Optimal Sampling Strategies for the Measurement of Spin–Spin Relaxation Times

It is shown how Cramér–Rao theory may be used to determine the optimal sampling pattern for measuring the NMR spin–spin relaxation time,T₂. The results may also be applied to the measurement of any other exponential decay, including some pulse sequences for measuring the spin–lattice relaxation time,T₁. The optimal sampling pattern involves placing 22% of the sample points at zero time and the remaining 78% at 1.28T₂, or, more practically and almost as accurately, one point at zero and four at 1.30T₂. These sampling patterns are very different from those commonly used. The Cramér–Rao results are compared with experimental measurements and computer simulations. Some limitations of the method are described, and its extension to the simultaneous measurement of a range ofT₂values is addressed.