. Thorpe, and A. Lambert, “Atmospheric turbulence visualization with wide-area motion-blur restoration,” J. Opt. Soc. Am. A 16, 1751-1758 (1999).
[CrossRef]

T. J. Schulz, “Multi-frame blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064-1073 (1993).
[CrossRef]

S. Prasad, “Fisher-information-based analysis of a phase-diversity-speckle imaging system,” J. Opt. Soc. Am. A 21, 2073-2088 (2004).
[CrossRef]

Math. Program. (1)

D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program. 45, 503-528 (1989).
[CrossRef]

Opt. Lett. (4)

Proc. SPIE (10)

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, and D. C. Johnston, “Space-object identification using phase-diverse speckle,” Proc. SPIE 3170, 2-15 (1997).
[CrossRef]

J. H. Seldin, R. G. Paxman, V. G. Zarafis, L. Benson, and R. E. Stone, “Closed-loop wavefront sensing for a sparse-aperture multiple-telescope array using broadband phase diversity,” Proc. SPIE 4091, 48-63 (2000).
[CrossRef]

R. G. Paxman, B. J. Thelen, and J. J. Miller, “Optimal simulation of volume turbulence with phase screens,” Proc. SPIE 3763-01, 2-10 (1999).
[CrossRef]

J. H. Seldin and R. G. Paxman, “Phase-diverse speckle reconstruction of solar data,” Proc. SPIE 2302, 268-280 (1994).
[CrossRef]

R. A. Gonsalves and R. Chidlaw, “Wavefront sensing by phase retrieval,” Proc. SPIE 207, 32-39 (1979).

J. R. Fienup, B. J. Thelen, R. G. Paxman, and D. A. Carrara, “Comparison of phase diversity and curvature wavefront sensing,” Proc. SPIE 3353, 930-940 (1998).
[CrossRef]

C. J. Carrano, “Speckle imaging over horizontal paths,” Proc. SPIE 4825, 109-120 (2002).
[CrossRef]

C. J. Carrano, “Progress in horizontal and slant-path imaging using speckle imagery,” Proc. SPIE 5001, 56-64 (2003).
[CrossRef]

C. J. Carrano, “Anisoplanatic performance of horizontal-path speckle imaging,” Proc. SPIE 5162, 14-27 (2003).
[CrossRef]

C. J. Carrano, “Mitigating atmospheric effects in high-resolution infrared surveillance imagery with bispectral speckle imaging,” Proc. SPIE 6316, 631602 (2006).
[CrossRef]

Other (8)

J. C. Dainty, “Stellar speckle imaging,” in Topics in Applied Physics: Laser Speckle and Related Phenomena, 2nd ed., J.C.Dainty, ed. (Springer-Verlag, 1984), pp. 297-328.

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Phase-diverse speckle interferometry,” in Signal Recovery and Synthesis IV, Vol. 11 of OSA Technical Digest Series 1992 (Optical Society of American, 1992).

R. G. Paxman and J. H. Seldin, “Fine-resolution imaging of solar features using phase-diverse speckle imaging,” in Proceedings of the 13th Sacramento Peak Summer Workshop, Real Time and Post-Facto Solar Image Correction, R.R.Raddick, ed. (National Solar Observatory, 1994), pp. 112-118.

J. H. Seldin, R. G. Paxman, and B. L. Ellerbroek, “Post-detection correction of compensated imagery using phase-diverse speckle,” in Adaptive Optics, Vol. 23 of OSA Technical Digest Series (Optical Society of America, 1995), pp. 471-476.

J. H. Seldin, R. G. Paxman, B. L. Ellerbroek, and D. C. Johnston, “Phase-diverse speckle restorations of artificial satellites imaged with adaptive-optics compensation,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (addendum) (Optical Society of America, 1996).

R. G. Paxman, J. H. Seldin, and C. U. Keller, “Phase-diversity data sets and processing strategies,” in High Resolution Solar Physics: Theory, Observations, and Techniques, T.R.Rimmele, K.S.Balasubramaniam, and R.R.Raddick, eds., Astron. Soc. Pac. Conf. Ser. 13, 311-329 (1999).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

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Figures (11)

Fig. 1
Fig. 1

Volume turbulence induces space-variant blur. Light emanating from spatially separated object points will encounter different volumes of turbulence, thereby yielding PSFs with differing shapes.

Fig. 2
Fig. 2

Data-collection scheme for phase-diverse speckle imaging. Short-exposure in- and out-of-focus image pairs are collected for each of multiple turbulence realizations.

Fig. 3
Fig. 3

Distributed-phase-screen model used to approximate the effects of volume turbulence.

Fig. 4
Fig. 4

Object and examples of image data simulated with three phase screens.

Fig. 5
Fig. 5

Space variance associated with three-phase-screen simulation. A five-point object is given in (a). Images of (a) are shown in (b) through (f) for five different turbulence realizations. The space variance is manifest by both the distortion and the variations in PSF shape.

