Deconvolution of disoriented fiber diffraction data using iterative convolution and local regression

Computationally efficient procedures are described for the deconvolution of disoriented fiber diffraction data to the resolution limit of measurable intensity in the patterns. The methods can be applied to diffraction data from imperfectly parallel arrays of one-dimensionally periodic rods or two-dimensionally periodic sheets, randomly rotated about their unique axes, to derive a representation of the intensity distribution corresponding to perfectly parallel orientation. With use of angular convolution and local angular regression, a set of uniform cylindrically averaged squared structure factors are iteratively adjusted, subject to a minimum-wavelength constraint, until they produce a disoriented pattern that fits the observed diffraction data. The results from this deconvolution provide a measure of the properly scaled cylindrically averaged squared structure factors, which can be used with other structural information to construct a physically plausible trial model suitable for further refinement. Sample deconvolutions of simulated X-ray patterns from partially oriented gap junction membranes are presented and the results from point-model deconvolutions are compared to those from constrained deconvolutions that began with the transform of a physically plausible trial model.