FBR: a robust method to determine the basis matrix of the Bravais lattice from oscillation images

The FBR (Fourier basis reconstruction) method described in this paper has b een designed to determine the basis matrix of the Bravais lattice with resp ect to the laboratory frame of reference and without prior knowledge of cel l constants, particularly for protein crystals of comparatively low quality . It is based on Fourier analysis of a three-dimensional intensity distribu tion in reciprocal space, which is directly obtained from observed intensit y distributions, provided that they are recorded by the rotation method usi ng a fixed X-ray wavelength, resulting in a direct-space determination of t he basis vectors. After a description of the motivation and theory behind t he method, it is tested by application to numerically generated images of a virtual sample crystal and to experimental data of a lysozyme crystal with well known cell constants. Finally, FBR is applied to a set of images of b acteriorhodopsin crystals suffering from strong anisotropic spot broadening ; this case provided the original motivation for the present work.