Fig. 6
Fig. 6

Object, diffraction-limited image, and PDS object estimate for GeOp matched case. Both Nyquist-sampled (upper row) and up-sampled (lower row) versions of these images are given. PDS achieves near-diffraction-limited resolution.

Fig. 7
Fig. 7

Scatter plots—from the matched case—of PDS-estimated aberration coefficients versus true aberration coefficients for phase screens 1,2,3, and five realizations. Here the numbering is such that phase screen 1 is closest to the pupil and phase screen 3 is closest to the object. The index j on the plots refers to aberration realization. These results show that in the matched case, the PDS algorithm generates relatively accurate aberration coefficients.  

Fig. 8
Fig. 8

Examples of data simulated with 20 phase screens.

Fig. 9
Fig. 9

Object, diffraction-limited image, and PDS object estimates for the two mismatched simulation experiments. Both Nyquist-sampled (upper row) and up-sampled (lower row) versions of these images are given. The third column shows results where the data were generated using 20 phase screens and GeOp, and only three phase screens were used in estimating the object from the data. The fourth column shows results where the data were generated using 20 phase screens and a Fresnel propagation model, and again only three phase screens were used to estimate the object. Note that PDS achieves close to diffraction-limited resolution in both cases, though there is a perceptible loss in quality for the estimates based on Fresnel data.

Fig. 10
Fig. 10

Schematic for proposed PDS multiconjugate adaptive-optics system. PD image pairs continually accumulate to form a time series of data. At time t 0 , a window of the J most-recently accumulated image pairs are processed using the PDS algorithm. Distributed-phase-screen estimates for the most recent realization, corresponding to time t 0 , are then applied as phase corrections in the appropriate conjugate planes. The sliding-window construct affords near-real-time correction.

Fig. 11
Fig. 11

Simulation results for PDS multiconjugate AO compensation. The first and third rows show the ten (noiseless) conventional images corresponding to the original PDS image pairs generated with the Fresnel propagation model utilizing 19 phase screens. Based on noisy realizations of these conventional images and the corresponding diversity images, we estimated for all ten realizations the aberrations at the three different plane locations and then compensated for the most recent in the appropriate conjugate planes. The second and fourth rows of images are the resultant (noiseless) multiconjugate compensated imagery. All of the compensated images show significant improvement over their uncompensated counterparts.

Tables (3)

Tables Icon

Table 1 Overview of Simulation Results

Tables Icon

Table 2 Parameters Characterizing Horizontal-Path Simulation Data Generation

Tables Icon

Table 3 Phase Screen Locations Relative to Pupil and Incremental r o for the GeOp Matched Simulation Experiment

Equations (19)

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

ϕ j ( u , x ) = l = 1 L ϕ j l [ ( 1 z l R ) u + z l R x ] ,
x = x f o ( R f o ) ,
ϕ j ( u , x ) = l = 1 L ϕ j l [ ( 1 z l R ) u ( R f o R f o ) z l x ] .
ϕ j l ( u ) = m α j l m ψ l m ( u ) ,
s j k ( x , x ) = h j k ( x x , x ) 2 x h j k ( x , x ) 2 ,
h j k ( x , x ) = F { H j k ( u , x ) } ,
H j k ( u , x ) = H ( u ) exp { i [ ϕ j ( u , x ) + θ k ( u ) ] } .
F { c ( u ) } = u c ( u ) exp ( i 2 π x , u N ) ,
g j k ( x ) = x f ( x ) s j k ( x , x ) ,
{ d j k ( x ) } , { j = 1 , 2 , J k = 1 , 2 , , K } ,
d j k ( x ) = P [ g j k ( x ) ] + ϵ j k ( x ) ,
d ̃ j k ( x ) d j k ( x ) + σ ϵ 2 ,
g ̃ j k ( x ) g j k ( x ) + σ ϵ 2 ;
d ̃ j k ( x ) P [ g ̃ j k ( x ) ] .
L ( f , { α j } ) = j = 1 J k = 1 K x { d ̃ j k ( x ) ln [ g ̃ j k ( x ) ] g ̃ j k ( x ) }
= j = 1 J k = 1 K x { d ̃ j k ( x ) ln [ g ̃ j k ( x ) ] } J K x f ( x ) J K N 2 σ ϵ 2 ,
L ( f , { α j } ) f ( x ) = j = 1 J k = 1 K x d ̃ j k ( x ) g ̃ j k ( x ) s j k ( x , x ) J K .
L ( f , { α j } ) α j l m = k = 1 K x d ̃ j k ( x ) g ̃ j k ( x ) [ x f ( x ) s j k ( x , x ) α j l m ] ,
s j k ( x , x ) α j l m = 2 S o I ( h j k * ( x x , x ) F { ψ j l m [ ( 1 z l R ) u ( R f o R f o ) z l x ] H j k ( u , x ) exp ( i 2 π x , u N ) } ) ,

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