Extraction of the Missing Low-Q Data from Small-Angle Scattering Data

A new method is presented that recovers the scatter intensity curve at low Q values from small-angle neutron scattering data. The method uses only the measured data, requiring no extrapolation of the scatter curve nor any a priori knowledge of the maximum chord length, radius of gyration or molecular weight of the particle under investigation. It is assumed that the incoherent level would have been extracted from the data in the normal course of events but any errors do not affect the method presented. The distance distribution function of any particle has a restricted extension in real space and any nonzero value beyond the maximum size of the particle is due to the effects of missing data segments and noise on the measured data. The effects due to the missing and noisy data are isolated from the distance distribution of the particle and a suitably scaled template particle is used to fill in the missing distribution data segment. The inverse transform of the new distribution function returns the missing low-Q scatter data and to some extent cancels out the noise. While the method is generally explored using noise-free analytically derived particles, its application to real experimental data is demonstrated.