Determination of sample time for T1 measurement

In spin-lattice relaxation time measurements, the relaxation time T1 is est imated from measuring the longitudinal magnetization during its return to t hermal equilibrium from an initial (nonequilibrium) state. T1 estimation er ror depends on a number of factors, including the sample spacing, number of sample points, target T1 range, etc. We describe here a sample-time determ ination method based on the principles of optimal experimental design, A tw o-parameter model and a more general three-parameter model of the general T 1 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 fo r easy calculation of optimum sample times, if a prior T1 estimate or a pro bable 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, ta rget T1 range, etc.