Abstract

The phase-retrieval problem consists of the reconstruction of an object from the modulus of its Fourier transform or, equivalently, from its autocorrelation. This paper describes a number of results relating to the reconstruction of the support of an object from the support of its autocorrelation. Methods for reconstructing the object’s support are given for objects whose support is convex and for certain objects consisting of collections of distinct points. The uniqueness of solutions is discussed. In addition, for the objects consisting of collections of points, a simple method is shown for completely reconstructing the object functions.

© 1982 Optical Society of America

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  1. See, for example, H. P. Baltes, ed., Inverse Source Problems in Optics (Springer-Verlag, New York, 1978).
  2. J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3, 27–29 (1978); "Space object imaging through the turbulent atmosphere," Opt. Eng. 18, 529–534 (1979).
  3. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978).
  4. H. W. E. Jung, "Uber die kleinste Kugel, die eine raumliche Figur einschliesst," Z. Reine Agnew. Math. 123, 241 (1901).
  5. J. Christou, "Imaging of star clusters from speckle interferometry," Opt. Commun. 37, 331–334 (1981).
  6. J. R. Fienup and T. R. Crimmins, "Determining the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 70, 1581(A) (1980).

1981

J. Christou, "Imaging of star clusters from speckle interferometry," Opt. Commun. 37, 331–334 (1981).

1980

J. R. Fienup and T. R. Crimmins, "Determining the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 70, 1581(A) (1980).

1978

1901

H. W. E. Jung, "Uber die kleinste Kugel, die eine raumliche Figur einschliesst," Z. Reine Agnew. Math. 123, 241 (1901).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978).

Christou, J.

J. Christou, "Imaging of star clusters from speckle interferometry," Opt. Commun. 37, 331–334 (1981).

Crimmins, T. R.

J. R. Fienup and T. R. Crimmins, "Determining the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 70, 1581(A) (1980).

Fienup, J. R.

J. R. Fienup and T. R. Crimmins, "Determining the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 70, 1581(A) (1980).

J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3, 27–29 (1978); "Space object imaging through the turbulent atmosphere," Opt. Eng. 18, 529–534 (1979).

Jung, H. W. E.

H. W. E. Jung, "Uber die kleinste Kugel, die eine raumliche Figur einschliesst," Z. Reine Agnew. Math. 123, 241 (1901).

J. Opt. Soc. Am.

J. R. Fienup and T. R. Crimmins, "Determining the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 70, 1581(A) (1980).

Opt. Commun.

J. Christou, "Imaging of star clusters from speckle interferometry," Opt. Commun. 37, 331–334 (1981).

Opt. Lett.

Z. Reine Agnew. Math.

H. W. E. Jung, "Uber die kleinste Kugel, die eine raumliche Figur einschliesst," Z. Reine Agnew. Math. 123, 241 (1901).

Other

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978).

See, for example, H. P. Baltes, ed., Inverse Source Problems in Optics (Springer-Verlag, New York, 1978).

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