Convolutional approach to the normalization of intensity scattered by polycrystalline substances

A theory is presented describing convolutional properties of the reduced intensity distribution (intensity divided by the square of the atomic factor and multiplied by the scattering-vector length). The approximation used, verified on model data, leads to a relation between the effect of the multiple running average routine applied to reduced intensity and both normalization constant and local atomic density in the neighbourhood of any given atom. This enables an estimate of the normalization constant and the local density to be made with a high degree of accuracy. The effect of the choice of adjustable parameters in the running average routine is discussed. The procedure to calculate the interference function in the presence of an unknown background varying slowly with the scattering vector is presented.