Diffusion-Diffraction Phenomenon in multi-PFG experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the diffraction-like non-monotonic patterns that the signal attenuation curves exhibit [1]. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs as shown in Figure 1. When gradients of the same strength are applied along the direction perpendicular to the boundaries, diffusion pulse durations (δ) are small, and for extreme values of the diffusion times (∆) and mixing times (tm), the MR signal attenuation is given by