On the use of modification functions when Fourier transforming total scattering data

When Fourier transforming radiation total scattering data to the pair distribution function it is common to use a `modification' function to help reduce the termination ripples that would otherwise occur as a result of the finite range and counting statistics of the scattering data. One of the most common functions employed was proposed by Lorch [J. Phys. C Solid State Phys. (1969), 2, 229-237]. In a recent article [Soper & Barney (2011). J. Appl. Cryst.44, 714-726] a revised version of this function was proposed. Here the effectiveness of these two functions at removing spurious structure from Fourier transformed data is compared. It is found that the two functions produce equivalent results, unless the broadening is allowed to increase with r, in which case the revised Lorch function is better at suppressing spurious oscillations. The presence of counting statistics produces a marked increase in the amplitude of the truncation oscillations.