Ernst angle

In nuclear magnetic resonance spectroscopy and magnetic resonance imaging, the Ernst angle is the flip angle that maximizes the steady-state signal for a spin with a spin–lattice relaxation time ${\displaystyle T_{1}}$ using a flip repetition time ${\displaystyle T_{R}}$, assuming transverse magnetization is eliminated between flips. The Ernst angle ${\displaystyle \theta }$ is calculated using the following relationship, derived by Richard R. Ernst, who won the 1991 Nobel Prize in Chemistry:

$${\displaystyle \theta =\arccos(e^{-T_{R}/T_{1}})}$$

The derivation of the Ernst angle equation explicitly assumes that all transverse magnetization is completely eliminated between repetition times. This elimination is achieved in practice through spoiler gradients (in MRI) or by using a long enough ${\displaystyle T_{R}}$ for complete ${\displaystyle T_{2}}$ decay (in NMR).