Quadratic spacing of the effective gradient area for spatially encoded diffusion NMR

Diffusion NMR experiments rely on the measurement of signal attenuation as a function of the area of diffusion-encoding pulsed magnetic-field gradients. In conventional experiments, arbitrary series of gradient values can be used, and different gradient spacing strategies have different advantages. Ultrafast diffusion NMR relies on the spatial parallelisation of effective gradient area values to collect full 2D diffusion data sets in a single scan. Until recently, only linear spacing was available. We have shown that quadratic spacing can be achieved using a tailored frequency swept pulse. Here we describe the design of the pulse and validate it with numerical spin simulations, that make it possible to check the effect of the quadratic spacing pulse at different stages of the pulse sequence. We also show that quadratic spacing makes it possible to use a recently reported analysis method for diffusion NMR, the Matrix Pencil Method. We describe the results obtained with the MPM and those obtained with the direct exponential curve resolution algorithm (DECRA), which also requires quadratic gradient spacing. Overall, these developments open new opportunities for applications of spatially encoded diffusion experiments, such as ultrafast DOSY NMR and ultrafast Laplace NMR.