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Eigenvalue filtering in the refinement of crystal and orientation parameters for oscillation photography
Author(s) -
Reeke G. N.
Publication year - 1984
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889884011444
Subject(s) - eigenvalues and eigenvectors , orientation (vector space) , oscillation (cell signaling) , optics , crystal (programming language) , range (aeronautics) , geometry , wavelength , algorithm , symmetry (geometry) , computer science , mathematics , materials science , physics , chemistry , biochemistry , quantum mechanics , composite material , programming language
Selective application of only parameter shifts with large eigenvalues permits singular or near‐singular least‐squares problems to be solved. This `eigenvalue filtering' process has been applied to the refinement of the unit‐cell, crystal‐orientation and reflecting‐range parameters needed to process oscillation films. Eigenvalue filtering permits automatic identification and determination of just those combinations of parameters that are most relevant for processing films from a particular crystal in a particular setting. The procedure may be carried out with alignment information from an individual data film or from multiple alignment films taken at different spindle angles. Eigenvalue filtering has been incorporated in a refinement program that minimizes discrepancies between observed and calculated fractions recorded for partially recorded reflections. This permits the reflecting range (combined mosaic spread, beam cross‐fire, and wavelength spread) to be refined along with the unit‐cell and orientation parameters. Observed fractions recorded may be obtained by visual estimation prior to film scanning, or the program may be used in a `post‐refinement' mode with data obtained from actual intensity measurements. The relatively unreliable information represented by the positions of spots on the film is not used except for indexing. The program handles crystals of any symmetry in any setting and the oscillation spindle may be inclined from normal beam geometry. The mis‐setting angles are defined in a crystal‐fixed coordinate system, making it easy to compare refinement results for data taken at different spindle angles.