Abstract

A recent comment has pointed out that some practically important aberration modes have zero curvature and in consequence seem difficult to sense using phase-diversity approaches that are equivalent to curvature sensing. Here we comment on the approaches that should be adopted when faced with a need to measure such aberration modes.

© 2007 Optical Society of America

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  1. C. Campbell, "Wave-front sensing by use of a Green's function solution to the intensity transport equation: comment," J. Opt. Soc. Am. A 24, xxx-xxx (2007).
    [CrossRef]
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    [CrossRef]
  3. P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wave-front sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. A. H. Greenaway, "Diffraction-limited pictures from single turbulence-degraded images in astronomy," Opt. Commun. 42, 157-161 (1982).
    [CrossRef]
  9. R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "Application of dispersion-relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
    [CrossRef]
  10. R. Barakat and G. Newsam, "Necessary conditions for a unique solution to two-dimensional phase recovery," J. Math. Phys. 25, 3190-3193 (1984).
    [CrossRef]
  11. P. van Toorn, A. H. Greenaway, and A. M. J. Huiser, "Phaseless object reconstruction," Opt. Acta 31, 767-774 (1984).
    [CrossRef]
  12. H. I. Campbell, S. Zhang, S. Restaino, and A. H. Greenaway, "Generalized phase diversity for wave-front sensing," Opt. Lett. 29, 2707-2709 (2004).
    [CrossRef] [PubMed]

2007

C. Campbell, "Wave-front sensing by use of a Green's function solution to the intensity transport equation: comment," J. Opt. Soc. Am. A 24, xxx-xxx (2007).
[CrossRef]

2004

2003

2000

1988

1984

R. Barakat and G. Newsam, "Necessary conditions for a unique solution to two-dimensional phase recovery," J. Math. Phys. 25, 3190-3193 (1984).
[CrossRef]

P. van Toorn, A. H. Greenaway, and A. M. J. Huiser, "Phaseless object reconstruction," Opt. Acta 31, 767-774 (1984).
[CrossRef]

1983

1982

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. (Bellingham) 21, 829-832 (1982).

A. H. Greenaway, "Diffraction-limited pictures from single turbulence-degraded images in astronomy," Opt. Commun. 42, 157-161 (1982).
[CrossRef]

1976

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "The phase problem," Proc. R. Soc. London, Ser. A 350, 191-212 (1976).
[CrossRef]

1974

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "Application of dispersion-relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Barakat, R.

R. Barakat and G. Newsam, "Necessary conditions for a unique solution to two-dimensional phase recovery," J. Math. Phys. 25, 3190-3193 (1984).
[CrossRef]

Blanchard, P. M.

Burge, R. E.

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "The phase problem," Proc. R. Soc. London, Ser. A 350, 191-212 (1976).
[CrossRef]

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "Application of dispersion-relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Campbell, C.

C. Campbell, "Wave-front sensing by use of a Green's function solution to the intensity transport equation: comment," J. Opt. Soc. Am. A 24, xxx-xxx (2007).
[CrossRef]

Campbell, H. I.

Fiddy, M. A.

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "The phase problem," Proc. R. Soc. London, Ser. A 350, 191-212 (1976).
[CrossRef]

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "Application of dispersion-relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Fisher, D. J.

Gonsalves, R. A.

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. (Bellingham) 21, 829-832 (1982).

Greenaway, A. H.

H. I. Campbell, S. Zhang, S. Restaino, and A. H. Greenaway, "Generalized phase diversity for wave-front sensing," Opt. Lett. 29, 2707-2709 (2004).
[CrossRef] [PubMed]

S. C. Woods and A. H. Greenaway, "Wave-front sensing by use of a Green's function solution to the intensity transport equation," J. Opt. Soc. Am. A 20, 508-512 (2003).
[CrossRef]

P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wave-front sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000).
[CrossRef]

P. van Toorn, A. H. Greenaway, and A. M. J. Huiser, "Phaseless object reconstruction," Opt. Acta 31, 767-774 (1984).
[CrossRef]

A. H. Greenaway, "Diffraction-limited pictures from single turbulence-degraded images in astronomy," Opt. Commun. 42, 157-161 (1982).
[CrossRef]

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "The phase problem," Proc. R. Soc. London, Ser. A 350, 191-212 (1976).
[CrossRef]

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "Application of dispersion-relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Huiser, A. M. J.

P. van Toorn, A. H. Greenaway, and A. M. J. Huiser, "Phaseless object reconstruction," Opt. Acta 31, 767-774 (1984).
[CrossRef]

Newsam, G.

R. Barakat and G. Newsam, "Necessary conditions for a unique solution to two-dimensional phase recovery," J. Math. Phys. 25, 3190-3193 (1984).
[CrossRef]

Restaino, S.

Roddier, F.

Ross, G.

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "The phase problem," Proc. R. Soc. London, Ser. A 350, 191-212 (1976).
[CrossRef]

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "Application of dispersion-relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Teague, M. R.

van Toorn, P.

P. van Toorn, A. H. Greenaway, and A. M. J. Huiser, "Phaseless object reconstruction," Opt. Acta 31, 767-774 (1984).
[CrossRef]

Woods, S. C.

Zhang, S.

Appl. Opt.

J. Math. Phys.

R. Barakat and G. Newsam, "Necessary conditions for a unique solution to two-dimensional phase recovery," J. Math. Phys. 25, 3190-3193 (1984).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

S. C. Woods and A. H. Greenaway, "Wave-front sensing by use of a Green's function solution to the intensity transport equation," J. Opt. Soc. Am. A 20, 508-512 (2003).
[CrossRef]

C. Campbell, "Wave-front sensing by use of a Green's function solution to the intensity transport equation: comment," J. Opt. Soc. Am. A 24, xxx-xxx (2007).
[CrossRef]

J. Phys. D

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "Application of dispersion-relations (Hilbert transforms) to phase retrieval," J. Phys. D 7, L65-L68 (1974).
[CrossRef]

Opt. Acta

P. van Toorn, A. H. Greenaway, and A. M. J. Huiser, "Phaseless object reconstruction," Opt. Acta 31, 767-774 (1984).
[CrossRef]

Opt. Commun.

A. H. Greenaway, "Diffraction-limited pictures from single turbulence-degraded images in astronomy," Opt. Commun. 42, 157-161 (1982).
[CrossRef]

Opt. Eng. (Bellingham)

R. A. Gonsalves, "Phase retrieval and diversity in adaptive optics," Opt. Eng. (Bellingham) 21, 829-832 (1982).

Opt. Lett.

Proc. R. Soc. London, Ser. A

R. E. Burge, M. A. Fiddy, A. H. Greenaway, and G. Ross, "The phase problem," Proc. R. Soc. London, Ser. A 350, 191-212 (1976).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

(a) shows an astigmatic wavefront that is used to generate an error signal using phase diversity based on defocus. In (b) the error signal generated from a uniformly illuminated (i.e., hard-edged) pupil is shown. Note that the error signal is confined to the edge. For a soft-edged pupil (in this case a Gaussian profile with 10% drop in flux from center to rim) the error signal shown in (c) is uniformly distributed but of lower amplitude.

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