Abstract

A new method for solving the phase problem in two dimensions is presented. The solution is noniterative and is based on locating the zeros of one-dimensional strips of a single two-dimensional intensity distribution. A numerical example is included.

© 1985 Optical Society of America

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References

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  1. J. W. Wood, M. A. Fiddy, R. E. Burge, Opt. Lett. 6, 514 (1981)
    [CrossRef] [PubMed]
  2. J. R. Fienup, Appl. Opt. 21, 2758 (1982).
    [CrossRef] [PubMed]
  3. R. E. Burge, M. A. Fiddy, A. H. Greenaway, G. Ross, Proc. R. Soc. London Ser. A 350, 191 (1976).
    [CrossRef]
  4. J. L. C. Sanz, T. S. Huang, J. Opt. Soc. Am. 73, 1446 (1983).
    [CrossRef]
  5. M. H. Hayes, J. H. McClellan, Proc. IEEE 70, 197 (1982).
    [CrossRef]
  6. M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
    [CrossRef]
  7. P. J. Napier, R. H. T. Bates, Astron. Astrophys. Suppl. 15, 427 (1974).
  8. J. W. Wood, T. J. Hall, M. A. Fiddy, Opt.Acta 30, 511 (1983).
    [CrossRef]
  9. J. R. Fienup, Opt. Lett. 3, 27 (1978).
    [CrossRef] [PubMed]

1983 (2)

J. L. C. Sanz, T. S. Huang, J. Opt. Soc. Am. 73, 1446 (1983).
[CrossRef]

J. W. Wood, T. J. Hall, M. A. Fiddy, Opt.Acta 30, 511 (1983).
[CrossRef]

1982 (3)

J. R. Fienup, Appl. Opt. 21, 2758 (1982).
[CrossRef] [PubMed]

M. H. Hayes, J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
[CrossRef]

1981 (1)

1978 (1)

1976 (1)

R. E. Burge, M. A. Fiddy, A. H. Greenaway, G. Ross, Proc. R. Soc. London Ser. A 350, 191 (1976).
[CrossRef]

1974 (1)

P. J. Napier, R. H. T. Bates, Astron. Astrophys. Suppl. 15, 427 (1974).

Bates, R. H. T.

P. J. Napier, R. H. T. Bates, Astron. Astrophys. Suppl. 15, 427 (1974).

Burge, R. E.

J. W. Wood, M. A. Fiddy, R. E. Burge, Opt. Lett. 6, 514 (1981)
[CrossRef] [PubMed]

R. E. Burge, M. A. Fiddy, A. H. Greenaway, G. Ross, Proc. R. Soc. London Ser. A 350, 191 (1976).
[CrossRef]

Fiddy, M. A.

J. W. Wood, T. J. Hall, M. A. Fiddy, Opt.Acta 30, 511 (1983).
[CrossRef]

J. W. Wood, M. A. Fiddy, R. E. Burge, Opt. Lett. 6, 514 (1981)
[CrossRef] [PubMed]

R. E. Burge, M. A. Fiddy, A. H. Greenaway, G. Ross, Proc. R. Soc. London Ser. A 350, 191 (1976).
[CrossRef]

Fienup, J. R.

Greenaway, A. H.

R. E. Burge, M. A. Fiddy, A. H. Greenaway, G. Ross, Proc. R. Soc. London Ser. A 350, 191 (1976).
[CrossRef]

Hall, T. J.

J. W. Wood, T. J. Hall, M. A. Fiddy, Opt.Acta 30, 511 (1983).
[CrossRef]

Hayes, M. H.

M. H. Hayes, J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
[CrossRef]

Huang, T. S.

McClellan, J. H.

M. H. Hayes, J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

Napier, P. J.

P. J. Napier, R. H. T. Bates, Astron. Astrophys. Suppl. 15, 427 (1974).

Ross, G.

R. E. Burge, M. A. Fiddy, A. H. Greenaway, G. Ross, Proc. R. Soc. London Ser. A 350, 191 (1976).
[CrossRef]

Sanz, J. L. C.

Wood, J. W.

J. W. Wood, T. J. Hall, M. A. Fiddy, Opt.Acta 30, 511 (1983).
[CrossRef]

J. W. Wood, M. A. Fiddy, R. E. Burge, Opt. Lett. 6, 514 (1981)
[CrossRef] [PubMed]

Appl. Opt. (1)

Astron. Astrophys. Suppl. (1)

P. J. Napier, R. H. T. Bates, Astron. Astrophys. Suppl. 15, 427 (1974).

IEEE Trans. Acoust. Speech Signal Process. (1)

M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Opt.Acta (1)

J. W. Wood, T. J. Hall, M. A. Fiddy, Opt.Acta 30, 511 (1983).
[CrossRef]

Proc. IEEE (1)

M. H. Hayes, J. H. McClellan, Proc. IEEE 70, 197 (1982).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

R. E. Burge, M. A. Fiddy, A. H. Greenaway, G. Ross, Proc. R. Soc. London Ser. A 350, 191 (1976).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

a, A test pixel object; b, the reconstruction by the method described in the text.

Equations (1)

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F ( z ) = F ( x + i y ) = | F ( z ) | exp [ i ϕ ( z ) ] = a a f ( t ) exp [ y t ] exp [ ixt ] d t = a a f ( t ) exp [ izt ] d t = j ( 1 z / z j ) .

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