Abstract

We show in benchtop experiments that wave-front phase estimation by phase diversity can be significantly improved by simultaneous amplitude estimation. Processing speed, which will be important for real-time wave-front control applications, can be enhanced by use of small-format detectors with pixels that do not fully sample the diffraction limit. Using an object-independent phase-diversity algorithm, we show that, for both pointlike and extended objects, the fidelity of the phase and amplitude estimates degrades gracefully, rather than catastrophically, as the sampling becomes coarser. We show in simulation that the same algorithm also improves the fidelity of image reconstruction of complex targets.

© 2002 Optical Society of America

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  1. R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
    [CrossRef]
  2. R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
    [CrossRef]
  3. M. G. Löfdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. 107, 243–264 (1994).
  4. J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).
  5. D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
    [CrossRef]
  6. R. G. Paxman, J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
    [CrossRef]
  7. C. Roddier, F. Roddier, “Combined approach to the Hubble Space Telescope wave-front distortion analysis,” Appl. Opt. 32, 2992–3008 (1993).
    [CrossRef] [PubMed]
  8. J. R. Fienup, J. C. Marron, T. J. Schulz, J. H. Seldin, “Hubble Space Telescope characterized by using phase-retrieval algorithms,” Appl. Opt. 32, 1747–1767 (1993).
    [CrossRef] [PubMed]
  9. J. E. Krist, C. J. Burrows, “Phase-retrieval analysis of pre- and post-repair Hubble Space Telescope images,” Appl. Opt. 34, 4951–4964 (1995).
    [CrossRef] [PubMed]
  10. M. Mountain, F. Gillett, R. Kurz, “The Gemini 8m telescopes project,” in Optical Telescopes of Today and Tomorrow, A. L. Ardeberg, ed., Proc. SPIE2871, 15–23 (1996).
    [CrossRef]
  11. For information on the Next Generation Space Telescope, see http://www.ngst.nasa.gov .
  12. G. B. Scharmer, “Object-independent fast phase-diversity,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Astron. Soc. Pac. Conf. Ser.183, 330–341 (1999).
  13. M. G. Löfdahl, G. B. Scharmer, W. Wei, “Calibration of a deformable mirror and Strehl ratio measurements by use of phase diversity,” Appl. Opt. 39, 94–103 (2000).
    [CrossRef]
  14. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
    [CrossRef]
  15. M. Lloyd-Hart, S. M. Jefferies, E. K. Hege, J. R. P. Angel, “Wave-front sensing with time-of-flight phase diversity,” Opt. Lett. 26, 402–404 (2001).
    [CrossRef]
  16. J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).
  17. R. A. Gonsalves, “Compensation of scintillation with a phase-only adaptive optic,” Opt. Lett. 22, 588–590 (1997).
    [CrossRef] [PubMed]
  18. R. Chidlaw, A. Devaney, R. A. Gonsalves, “Analytical studies of phase estimation techniques,” Defense Technical ReportRADC-TR-79-221-Vol. 1 (Rome Air Development Center, Griffiss Air Force Base, New York, 1979).
  19. D. Dravins, L. Lindegren, E. Mezey, A. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
    [CrossRef]
  20. R. Irwan, R. G. Lane, “Phase retrieval with prior information,” J. Opt. Soc. Am. A 15, 2302–2311 (1998).
    [CrossRef]
  21. W-Y. V. Leung, R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” in Image Reconstruction from Incomplete Data, M. A. Fiddy, R. P. Millane, eds., Proc. SPIE4123, 73–83 (2000).
    [CrossRef]
  22. E. K. Hege, “First order imaging methods: an introduction,” in Diffraction-Limited Imaging with Very Large Telescopes, D. M. Alloin, J.-M. Mariotti, eds. (Kluwer Academic, Boston, Mass., 1989), pp. 113–124.
    [CrossRef]
  23. W. H. Press, S. A. Teukolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press, Cambridge, UK, 1992).
  24. R. K. Piña, R. C. Puetter, “Incorporation of spatial information in Bayesian image reconstruction: the maximum residual likelihood criterion,” Publ. Astron. Soc. Pac. 104, 1096–1103 (1992).
    [CrossRef]

2001 (1)

