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- W2067562837 abstract "Abstract A mathematical technique is described which operates on the moduli of the X-ray reflections, generates all possible combinations of phase values, and screens the phase combinations according to a set of criteria involving some known… -or postulated…-properties of the electron-density distribution. The technique is an image-recognition procedure focussed on the interpretation of the average values ϱ n of the electron density, and making use of the equation ϱ n ∞ F n (0) ( F n (0) is the n th autoconvolution of F ( h ) at h = 0. The choice of the phases is based upon the physical interpretation of some of the mathematical parameters, and upon the degree of compatibility of each set of phases with the criteria chosen a priori . The interpretation of the ϱ n is considered in detail within the mathematical framework of a step function, namely of a function which takes only a small number of discrete values; in this case the method is shown to be equivalent to applying a test of smoothness to the family of Fourier transforms which can be generated with the given moduli. The technique is well-suited for routine analysis on a computer, and several applications are described; the examples are myelin and a variety of lipid-water phases, all centrosymmetric structures which display a crystalline order in one, two or three dimensions. A discussion of the mathematical treatment suggests possible generalizations not restricted to centrosymmetric structures at subatomic resolution." @default.
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- W2067562837 date "1972-02-01" @default.
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- W2067562837 title "A pattern-recognition approach to the phase problem: Application to the X-ray diffraction study of biological membranes and model systems" @default.
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- W2067562837 doi "https://doi.org/10.1016/0022-2836(72)90335-x" @default.
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