Using pulsed-field-gradient (PFG) sequences, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Differences in the characteristics of attenuation curves also permit distinguishing different pore shapes and distributions using the N-PFG technique. Using an even number of PFG pairs, an approximation to the average pore size can be obtained even when the sample contains pores with a broad distribution of sizes. Multi-PFG sequences can also be used to differentiate free and multi-compartment diffusion, and to estimate compartment sizes and orientations, and to distinguish microscopic and ensemble anisotropy.