How to Set the Flip Angle to Maximize the Sensitivity per Hour: Meaning of Ernst Angle

  • Summary


A flip angle b smaller than 90 degree is often applied in the single-pulse measurements for long T1 samples to accumulate the signals with a short recycle delay RD. Signal sensitivity per scan as a function of b shown below indicates maxima with smaller flip angles bopt when T1 becomes longer than RD, or when x=RD/T1 becomes smaller.
The angle bopt is called Ernst angle and given by cos bopt = exp(RD/1) [1,2].

Some combinations of RD and βopt to be set in the experiments are summarized below:

As shown left, measurements with an appropriate combination of RD and bopt may maximize the signal sensitivity per hour [3].


  1. R. R. Ernst, G. Bodenhausen, and A. Wokaun, “Principles of Nuclear Magnetic Resonance in One and Two Dimensions”, Clarendon Press, 1987, pp124-125.
  2. T. D. W. Claridge, “High-Resolution NMR Techniques in Organic Chemistry”, Second Ed., Elsevier, 2009, pp99-102.
  3. T. Nakai, New Glass, 28(2), 17-28 (2013).


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