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Related Experiment Videos

Phase retrieval by iterated projections.

Veit Elser1

  • 1Department of Physics, Cornell University, Ithaca, New York 14853-2501, USA. ve10@cornell.edu

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 25, 2003
PubMed
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A novel iterative "difference map" unifies phase retrieval strategies. This method enhances optical phase retrieval and enables crystallographic phase retrieval for complex structures.

Area of Science:

  • Computational physics
  • Crystallography
  • Image processing

Background:

  • Phase retrieval is crucial in optics and crystallography.
  • Existing methods like Fienup's hybrid input-output algorithm have limitations.
  • Alternating projection schemes can suffer from stagnation.

Purpose of the Study:

  • To unify diverse phase retrieval strategies using a single iterative framework.
  • To improve upon existing methods in optical and crystallographic phase retrieval.
  • To provide a geometric understanding of the iterative process and avoid stagnation.

Main Methods:

  • Construction of an iterative "difference map" using elementary projections and real parameters.
  • Application of the difference map to optical phase retrieval with Fourier modulus and object support constraints.

Related Experiment Videos

  • Adaptation of the difference map for crystallographic phase retrieval using object histogram or atomicity constraints.

    • Main Results:

    • The difference map reproduces Fienup's hybrid input-output map under specific parameter choices.
    • The geometric construction clarifies the relationship between fixed points and the recovered object.
    • The method avoids stagnation issues common in alternating projection schemes.
    • Successful phase retrieval for structures containing hundreds of atoms using synthetic data.

    Conclusions:

    • The unified difference map approach offers a versatile and effective framework for phase retrieval.
    • This method shows significant promise for complex crystallographic structure determination.
    • The geometric insights provided enhance the understanding of phase retrieval algorithms.