2000 (1)

1998 (1)

1997 (2)

R. A. Gonsalves, “Compensation of scintillation with a phase-only adaptive optic,” Opt. Lett. 22, 588–590 (1997).
[CrossRef] [PubMed]

D. Dravins, L. Lindegren, E. Mezey, A. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

1995 (1)

1994 (1)

M. G. Löfdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. 107, 243–264 (1994).

1993 (2)

1992 (2)

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

R. K. Piña, R. C. Puetter, “Incorporation of spatial information in Bayesian image reconstruction: the maximum residual likelihood criterion,” Publ. Astron. Soc. Pac. 104, 1096–1103 (1992).
[CrossRef]

1988 (1)

1982 (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

Angel, J. R. P.

Burrows, C. J.

Carrara, D. A.

J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).

Chidlaw, R.

R. Chidlaw, A. Devaney, R. A. Gonsalves, “Analytical studies of phase estimation techniques,” Defense Technical ReportRADC-TR-79-221-Vol. 1 (Rome Air Development Center, Griffiss Air Force Base, New York, 1979).

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
[CrossRef]

Devaney, A.

R. Chidlaw, A. Devaney, R. A. Gonsalves, “Analytical studies of phase estimation techniques,” Defense Technical ReportRADC-TR-79-221-Vol. 1 (Rome Air Development Center, Griffiss Air Force Base, New York, 1979).

Dravins, D.

D. Dravins, L. Lindegren, E. Mezey, A. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Ellerbroek, B. L.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).

Fienup, J. R.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press, Cambridge, UK, 1992).

Ford, S. D.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Gillett, F.

M. Mountain, F. Gillett, R. Kurz, “The Gemini 8m telescopes project,” in Optical Telescopes of Today and Tomorrow, A. L. Ardeberg, ed., Proc. SPIE2871, 15–23 (1996).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, “Compensation of scintillation with a phase-only adaptive optic,” Opt. Lett. 22, 588–590 (1997).
[CrossRef] [PubMed]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
[CrossRef]

R. Chidlaw, A. Devaney, R. A. Gonsalves, “Analytical studies of phase estimation techniques,” Defense Technical ReportRADC-TR-79-221-Vol. 1 (Rome Air Development Center, Griffiss Air Force Base, New York, 1979).

Hege, E. K.

M. Lloyd-Hart, S. M. Jefferies, E. K. Hege, J. R. P. Angel, “Wave-front sensing with time-of-flight phase diversity,” Opt. Lett. 26, 402–404 (2001).
[CrossRef]

E. K. Hege, “First order imaging methods: an introduction,” in Diffraction-Limited Imaging with Very Large Telescopes, D. M. Alloin, J.-M. Mariotti, eds. (Kluwer Academic, Boston, Mass., 1989), pp. 113–124.
[CrossRef]

Hunt, B. R.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Irwan, R.

Jefferies, S. M.

Johnston, D. C.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).

Krist, J. E.

Kurz, R.

M. Mountain, F. Gillett, R. Kurz, “The Gemini 8m telescopes project,” in Optical Telescopes of Today and Tomorrow, A. L. Ardeberg, ed., Proc. SPIE2871, 15–23 (1996).
[CrossRef]

Lane, R. G.

R. Irwan, R. G. Lane, “Phase retrieval with prior information,” J. Opt. Soc. Am. A 15, 2302–2311 (1998).
[CrossRef]

W-Y. V. Leung, R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” in Image Reconstruction from Incomplete Data, M. A. Fiddy, R. P. Millane, eds., Proc. SPIE4123, 73–83 (2000).
[CrossRef]

Leung, W-Y. V.

W-Y. V. Leung, R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” in Image Reconstruction from Incomplete Data, M. A. Fiddy, R. P. Millane, eds., Proc. SPIE4123, 73–83 (2000).
[CrossRef]

Lindegren, L.

D. Dravins, L. Lindegren, E. Mezey, A. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Lloyd-Hart, M.

Löfdahl, M. G.

M. G. Löfdahl, G. B. Scharmer, W. Wei, “Calibration of a deformable mirror and Strehl ratio measurements by use of phase diversity,” Appl. Opt. 39, 94–103 (2000).
[CrossRef]

M. G. Löfdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. 107, 243–264 (1994).

Marron, J. C.

