Two-Dimensional Phase Restoration

  • R. H. T. Bates
  • W. R. Fright


The constraints laid on the phase of a Fourier transform by its intensity are reviewed in the contexts of well known phase problems. The considerable differences between phase problems involving one-dimensional and multi-dimensional images, and finite-sized (as arise in astronomy, for instance) and periodic (as occur in crystallography) images, are explained. The crucial importance, for uniqueness questions, of the concept of the image-form (and also its most compact manifestation) is emphasised, as is the almost always unique connection between the image-form of a positive multi-dimensional image and the intensity of its Fourier transform. The current status of phase recovery algorithms, as regards Fourier transforms of finite-sized images, is assessed. The necessity for composite algorithms, incorporating simple but powerful constructions, is pleaded and reinforced by computational examples illustrating our previously reported defogging routine and a new procedure called fringe magnification.


Image Space Fourier Space Phase Retrieval Phase Problem Central Lobe 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • R. H. T. Bates
    • 1
  • W. R. Fright
    • 1
  1. 1.Electrical and Electronic Engineering DepartmentUniversity of CanterburyChristchurchNew Zealand

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