Abstract

Aspects of phase problems for two-dimensional periodic images that occur in crystallography are examined. It is shown that such problems do not have unique solutions in general, but are underdetermined. The presence of a priori information constrains the solution, and an error metric is described that quantifies this effect. Explicit forms for the error metric are derived that describe the effects of a restricted support and symmetry in the image, and examples are presented.

© 1993 Optical Society of America

Reconstructing symmetric images from their undersampled Fourier intensities

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