The sampling theorem and small-angle scattering

All information about the scattering sample obtainable from small-angle scattering data is shown to be contained in the discrete measured points of a scattering curve distorted by arbitrary collimation conditions, provided that the interval Δh between adjacent measured points fulfils the condition Δh ≤ π/L, where L is the largest correlation distance in the sample; h = 4πλ⁻¹sinθ; λ is the scattered wavelength; and 2θ is the scattering angle. A simple technique has been developed for separation of part of the noise. It is shown that if the total time for measuring a scattering curve is held constant, a scattering curve recorded with Δh equal to the sampling-point interval π/L gives results like those obtained for a scattering curve recorded with a measured point distance smaller than that sampling-point interval. Therefore, Δh should be chosen to be small enough to guarantee that Δh ≤ π/L. Furthermore, a technique has been developed to calculate missing data points from the measured intensities. The condition Δh ≤ π/L has been found to be important for this calculation.