Dear Authors, congratulations with the new manuscript. Just a comment on the background correction. You are citing our work for the SIFTER background (Vanas et al. 2023) with a statement that SIDRE decay compensates for a part of the SIFTER background. This is of course true, but this part is only 50%. Please note that in the cited paper we demonstrated theoretically that (i) the unmodulated part of the SIFTER signal has different shape than the intermolecular background contribution to the modulated part (thus, the unmodulated part needs to be subtracted before correcting the modulated part for the intermolecular background); (ii) the intermolecular background contribution for the modulated part of the SIFTER signal is half sum of the SIDRE and of the product of two Hahn echo decays going in the opposite directions. The unmodulated part of the SIFTER signal in your case (low spin concentration) should indeed be similar to the SIDRE signal, but, once again, dividing the entire SIFTER signal by the SIDRE signal is an inaccurate background correction. SIDRE decay is steeper as compared to the combination of two Hahn echoes, thus the correct intermolecular background for the modulated part of the SIFTER signal is less steep as compared to SIDRE. Accordingly, with your background correction procedure (dividing everything by SIDRE signal) you are getting artificially narrowed distance distribution. In your measurements this effect is relatively weak but visible e.g. in the Figure 10(C).

Best regards, Maxim Yulikov