Abstract

It is shown that a band-limited spectrum of a nonnegative object can be represented as the autoconvolution of a spectrum whose cutoff frequency is half of the band limit. This permits spectral-magnitude-only reconstruction with a nonnegativity constraint without a support constraint. A magnitude-only reconstruction method using a conjugate-gradient procedure is developed and is investigated by computer simulations.

© 1996 Optical Society of America

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  1. R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).
  2. J. R. Fienup, Opt. Lett. 3, 27 (1978).
    [CrossRef] [PubMed]
  3. J. R. Fienup, Appl. Opt. 21, 2758 (1982).
    [CrossRef] [PubMed]
  4. M. H. Hayes, IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140 (1982).
    [CrossRef]
  5. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).
  6. A. Labeyrie, Astron. Astrophys. 6, 85 (1970).
  7. B. L. McGlamery, Proc. SPIE 74, 225 (1976).
  8. J. H. Seldin, J. R. Fienup, J. Opt. Soc. Am. A 7, 428 (1990).
    [CrossRef]

1990 (1)

1982 (2)

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

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

1978 (1)

1976 (1)

B. L. McGlamery, Proc. SPIE 74, 225 (1976).

1972 (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

1970 (1)

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Fienup, J. R.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Hayes, M. H.

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

Labeyrie, A.

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

McGlamery, B. L.

B. L. McGlamery, Proc. SPIE 74, 225 (1976).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Seldin, J. H.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Appl. Opt. (1)

Astron. Astrophys. (1)

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

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. A (1)

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Proc. SPIE (1)

B. L. McGlamery, Proc. SPIE 74, 225 (1976).

Other (1)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

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