Ernst angle
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| - | The Ernst angle is the tip angle for a particular spin that will yield the maximum signal in the least amount of time when signal averaging over many transients. The the following equation relates the Ernst angle, theta, to the experimental interpulse delay, d1; the duration of the fid acquisition, at; and the T<sub>1</sub> relaxation time of the spin in question, T<sub>1</sub>: | + | The Ernst angle<cite>ernst1</cite> is the tip angle for a particular spin that will yield the maximum signal in the least amount of time when signal averaging over many transients. The the following equation relates the Ernst angle, theta, to the experimental interpulse delay, d1; the duration of the fid acquisition, at; and the T<sub>1</sub> relaxation time of the spin in question, T<sub>1</sub>: |
<math>cos(\theta)=e^{-(d1+at)/T_1}</math> | <math>cos(\theta)=e^{-(d1+at)/T_1}</math> | ||
| Line 7: | Line 7: | ||
For example, if one wishes to get the best signal from a resonance with T<sub>1</sub>=3 sec, and one wishes to use d1=1sec and at=2sec, the optimal tip angle is 68 degrees. | For example, if one wishes to get the best signal from a resonance with T<sub>1</sub>=3 sec, and one wishes to use d1=1sec and at=2sec, the optimal tip angle is 68 degrees. | ||
| - | + | <biblio> | |
| + | #ernst1 bibtex=@article{ernst1966application, | ||
| + | title={{Application of Fourier transform spectroscopy to magnetic resonance}}, | ||
| + | author={Ernst, RR and Anderson, WA}, | ||
| + | journal={Review of Scientific Instruments}, | ||
| + | volume={37}, | ||
| + | pages={93}, | ||
| + | year={1966}, | ||
| + | url={http://dx.doi.org/10.1063/1.1719961} | ||
| + | } | ||
| + | </biblio> | ||
[[Category:NMR concept]] [[Category:T1]] [[Category:T1 relaxation]] [[Category:Experiment optimization]] | [[Category:NMR concept]] [[Category:T1]] [[Category:T1 relaxation]] [[Category:Experiment optimization]] | ||
Revision as of 17:41, 29 March 2010
The Ernst angle[1] is the tip angle for a particular spin that will yield the maximum signal in the least amount of time when signal averaging over many transients. The the following equation relates the Ernst angle, theta, to the experimental interpulse delay, d1; the duration of the fid acquisition, at; and the T1 relaxation time of the spin in question, T1:
This relationship was developed by Richard Ernst, winner of the 1991 Nobel Prize in Chemistry.
For example, if one wishes to get the best signal from a resonance with T1=3 sec, and one wishes to use d1=1sec and at=2sec, the optimal tip angle is 68 degrees.
