Abstract

A solution to the phase-retrieval problem when the unknown phase is small is presented. The solution specifies the even and odd parts of the unknown phase in two separate equations. The odd part requires a single intensity measurement, and the even part requires two measurements. Phase diversity is used for the second measurement, and computer simulations are given.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Walther, Opt. Acta. 10, 41 (1963).
    [CrossRef]
  2. R. Gerchberg and W. Saxton, Optik 34, 275 (1971).
  3. R. Gonsalves, J. Opt. Soc. Am. 66, 961 (1976).
  4. M. Teague, J. Opt. Soc. Am. 72, 1199 (1982).
  5. B. Ellerbroek and D. Morrison, Proc. SPIE 351, 90 (1982).
    [CrossRef]
  6. W. Wild, Opt. Lett. 23, 573 (1998).
    [CrossRef]
  7. R. Gonsalves, Opt. Eng. 21, 829 (1982).
    [CrossRef]
  8. R. Paxman and J. Fienup, J. Opt. Soc. Am. A 5, 914 (1988).
    [CrossRef]
  9. R. Kendrick, D. Acton, and A. Duncan, Appl. Opt. 33, 6533 (1994).
    [CrossRef] [PubMed]
  10. J. Fienup, Opt. Lett. 3, 27 (1978).
    [CrossRef] [PubMed]

1998 (1)

1994 (1)

1988 (1)

1982 (3)

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

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

B. Ellerbroek and D. Morrison, Proc. SPIE 351, 90 (1982).
[CrossRef]

1978 (1)

1976 (1)

1971 (1)

R. Gerchberg and W. Saxton, Optik 34, 275 (1971).

1963 (1)

A. Walther, Opt. Acta. 10, 41 (1963).
[CrossRef]

Acton, D.

Duncan, A.

Ellerbroek, B.

B. Ellerbroek and D. Morrison, Proc. SPIE 351, 90 (1982).
[CrossRef]

Fienup, J.

Gerchberg, R.

R. Gerchberg and W. Saxton, Optik 34, 275 (1971).

Gonsalves, R.

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

R. Gonsalves, J. Opt. Soc. Am. 66, 961 (1976).

Kendrick, R.

Morrison, D.

B. Ellerbroek and D. Morrison, Proc. SPIE 351, 90 (1982).
[CrossRef]

Paxman, R.

Saxton, W.

R. Gerchberg and W. Saxton, Optik 34, 275 (1971).

Teague, M.

Walther, A.

A. Walther, Opt. Acta. 10, 41 (1963).
[CrossRef]

Wild, W.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Acta. (1)

A. Walther, Opt. Acta. 10, 41 (1963).
[CrossRef]

Opt. Eng. (1)

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

Opt. Lett. (2)

Optik (1)

R. Gerchberg and W. Saxton, Optik 34, 275 (1971).

Proc. SPIE (1)

B. Ellerbroek and D. Morrison, Proc. SPIE 351, 90 (1982).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Top left, original phase; top right, estimate for σ=0.2; lower left, estimate for σ=0.4; lower right, estimate for σ=0.8.

Equations (10)

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

H=A1+iT.
H=A+iV+W,
pe=a2+y2+v2,
po=2ay.
y=0.5p0/a.
ATo=ImY.
v=pe-a2-y21/2,
ATe=ReV.
pDe=a2+y2+v+z2=pe+2vz+z2,
v=0.5pDe-pe-z2/z.

Metrics