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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 T_1 using a flip repetition time T_R , assuming transverse magnetization is eliminated between flips. The Ernst angle \theta is calculated using the following relationship, derived by Richard R. Ernst, who won the 1991 Nobel Prize in Chemistry: \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 T_R for complete T_2 decay (in NMR).

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Article summary

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 T_1 using a flip repetition time T_R , assuming transverse magnetization is eliminated between flips. The Ernst angle \theta is calculated using the following relationship, derived by Richard R. Ernst, who won the 1991 Nobel Prize in Chemistry: \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 T_R for complete T_2 decay (in NMR).

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