The Effects of Noise on the Missing-Data-Residue Technique

Abstract

The missing‐data‐residue technique is a method of recovering the scatter intensity curve at low‐Q values from small‐angle scattering data. The effect on the missing‐data‐residue technique of the addition of varying degrees of noise to truncated analytical particles is investigated, with the noise levels varying from 0 to ±10%. The effects of smoothing of the data prior to the application of the technique are also investigated. The results for nonsmoothed data are shown to degrade in proportion to the noise level and it is shown that an estimate of the noise level gives an estimate of the potential error on the result. The five‐point moving‐average smoothing used is shown to improve the variance of the returned zero‐angle scatter intensity but at the expense of potentially introducing a small error. Results for both smoothed and nonsmoothed data are compared and it is shown that smoothing of the data is preferable, even at relatively low noise levels. For both smoothed and nonsmoothed data, a correlation is shown to exist between the error on the first known I(Q) data point and the returned I(0).

On the Retrieval of Particle Size Distributions from Small-Angle Scattering Data: the Influence of Statistical Data Dispersion

“…The influence of a limited scattering vector range [l(hmin),l(hmax)] (Mulato, Tygel & Chambouleyron, 1997;Doherty & Poland, 1996) and of noise (Doherty & Poland, 1996;Von Damaschun, Mtiller & Ptirschel, 1971) on the correctness of the D(r) retrieval process has been addressed. In Mulato et al (1997), l(h) data ~ 1998 International Union of Crystallography Printed in Great Britain -all rights reserved resulting from known D(r) distributions were truncated at different h ..... and dcconvoluted to establish the reliability of the method as a function of h ...... .…”