Mezey, E.

D. Dravins, L. Lindegren, E. Mezey, A. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Miller, J. J.

J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).

Mountain, M.

M. Mountain, F. Gillett, R. Kurz, “The Gemini 8m telescopes project,” in Optical Telescopes of Today and Tomorrow, A. L. Ardeberg, ed., Proc. SPIE2871, 15–23 (1996).
[CrossRef]

Paxman, R. G.

R. G. Paxman, T. J. Schulz, 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, J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A 5, 914–923 (1988).
[CrossRef]

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).

Piña, R. K.

R. K. Piña, R. C. Puetter, “Incorporation of spatial information in Bayesian image reconstruction: the maximum residual likelihood criterion,” Publ. Astron. Soc. Pac. 104, 1096–1103 (1992).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press, Cambridge, UK, 1992).

Puetter, R. C.

R. K. Piña, R. C. Puetter, “Incorporation of spatial information in Bayesian image reconstruction: the maximum residual likelihood criterion,” Publ. Astron. Soc. Pac. 104, 1096–1103 (1992).
[CrossRef]

Reiley, M. F.

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).

Roddier, C.

Roddier, F.

Roggeman, M. C.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Rountree, J. C.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Scharmer, G. B.

M. G. Löfdahl, G. B. Scharmer, W. Wei, “Calibration of a deformable mirror and Strehl ratio measurements by use of phase diversity,” Appl. Opt. 39, 94–103 (2000).
[CrossRef]

M. G. Löfdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. 107, 243–264 (1994).

G. B. Scharmer, “Object-independent fast phase-diversity,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Astron. Soc. Pac. Conf. Ser.183, 330–341 (1999).

Schulz, T. J.

J. R. Fienup, J. C. Marron, T. J. Schulz, J. H. Seldin, “Hubble Space Telescope characterized by using phase-retrieval algorithms,” Appl. Opt. 32, 1747–1767 (1993).
[CrossRef] [PubMed]

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

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Schulze, K. J.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Seldin, J. H.

J. R. Fienup, J. C. Marron, T. J. Schulz, J. H. Seldin, “Hubble Space Telescope characterized by using phase-retrieval algorithms,” Appl. Opt. 32, 1747–1767 (1993).
[CrossRef] [PubMed]

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).

Shepard, D. G.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Stribling, B. E.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press, Cambridge, UK, 1992).

Thelan, B. J.

J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).

Tyler, D. W.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

van Kampen, W. B.

J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).

van Kampen, W. C.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Vettering, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press, Cambridge, UK, 1992).

Wei, W.

Welsh, B. M.

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

Young, A.

D. Dravins, L. Lindegren, E. Mezey, A. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Appl. Opt. (4)

Astron. Astrophys. (1)

M. G. Löfdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. 107, 243–264 (1994).

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

Opt. Eng. (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
[CrossRef]

Opt. Lett. (2)

Publ. Astron. Soc. Pac. (2)

D. Dravins, L. Lindegren, E. Mezey, A. Young, “Atmospheric intensity scintillation of stars. I. Statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

R. K. Piña, R. C. Puetter, “Incorporation of spatial information in Bayesian image reconstruction: the maximum residual likelihood criterion,” Publ. Astron. Soc. Pac. 104, 1096–1103 (1992).
[CrossRef]

Other (11)

R. Chidlaw, A. Devaney, R. A. Gonsalves, “Analytical studies of phase estimation techniques,” Defense Technical ReportRADC-TR-79-221-Vol. 1 (Rome Air Development Center, Griffiss Air Force Base, New York, 1979).

J. H. Seldin, B. J. Thelan, D. A. Carrara, R. G. Paxman, J. J. Miller, W. B. van Kampen, “Phase-diverse wavefront sensing and multi-frame image reconstruction,” ERIM International Rep. 463000-7-F (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999).

