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Erwin Hahn discovered spin echo signals, in which radiofrequency pulses restore an observable signal from nuclear spins that have apparently lost phase coherence. A spread of static magnetic fields makes different spins precess at different rates; suitable later pulses allow this reversible dephasing to refocus. The echo amplitude then probes relaxation and diffusion, rather than being determined solely by static field inhomogeneity. His 1950 analysis made pulsed nuclear magnetic resonance a method for distinguishing different causes of signal decay.^[ref]

A physicist who developed spin echo methods and studied nuclear magnetic resonance and optics.^[ref]

Erwin Louis Hahn's 1950 apparatus enclosed liquid samples in the coil of a tuned LC circuit, coupled to a gated radio transmitter and radio receiver. One transmitter quadrupled a crystal oscillator's 7.5 MHz to 30 MHz. A separate proton resonance regulator stabilized the static magnetic field.^[ref]

Waiting for thermal equilibrium prepared nuclear polarization. Oscilloscope photographs compared glycerol proton echoes at different field homogeneity: echo width changed; echo time followed twice the pulse separation. Receiver saturation obscured early free induction decay; transmitter leakage required care. The delayed signal tested refocusing; diffusion could still attenuate it.^[ref]

Hahn analyzed equal pulses as well as noting improved recovery with a second pulse twice as long; the ideal sequence above isolates that latter case.^[ref]

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]