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9 November 1993 Crystallographic image reconstruction problem
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The crystallographic X-ray diffraction experiment gives the amplitudes of the Fourier series expansion of the electron density distribution within the crystal. The 'phase problem' in crystallography is the determination of the phase angles of the Fourier coefficients required to calculate the Fourier synthesis and reveal the molecular structure. The magnitude of this task varies enormously as the size of the structures ranges from a few atoms to thousands of atoms, and the number of Fourier coefficients ranges from hundreds to hundreds of thousands. The issue is further complicated for large structures by limited resolution. This problem is solved for 'small' molecules (up to 200 atoms and a few thousand Fourier coefficients) by methods based on probabilistic models which depend on atomic resolution. These methods generally fail for larger structures such as proteins. The phase problem for protein molecules is generally solved either by laborious experimental methods or by exploiting known similarities to solved structures. Various direct methods have been attempted for very large structures over the past 15 years, with gradually improving results -- but so far no complete success. This paper reviews the features of the crystallographic image reconstruction problem which render it recalcitrant, and describes recent encouraging progress in the application of maximum entropy methods to this problem.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Lynn F. Ten Eyck "Crystallographic image reconstruction problem", Proc. SPIE 2029, Digital Image Recovery and Synthesis II, (9 November 1993);

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