W-Y. V. Leung, R. G. Lane, “Blind deconvolution of images blurred by atmospheric speckle,” in Image Reconstruction from Incomplete Data, M. A. Fiddy, R. P. Millane, eds., Proc. SPIE4123, 73–83 (2000).
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E. K. Hege, “First order imaging methods: an introduction,” in Diffraction-Limited Imaging with Very Large Telescopes, D. M. Alloin, J.-M. Mariotti, eds. (Kluwer Academic, Boston, Mass., 1989), pp. 113–124.
[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vettering, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge, U. Press, Cambridge, UK, 1992).

J. H. Seldin, M. F. Reiley, R. G. Paxman, B. E. Stribling, B. L. Ellerbroek, D. C. Johnston, “Space-object identification using phase-diverse speckle,” in Digital Image Recovery and Synthesis III, T. J. Schulz, ed., Proc. SPIE3170, 2–15 (1997).

D. W. Tyler, S. D. Ford, B. R. Hunt, R. G. Paxman, M. C. Roggeman, J. C. Rountree, T. J. Schulz, K. J. Schulze, J. H. Seldin, D. G. Shepard, B. E. Stribling, W. C. van Kampen, B. M. Welsh, “Comparison of image reconstruction algorithms using adaptive optics instrumentation,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 160–171 (1998).
[CrossRef]

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).
[CrossRef]

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[CrossRef]

For information on the Next Generation Space Telescope, see http://www.ngst.nasa.gov .

G. B. Scharmer, “Object-independent fast phase-diversity,” in High Resolution Solar Physics: Theory, Observations and Techniques, T. Rimmele, R. R. Radick, K. S. Balasubramaniam, eds., Astron. Soc. Pac. Conf. Ser.183, 330–341 (1999).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup used to record the true amplitude and phase variations, introduced by a plastic screen, and the phase-diverse focal-plane data.

Fig. 2
Fig. 2

Left, wave-front phases as measured by a phase-shifting interferometer. Right, the wave-front amplitudes (the square root of an intensity measurement in the pupil plane).

Fig. 3
Fig. 3

Maximally defocused images for the six experiments conducted. Top row, images of a point source with, from left to right, no pixel binning, 2 × 2, and 4 × 4. Bottom row, corresponding images of an extended source.

Fig. 4
Fig. 4

Input-output scheme for the PD algorithm.

Fig. 5
Fig. 5

Histogram of the residual focal-plane errors after convergence for the case of a point source with no binning. A Gaussian (dashed curve) was fitted to the core of the curve and has a standard deviation of 1.02, indicating that the wave front was estimated almost as closely as the noise in the image data will allow.

Fig. 6
Fig. 6

Examples of reconstructed phases and amplitudes. Left column, phases reconstructed assuming unit amplitudes. Middle column, phases reconstructed with simultaneous amplitude estimation. Right column, estimated amplitudes. Top row, measured amplitudes and phases, repeated from Fig. 2. Second row, reconstruction from point-source data with no binning. Third row, point-source data with 4 × 4 binning. Bottom row, extended source data with 4 × 4 binning.

Fig. 7
Fig. 7

Left, object estimate from unbinned image data with amplitude estimation. Center, true object image. Right, object estimate without amplitude estimation.

Fig. 8
Fig. 8

(a) True object used for numerical simulation of object reconstruction. (b) Blurred image with photon and read noise added (best-focus frame from phase-diverse image set). (c) Reconstructed image with both phase and amplitude pupil-plane estimation. (d) Reconstructed image with phase-only estimation.

Tables (2)

Tables Icon

Table 1 Residual rms Phase and Amplitude Errors with Simultaneous Estimation

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Table 2 Residual rms Phase Error without Simultaneous Amplitude Estimation

Equations (13)

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ψu=j=4J qjZju,
Pu=Nθ2η1uuW2uθ2η1u21/2,
ψu=ϕη2u.
ηiu=Ai exp-u2σi2
hˆk=aˆkaˆk*,
aˆkx=N-2sku WuPuexp+iψu+ckξuexp-2πiux/N.
gˆkx=fˆxhˆkx.
gkx=dkxbx.
fˆx=N-2ukGkuHˆk*uγ+kHˆkuHˆk*u×exp-2πiux/N,
=kx0rkx  rkx21/2,
rkx=gkx-gˆkxgˆkx+n21/2 Mkx
Mkx=1 for gkx>Θ
=0 otherwise.

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