Two-Dimensional Phase Restoration

R. H. T. Bates and W. R. Fright
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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

A chapter in Fourier Techniques and Applications, 1985, pp 121-148 from Springer

Abstract: 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.

Keywords: Image Space; Fourier Space; Phase Retrieval; Phase Problem; Central Lobe (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4613-2525-3_7

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