Figure 2.

Selective sensing of averages and variances arising from the gradient distributions by (a) symmetric-NOGSE (sNOGSE) and (c) asymmetric-NOGSE (aNOGSE) sequences. The corresponding modulation waveforms f(t) and f ₀(t) are shown in panel (b) and (d) for sNOGSE and aNOGSE respectively. (e) Normalized NOGSE signals expected as a function of the delay x, where $(N-\mathrm{2)}x+2y=T{E}_{NOGSE}=TE/2$. By normalizing signals for x ≪ y and then changing x, y while keeping all other parameters – including N and TE– constant, s- and a-NOGSE sequences enable the characterization of the IGDT effects. sNOGSE’ s waveform is symmetric vs the central π refocusing pulse; all cross-terms with the internal gradients are thus zero, freeing the experiment from all internal gradients effects (panel c, black solid line). By contrast, the aNOGSE’ s waveform will be affected by both the 1^st and 2^nd order effects related to the internal gradient cross-terms. The legends describes the different weightings of these attenuation factors stemming from the background gradient distributions. The quantities $\mathrm{\Delta }{\beta }_{Cross}^{-}$ and $\mathrm{\Delta }{\beta }_{Cross}^{+}$ used to selectively determine the average $\langle G_0\rangle$ and variance $\langle {\left(\mathrm{\Delta }{G}_0\right)}^2\rangle$ are shown with arrows, where the different signs denote the application of the external gradient G parallel and anti-parallel to the background gradient direction. Other assumptions include $\langle G_0\rangle /G=0.1$, $\sqrt{\langle \mathrm{\Delta }{G}_0^2\rangle }/\langle G_0\rangle =1$ and N = 8.