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Optics Letters

Optics Letters


  • Vol. 5, Iss. 11 — Nov. 1, 1980
  • pp: 499–501

Ambiguity of the phase-reconstruction problem

A. M. J. Huiser and P. van Toorn  »View Author Affiliations

Optics Letters, Vol. 5, Issue 11, pp. 499-501 (1980)

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Is it possible to determine a function with a finite support from the modulus of its Fourier transform? This problem, the so-called phase problem, is studied theoretically and numerically. It is shown theoretically that, at least for a wide class of functions, such determination is not possible. The theory developed in this Letter is essentially two dimensional. Examples are given and studied numerically.

© 1980 Optical Society of America

Original Manuscript: July 16, 1980
Published: November 1, 1980

A. M. J. Huiser and P. van Toorn, "Ambiguity of the phase-reconstruction problem," Opt. Lett. 5, 499-501 (1980)

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  1. R. E. Burge et al., “The phase problem,” Proc. R. Soc. London A350, 1911976).
  2. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27 (1979). [CrossRef]
  3. Y. M. Burck, L. G. Sodin, “On the ambiguity of the phase reconstruction problem,” Opt. Commun. 30, 304 (1979). [CrossRef]
  4. W. Rudin, Functional Analysis (McGraw-Hill, New York, 1973), p. 181.
  5. A. H. Greenaway, “Proposal for phase recovery from a single intensity distribution,” Opt. Lett. 1, 10 (1977). In this Letter the case is considered in which S consists of two disconnected domains. [CrossRef] [PubMed]
  6. R. E. A. C. Paley, N. Wiener, “Fourier transforms in the complex domain,” Am. Math. Soc. Colloquium Proc. 29 (1934), p. 12.

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