= Stimulated echo
A <stimulated echo> is a delayed <nuclear magnetic resonance> <signal> produced by a sequence that stores part of a dephased <magnetization> pattern along the static <magnetic field> and later converts it back into detectable transverse <magnetization>. In a common ideal sequence, three $90^{\circ}$ pulses are applied at times $0$, $\tau$ and $\tau+T_{mathrm m}$. The selected <stimulated echo> appears a further $\tau$ after the third pulse, at $2\tau+T_{mathrm m}$.<Spin Echoes by Erwin Louis Hahn>[Page588, discussion of Eq.22-A and Figure6: three-pulse stimulated echo; Hahn's third-pulse time T is absolute]{ref}
The first interval lets spins with different <Larmor frequencies> accumulate different <phases>. The second pulse converts part of that frequency-dependent pattern into longitudinal <magnetization>. During the storage interval $T_{mathrm m}$ this component does not precess as transverse <magnetization> does. The third pulse returns part of the pattern to the transverse plane, where the appropriate contribution rephases. Storage retains a frequency-dependent population pattern, not a continuously rotating transverse vector.<Spin Echoes by Erwin Louis Hahn>[Page588 and Figure6: longitudinal components distributed approximately as cosine of frequency offset times pulse separation]{ref}
For an original ideal calculation, hold $\tau$ fixed and neglect <diffusion>, pulse errors and exchange. If $T_1$ is the <spin-lattice relaxation> time, the selected echo contribution obeys
$$
\frac{A(T_{mathrm m})}{A(0)}=e^{-T_{mathrm m}/T_1}.
$$
A storage interval $T_{mathrm m}=T_1\ln2$ therefore halves that contribution. The two transverse intervals still incur <transverse relaxation>; longitudinal storage does not undo every source of signal loss.
This distinction is useful for <diffusion> measurements when a longer observation interval is wanted without keeping the relevant pattern transverse throughout. A 1989 experiment used pulsed-gradient <stimulated echo> sequences to reduce particular background-gradient effects in heterogeneous samples. It tested specified pulse arrangements, rather than establishing that every <stimulated echo> removes every gradient error.<Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems by R. M. Cotts and others>[Abstract: pulsed-gradient sequences, cross-term cancellation conditions and experimental tests]{ref}
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