A problem with the direct sine-FT of the sM(s) is that different points have different uncertainties. Namely, the points at large s-values usually have larger uncertainties than those at low s-values (see, for example, Refs. ). Such behavior is mainly due to a fast decay of the background, predominantly given by atomic scattering, which scales as s -4 . As all the points in Eq. 5 enter the FT procedure with the same weights, the resulting RDF can be prone to the noise induced by these uncertainties. Besides, the error propagation from the s-space into r-space is an important issue that is well recognized in the X-ray diffraction community. The aforementioned issues are especially crucial for TRED experiments. First of all, in TRED, the measurements are done without the rotating sector device. Such a device evens out the effects of the fast-decaying background, which means that the noise for the large scattering angles in TRED is larger than in structural GED setups. Secondly, the measured signal is the difference signal (between excited and unexcited molecular ensembles), which means that the signal-tonoise ratio is worsened compared to structural study cases. To address a few of these problems, a new real-space inversion algorithm was recently proposed. It accounted explicitly for the expected behavior of the scattering signal and also the regularization technique to stabilize the problem.