TY - JOUR
T1 - Estimation of the density distribution from small-angle scattering data
AU - Hansen, Steen Laugesen
PY - 2016
Y1 - 2016
N2 - The one-dimensional density distribution for symmetrical scatterers is estimated from small-angle scattering data. The symmetry of the scatterers may be one dimensional (lamellar), two dimensional (cylindrical) or three dimensional (spherical). Previously this problem has been treated either by a two-step approach with the distance distribution as an intermediate [Glatter (1981). J. Appl. Cryst. 14, 101-108] or in a single step using spherical harmonics [Svergun, Feigin & Schedrin (1982). Acta Cryst. A38, 827-835]. A combination of these two methods is presented here, where the density distribution is estimated using constraints without the explicit use of an intermediate distribution. A maximum entropy constraint is introduced for this problem and the results are compared with the results of the conventional smoothness constraint. Bayesian methods are used for estimation of the overall noise level of the experimental data and for the maximum dimension of the density distribution. The method described is tested on both simulated and experimental data and shown to provide reliable estimates for the Guinier radius and maximum dimension. In both cases the effects of minor deviations from the assumed symmetry as well as incorrect background subtraction are studied.
AB - The one-dimensional density distribution for symmetrical scatterers is estimated from small-angle scattering data. The symmetry of the scatterers may be one dimensional (lamellar), two dimensional (cylindrical) or three dimensional (spherical). Previously this problem has been treated either by a two-step approach with the distance distribution as an intermediate [Glatter (1981). J. Appl. Cryst. 14, 101-108] or in a single step using spherical harmonics [Svergun, Feigin & Schedrin (1982). Acta Cryst. A38, 827-835]. A combination of these two methods is presented here, where the density distribution is estimated using constraints without the explicit use of an intermediate distribution. A maximum entropy constraint is introduced for this problem and the results are compared with the results of the conventional smoothness constraint. Bayesian methods are used for estimation of the overall noise level of the experimental data and for the maximum dimension of the density distribution. The method described is tested on both simulated and experimental data and shown to provide reliable estimates for the Guinier radius and maximum dimension. In both cases the effects of minor deviations from the assumed symmetry as well as incorrect background subtraction are studied.
U2 - 10.1107/S1600576716004969
DO - 10.1107/S1600576716004969
M3 - Journal article
SN - 0021-8898
VL - 49
SP - 856
EP - 865
JO - Journal of Applied Crystallography
JF - Journal of Applied Crystallography
ER -