Of the commonly used scattering geometries, only the Bonse–Hart technique is still affected by non-negligible slit smearing, although the corrections for that are well described and the data treatment is straightforward (Pauw et al., 2021 ▸ Adams et al., 2019 ▸). The beam size is often smaller than the pixel size of the approximately 100 µm large detector pixels, and the short wavelengths and small scattering probabilities do not lead to significant multiple scattering. Nowadays, small-angle X-ray scattering (SAXS) instruments are highly optimized such that corrections with respect to resolution and multiple scattering are unnecessary (Pauw, 2013 ▸). The detrimental effects of resolution and multiple scattering on the small-angle scattering method have been discussed for about 60–70 years (Guinier et al., 1955 ▸ Schmatz et al., 1974 ▸ Glatter & Kratky, 1982 ▸).

All of these considerations are interesting for both reactor-based instruments with velocity selectors and time-of-flight SANS instruments and may improve the reliability of the data treatment. In the later part of the article, deconvolution algorithms for multiple scattering and instrumental resolution of the elastic coherent signal as implemented in the program MuScatt are described. The first part of the paper deals with the multiple scattering effects of light water. Once the transition to this altered wavelength has happened, further incoherent multiple scattering is considered. The transfer to a single representative thermalized wavelength by the inelastic scattering – as a simplification – is assumed to happen by a single scattering event. The incoherent elastic scattering is treated by the theory of Chandrasekhar, allowing for multiple scattering even at large scattering angles. The other two channels display a nearly constant background as a function of the scattering angle. Its multiple scattering effects can be desmeared, as shown in the later sections of the article. The first channel contains the desired information on the experiment. It considers three channels for the coherent elastic, the incoherent elastic and the incoherent inelastic scattering processes. This article deals with multiple scattering effects that are important for the method of small-angle neutron scattering (SANS).

Arnold multi scatter