Resolution functions of time-of-flight small-angle neutron scattering instruments with rectangular apertures

Analytic forms are found for resolution functions of small-angle neutron scattering instruments. The expressions are developed as a function of momentum transfer (Q) rather than separately in terms of neutron wavelength (λ) and scattering angle (θ). Effects caused by the gravitational field as well as by quasi-elastic scattering are included. Explicit analytic forms for the transmission functions are proposed for both the incident and scattered beams, enabling careful analysis of any problem regarding small-angle scattering experiments. Due to the reciprocal mathematical relationship between λ, θ and Q, [λ, θ] space is employed to approach different aspects of the topic. Applications to time-of-flight instruments with rectangular apertures, including the choice of the most convenient instrumental parameters, the analysis of smearing effects and the data reduction to Q space, are presented.