Abstract

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  6. S. C. Woods and A. H. Greenaway, J. Opt. Soc. Am. A 20, 508 (2003).
    [CrossRef]
  7. S. Djidel and A. H. Greenaway, in 3rd International Workshop on Adaptive Optics in Industry and Medicine (Starline, Albuquerque, N.M., 2002), pp. 213–219.
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    [CrossRef]

2003

1999

1998

1988

1982

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[CrossRef]

M. R. Teague, J. Opt. Soc. Am. 72, 1199 (1982).

1975

P. Schiske, J. Phys. D Appl. Phys. 8, 1372 (1975).
[CrossRef]

Blanchard, P. M.

Browne, S. L.

Dayton, D. C.

Djidel, S.

S. Djidel and A. H. Greenaway, in 3rd International Workshop on Adaptive Optics in Industry and Medicine (Starline, Albuquerque, N.M., 2002), pp. 213–219.

Gonglewski, J. D.

Gonsalves, R. A.

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[CrossRef]

Greenaway, A. H.

S. C. Woods and A. H. Greenaway, J. Opt. Soc. Am. A 20, 508 (2003).
[CrossRef]

P. M. Blanchard and A. H. Greenaway, Appl. Opt. 38, 6692 (1999).
[CrossRef]

S. Djidel and A. H. Greenaway, in 3rd International Workshop on Adaptive Optics in Industry and Medicine (Starline, Albuquerque, N.M., 2002), pp. 213–219.

Kudryashov, A. V.

Roddier, F.

Sandven, S. P.

Schiske, P.

P. Schiske, J. Phys. D Appl. Phys. 8, 1372 (1975).
[CrossRef]

Teague, M. R.

Woods, S. C.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D Appl. Phys.

P. Schiske, J. Phys. D Appl. Phys. 8, 1372 (1975).
[CrossRef]

Opt. Eng.

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[CrossRef]

Other

S. Djidel and A. H. Greenaway, in 3rd International Workshop on Adaptive Optics in Industry and Medicine (Starline, Albuquerque, N.M., 2002), pp. 213–219.

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Figures (2)

Fig. 1
Fig. 1

Schematic of the measurement and wave-front planes showing the connection between wave-front shape and intensity.

Fig. 2
Fig. 2

Error signals dr, produced for (a) a distorted test wave front, using (b) a spherical aberration filter function and (c) a defocus filter function.

Equations (9)

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

Ψr=Ψrexpiφr,
ψξ=Hξ+Aξ,
Hξ=H*-ξ, Aξ=-A*-ξ.
j±r=dξψξF±ξexp-iξr2.
dr=j+r-j-r=2idξψξIξexp-irξ×dξψ*ξRξexpirξ-dξψξRξexp-irξ×dξψ*ξIξexpirξ.
dξHξIξexp-irξdξH*ξRξexpirξ-dξHξRξexp-irξdξH*ξIξexpirξ,
dξHξIξexp-irξdξA*ξRξexpirξ-dξAξRξexp-irξdξH*ξIξexpirξ,
dξAξIξexp-irξdξH*ξRξexpirξ-dξHξRξexp-irξdξA*ξIξexpirξ,
dξAξIξexp-irξdξA*ξRξexpirξ-dξAξRξexp-irξdξA*ξIξexpirξ;

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