Determination of sample time for T1 measurement.

In spin-lattice relaxation time measurements, the relaxation time T1 is estimated from measuring the longitudinal magnetization during its return to thermal equilibrium from an initial (nonequilibrium) state. T1 estimation error depends on a number of factors, including the sample spacing, number of sample points, target T1 range, etc. We describe here a sample-time determination method based on the principles of optimal experimental design. A two-parameter model and a more general three-parameter model of the general T1 measurement experiment are used in this study. Both linear and power-law sample spacing strategies are evaluated. The proposed method formulates the sample-time determination problem in closed form expressions that allow for easy calculation of optimum sample times, if a prior T1 estimate or a probable T1 distribution over the target range is given. Valuable insights can be gained from evaluation of these expressions concerning the relationship of T1 estimation error and the sample spacing, number of sample points, target T1 range, etc.