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Two-Dimensional Phase Restoration

In: Fourier Techniques and Applications

Author

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  • R. H. T. Bates

    (University of Canterbury, Electrical and Electronic Engineering Department)

  • W. R. Fright

    (University of Canterbury, Electrical and Electronic Engineering Department)

Abstract

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.

Suggested Citation

  • R. H. T. Bates & W. R. Fright, 1985. "Two-Dimensional Phase Restoration," Springer Books, in: John F. Price (ed.), Fourier Techniques and Applications, pages 121-148, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-2525-3_7
    DOI: 10.1007/978-1-4613-2525-3_7
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