The effect of disorientation on the intensity distribution of non-crystalline fibres. I. Theory

The intensity function in reciprocal space is derived for the case of non-crystalline fibres with a Gaussian distribution of orientations. An expression is found relating the observed intensity function with the weighted integral along a circle of the intensity derived from the molecular structure factor. From this result in the case where the layer-line width is very small a correction factor may be derived which, if applied to the observed intensity, yields the intensity which would be obtained from a perfectly orientated fibre. The general problem of correcting for disorientation can only be treated by a numerical deconvolution procedure.