Spin echo

Animation of spin echo, showing the response of spins (red arrows) in the blue Bloch sphere to the green pulse sequence

In magnetic resonance, a spin echo or Hahn echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation.[1] Modern nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) make use of this effect.

The NMR signal observed following an initial excitation pulse decays with time due to both spin relaxation and any inhomogeneous effects which cause spins in the sample to precess at different rates. The first of these, relaxation, leads to an irreversible loss of magnetisation. But the inhomogeneous dephasing can be removed by applying a 180° inversion pulse that inverts the magnetisation vectors.[2] Examples of inhomogeneous effects include a magnetic field gradient and a distribution of chemical shifts. If the inversion pulse is applied after a period t of dephasing, the inhomogeneous evolution will rephase to form an echo at time 2t. In simple cases, the intensity of the echo relative to the initial signal is given by e–2t/T2 where T2 is the time constant for spin–spin relaxation. The echo time (TE) is the time between the excitation pulse and the peak of the signal.[3]

Echo phenomena are important features of coherent spectroscopy which have been used in fields other than magnetic resonance including laser spectroscopy[4] and neutron scattering.

  1. ^ J. E. Tanner & E. O. Stejskal (2003). "Restricted Self-Diffusion of Protons in Colloidal Systems by the Pulsed-Gradient, Spin-Echo Method". The Journal of Chemical Physics. 49 (4): 1768. Bibcode:1968JChPh..49.1768T. doi:10.1063/1.1670306.
  2. ^ Malcolm H. Levitt; Ray Freeman (1979). "NMR population inversion using a composite pulse". Journal of Magnetic Resonance. 33 (2): 473–476. Bibcode:1979JMagR..33..473L. doi:10.1016/0022-2364(79)90265-8.
  3. ^ Dan J Bell and J Yeung. "Echo time". Radiopedia. Retrieved 2017-09-24.
  4. ^ Kurnit, N. A.; Abella, I. D.; Hartmann, S. R. (1964). "Observation of a photon echo". Physical Review Letters. 13 (19): 567–568. Bibcode:1964PhRvL..13..567K. doi:10.1103/PhysRevLett.13.567.