Table 1. Tests on simulated data sets calculated from geometric bodies.

The theoretical scattering was calculated up to a momentum transfer value of s _max = 4nm¹, and various noise levels (ranging from 1 to 400%) were added. The columns on the right-hand side from the nominal Shannon number N _S = s _max D _max/ display the optimum number of Shannon channels M _B that provides the best agreement with the ideal (noise-free) curve. In each case, the maximum noise level where useful information is still present in the entire curve is shown in bold.

			M B
Type of body	D max (nm)	N S	1%	5%	20%	50%	100%	200%	400%
(a) X-ray type data, strong oversampling
Oblate ellipsoid (half-axes 15, 15, 1nm)	30	38	41	39	39	38	38	38	25
Prolate ellipsoid (half-axes 1, 1, 15nm)	30	38	39	39	39	38	38	37	23
Hollow sphere (R in 2.5nm, R out 5nm)	10	13	14	14	13	13	13	12	11
Hollow cylinder (R in 2.5nm, R out 5nm, H 10nm)	14	18	19	19	18	18	18	16	14
Cube (5nm edge)	8.6	11	12	12	12	11	11	10	9
Solid sphere (radius 5nm)	10	13	15	14	14	14	14	14	13
(b) Neutron type data, medium oversampling
Oblate ellipsoid (half-axes 15, 15, 1nm)	30	38	38	38	38	38	38	37	25
Prolate ellipsoid (half-axes 1, 1, 15nm)	30	38	38	38	38	37	36	34	15
Hollow sphere (R in 2.5nm, R out 5nm)	10	13	13	13	13	12	11	11	10
Hollow cylinder (R in 2.5nm, R out 5nm, H 10nm)	14	18	18	18	18	17	16	16	14
Cube (5nm edge)	8.6	11	11	11	11	10	10	9	8
Solid sphere (radius 5nm)	10	13	13	13	13	13	13	11	10