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[[File:HahnEcho GWM.gif|right|thumb|400px|Spin echo animation showing the response of spins (red arrows) in the blue [[Bloch sphere]] to the green [[pulse sequence]] ]]
In [[Nuclear magnetic resonance|magnetic resonance]], a '''spin echo''' is the refocusing of [[Spin (physics)|spin]] magnetisation by a pulse of resonant [[electromagnetic radiation]]. Modern [[nuclear magnetic resonance]] and [[magnetic resonance imaging]] make use of this effect.

The [[Free induction decay|NMR signal]] observed following an initial excitation pulse decays with time due to both spin [[Relaxation (NMR)|relaxation]] and any ''inhomogeneous'' effects which cause different spins in the sample to [[Precession|precess]] at different rates. The first of these, relaxation, leads to an irreversible loss of magnetisation. However, the inhomogeneous dephasing can be removed by applying a 180° ''inversion'' pulse that inverts the magnetisation vectors. Examples of inhomogeneous effects include a magnetic field gradient and a distribution of [[chemical shift]]s. 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.

Echo phenomena are important features of coherent [[spectroscopy]] which have been used in fields other than magnetic resonance including [[laser spectroscopy]]<ref name=PhotonEcho>
{{cite journal
| author = Kurnit, N. A.; Abella, I. D.; Hartmann, S. R.
| title = Observation of a photon echo
| journal = Physical Review Letters
| year = 1964
| volume = 13
| pages = 567–568
| doi = 10.1103/PhysRevLett.13.567
| bibcode=1964PhRvL..13..567K}}
</ref> and [[Neutron spin echo|neutron scattering]]. Echoes were first detected in nuclear magnetic resonance by [[Erwin Hahn]] in 1950<ref name=hahn>
{{cite journal
| author = Hahn, E.L.
| title = Spin echoes
| journal = Physical Review
| year = 1950
| volume = 80
| pages = 580–594
| doi = 10.1103/PhysRev.80.580|bibcode = 1950PhRv...80..580H }}
</ref>
, and spin echoes are sometimes referred to as ''Hahn echoes''. In [[nuclear magnetic resonance]] and [[magnetic resonance imaging]], [[radiofrequency]] radiation is most commonly used.

==Principle==

The spin echo effect was explained by Erwin Hahn in his 1950 paper,<ref name=hahn/> and further developed by [[Herman Carr|Carr]] and [[Edward Mills Purcell|Purcell]] who pointed out the advantages of using a 180° refocusing pulse for the second pulse.<ref>
{{cite journal
| author = Carr, H. Y.; Purcell, E. M.
| title = Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments
| journal = Physical Review
| year = 1954
| volume = 94
| pages = 630–638
| doi = 10.1103/PhysRev.94.630|bibcode = 1954PhRv...94..630C }}
</ref> The pulse sequence may be better understood by breaking it down into the following steps:
{|align="center" width="100%" valign="middle" style="margin: 1em auto 1em auto; border: 0px; bgcolor: white;"
|-
| colspan = 2 | <center>[[File:SpinEcho GWM stills.jpg|800px|The spin echo sequence]]</center>
|- valign="top"
| width="50%" |
<ol style="list-style-type: upper-alpha; font-weight:bold">
<li>The vertical red arrow is the average magnetic moment of a group of spins, such as protons. All are vertical in the vertical magnetic field and spinning on their long axis, but this illustration is in a [[rotating reference frame]] where the spins are stationary on average.</li>
<li>A 90 degree pulse has been applied that flips the arrow into the horizontal (x-y) plane.
<li>Due to local magnetic field inhomogeneities (variations in the magnetic field at different parts of the sample that are constant in time), as the net moment precesses, some spins slow down due to lower local field strength (and so begin to progressively trail behind) while some speed up due to higher field strength and start getting ahead of the others. This makes the signal decay. </li>
</ol>
| width="50%"|
<ol start="4" style="list-style-type: upper-alpha; font-weight:bold">
<li>A 180 degree pulse is now applied so that the slower spins lead ahead of the main moment and the fast ones trail behind.</li>
<li>Progressively, the fast moments catch up with the main moment and the slow moments drift back toward the main moment.</li>
<li>Complete refocusing has occurred and at this time, an accurate T2 echo can be measured with all T2* effects removed. Quite separately, return of the red arrow towards the vertical (not shown) would reflect the T1 relaxation. 180 degrees is π radians so 180° pulses are often called π pulses.</li>
</ol>
|}

Several simplifications are used in this sequence: no [[decoherence]] is included and each spin experiences perfect pulses during which the environment provides no spreading. Six spins are shown above and these are not given the chance to dephase significantly. The spin echo technique is more useful when the spins have dephased more significantly such as in the animation below:

<center>[[File:SpinEcho2 GWM.gif|Spin echo animation with more spins and more dephasing]]</center>

==Spin echo decay==

A Hahn echo decay experiment can be used to measure the [[spin–spin relaxation]] time, as shown in the animation below. The size of the echo is recorded for different spacings of the two pulses. This reveals the decoherence which is not refocused by the π pulse. In simple cases, an [[exponential decay]] is measured which is described by the T2 time.

[[File:GWM HahnEchoDecay.gif|Spin echo decay]]

==Stimulated echo==

Hahn's 1950 paper<ref name=hahn/> showed that another method for generating spin echoes is to apply three successive 90° pulses. After the first 90° pulse, the magnetization vector spreads out as described above, forming what can be thought of as a “pancake” in the x-y plane. The spreading continues for a time <math>\tau</math>, and then a second 90° pulse is applied such that the “pancake” is now in the x-z plane. After a further time <math>T</math> a third pulse is applied and a stimulated echo is observed after waiting a time <math>\tau</math> after the last pulse.

==Photon echo==
Hahn echos have also been observed at optical frequencies.<ref name=PhotonEcho/> For this, resonant light is applied to a material with an [[Line broadening|inhomogeneously broadened]] absorption resonance. Instead of using two spin states in a magnetic field, photon echoes use two energy levels that are present in the material even in zero magnetic field.<ref>http://www.physics.montana.edu/oct/web/basics_of_octs.htm</ref>

== See also ==
*[[Nuclear magnetic resonance]]
*[[Magnetic resonance imaging]]
*[[Neutron spin echo]]
*[[Electron paramagnetic resonance]]
*[[Gradient Echo]]

==Animations and Simulations==
* http://scratch.mit.edu/projects/nevit/872879 Spin Echo Simulation
*[http://www.bigs.de/BLH/en/index.php?option=com_content&view=category&layout=blog&id=103&Itemid=271 The animation show pulse sequences like spin echo sequence]

== References ==
<References/>

== Textbooks ==

*{{cite book
|author = Ray Freeman
|title = Spin Choreography: Basic Steps in High Resolution NMR
|publisher = Oxford University Press
|year = 1999
|isbn = 978-0-19-850481-8
}}

*{{cite book
|author = Malcolm H. Levitt
|title = Spin Dynamics: Basics of Nuclear Magnetic Resonance
|publisher = Wiley
|year = 2001
|isbn = 978-0-471-48922-1
}}

*{{cite book
|author = Arthur Schweiger, Gunnar Jeschke
|title = Principles of Pulse Electron Paramagnetic Resonance
|publisher = Oxford University Press
|year = 2001
|isbn = 978-0-19-850634-8
}}

[[Category:Magnetic resonance imaging]]
[[Category:Nuclear magnetic resonance]]
[[Category:Quantum mechanics]]
[[Category:Scientific techniques]]
[[Category:Spectroscopy]]

Unit tangent bundle - Revision history

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