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 $\tau +T_{mathrmm}$. The selected stimulated echo appears a further $\tau$ after the third pulse, at $2\tau +T_{mathrmm}$.^[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 $T_{mathrmm}$ 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.^[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 obeysA storage interval $T_{mathrmm}=T_1\ln 2$ 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.^[ref]