= Spin echo
{title2=$90^\circ-\tau-180^\circ-\tau$}
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= Hahn echo
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{synonym}
A <spin echo> is a reappearance of transverse <magnetization> after a pulse sequence reverses an earlier spread of <phases>. An ensemble can have almost no net transverse <magnetization> while its components retain enough individual phase memory to reassemble. In the ideal <Hahn echo> below, a short 90° pulse prepares transverse <magnetization>, a 180° pulse follows after time $\tau$, and the <signal> refocuses at $t=2\tau$. The receiver observes freely precessing <magnetization>, as in <free induction decay>; no third driving pulse is needed at the echo time.
The useful distinction is between cancellation in an ensemble average and loss of recoverable phase memory. A static spread of <Larmor precession> <frequencies> can make <free induction decay> much faster than <transverse nuclear magnetization decay>. A <spin echo> can remove that static spread from the echo amplitude, allowing a more selective measurement of <transverse relaxation>. It does not in general reverse <noise>, <population relaxation>, or every interaction between <spins>.
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