Ernst Angle
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Ernst Angle
In nuclear magnetic resonance spectroscopy and magnetic resonance imaging, the Ernst angle is the flip angle (a.k.a. "tip" or "nutation" angle) for excitation of a particular spin that gives the maximal signal intensity in the least amount of time when signal averaging over many transients. In other words, the highest signal-to-noise ratio can be achieved in a given amount of time. This relationship was described by Richard R. Ernst, winner of the 1991 Nobel Prize in Chemistry. Consider a single pulse sequence consisting of (1) an excitation pulse with flip angle \theta_E, (2) the recording of the time domain signal (Free induction decay In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetization precessing about the magnetic field (conventionally along z). This non-e ..., FID) for a duration known as acquisition time a_t, and (3) a delay until the next excitation p ...
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Nuclear Magnetic Resonance Spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio waves into nuclear magnetic resonance, which is detected with sensitive radio receivers. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. As the fields are unique or highly characteristic to individual compounds, in modern organic chemistry practice, NMR spectroscopy is the definitive method to identify monomolecular organic compounds. The principle of NMR usually involves three sequential steps: # The alignment (polarization) of the magnetic nuclear spins in an applied, constant magnetic field B0. # The ...
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