A study of effects of different echo processing on diffusion spectra measured by the CPMG sequence in a constant gradient Igor Ser  sa a, b, * , Franci Bajd a, b , Ale  s Mohori  c a, b a Jo zef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia b Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia article info Article history: Received 29 November 2016 Received in revised form 14 August 2017 Accepted 4 September 2017 Available online 7 September 2017 Keywords: Diffusion spectrum Modulated gradients CPMG sequence Coherence pathway abstract Modulated gradient spin echo (MGSE) sequences are designed to measure diffusion spectrum by applying gradients that cause oscillation of the spin dephasing function and thus echo attenuation from which the diffusion spectrum at the frequency of the dephasing oscillation is calculated. In this study, the CPMG sequence performed in a constant gradient (constant gradient MGSE sequence) is analyzed. It is shown that the sequence produces a train of spin echoes that decays with the echo index multi- exponentially on the account of contributions from numerous coherence pathways. Therefore, its analysis by a mono-exponential decay model yields an incorrect diffusion spectrum ~ DðnÞ. It is also shown that by zero frequency filtering the echo signals are composed effectively only of the direct coherence pathway. The direct coherence pathway decays mono-exponentially with the echo index and its analysis by the mono-exponential decay model yields a correct diffusion spectrum DðnÞ. Furthermore, our experimental results as well as preliminary theoretical analysis indicate that the difference between the two diffusion spectra ~ DðnÞ DðnÞ is approximately equal for samples of identical external shape and the same diffusing liquid. This was demonstrated with constant gradient MGSE experiments on two different samples of an identical size, one containing bulk water and the other containing water in a porous material. The relation was found efficient in measuring diffusion spectra in samples with low SNR. © 2017 Elsevier Inc. All rights reserved. 1. Introduction Translational dynamics can be efficiently studied by various groups of NMR methods. The most common one is based on application of the pulsed gradient spin echo (PGSE) sequence [1] of which measurements can be interpreted by the propagator approach [2]. The propagator/PGSE analysis of the translational dynamics can be considered a time-based analysis as its results are dependent on the diffusion time D, which corresponds to the time separation between the two pulsed field gradients of the PGSE sequence. Another group of methods is based on the use of modulated gradient spin echo (MGSE) sequences in which effective modulated gradients GðtÞ combined with spin echo sequences are used to analyze translational dynamics as a function of frequency [3e6]. The analysis relies on a relation that the diffusion spectrum DðuÞ corresponds to the Fourier transform of the velocity auto- correlation function vðt 0 Þ vðt 00 Þ DðuÞ¼ 1 2 Z ∞ ∞ vð0Þvðt Þexpðiut Þdt : (1) The velocity autocorrelation function is associated with the spin echo attenuation lnðS MG =S 0 Þ¼ 1 2 Z t 0 dt 0 Z t 0 dt 00 F ðt 0 Þ vðt 0 Þvðt 00 ÞF ðt 00 Þ (2) via spin dephasing F ðtÞ¼ g R t 0 Gðt 0 Þdt 0 . By combining the relations in Eqs. (1) and (2) a relation between the spin echo attenuation and the diffusion spectrum is obtained [3,4]. lnðS MG =S 0 Þ¼p 1 Z ∞ 0 DðuÞjF ðuÞj 2 du: (3) * Corresponding author. Jo zef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia. E-mail address: igor.sersa@ijs.si (I. Ser sa). Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso http://dx.doi.org/10.1016/j.micromeso.2017.09.001 1387-1811/© 2017 Elsevier Inc. All rights reserved. Microporous and Mesoporous Materials 269 (2018) 152e155