Two-Stage Inversion-Recovery Experiments for Measurements of T₁

A theory for the optimal design of experiments for measuring values of T₁ using a two-stage design is developed. It is shown that a useful strategy in such designs is to make a preliminary rough estimate of T₁ and use the second stage to produce a refinement of the preliminary results. When the initial uncertainty interval for T₁ is large, the two-stage design produces results much less sensitive to the value of the true T₁ than those obtainable from a single-stage design. This leads to a significant improvement in the precision of estimates of T₁, and in circumstances that depend on the value of T₁ estimated in the first stage of the experiment, to a considerable saving in spectrometer time.