Spin echo · CPMG · measuring T2

The Spin Echo & Echo Trains

The phase fan opens, a 180° pulse mirrors it, and the fan closes again. Repeat the refocusing and the echo peaks trace out T₂ itself.

Ready.

Each thin arrow is one isochromat: a group of spins sharing a Larmor frequency. The thick red arrow is their sum.

|signal| T₂ envelope echo peaks

Every echo peak lands on the T₂ curve. Fitting those peaks is how a multi-echo sequence measures T₂.

Sequence and tissue

Echo spacing TE The first 180° comes at TE/2; echoes form at TE, 2TE, 3TE …

Echoes in the train A CPMG train: one excitation, many refocusing pulses.

Field inhomogeneity Sets T₂*: how fast the fan opens between echoes.

T₂ The true decay the echo peaks are chasing.

Isochromats More isochromats give a smoother, more realistic decay.

Playback speed Simulated milliseconds per second.

Show individual isochromats Trail of the sum

|signal|0.000

echoes so far0

last echo--

predicted e^−TE/T2--

t0 ms

What this figure is for

This is the figure to draw on the board when someone asks why we bother with a 180° pulse. The fan on the left is the whole argument: dephasing is ordering, not loss, and order can be reversed.

1/T2* = 1/T2 + γΔB₀ → echo(n·TE) = M₀ e^−n·TE/T2

Run the train and watch the peaks, not the wiggles. The signal between echoes is T₂*-limited and tells you mostly about your shim. The peaks are T₂-limited and tell you about the tissue. A multi-echo sequence fits an exponential through those red dots, which is exactly how a T₂ map is made.
Press FID only. With no refocusing you see the raw T₂* decay, and the signal is gone long before T₂ has run its course. The gap between that curve and the dashed envelope is what the 180° pulses buy back.
The inhomogeneity slider does not move the peaks. Push it to 20 Hz: the fan opens faster, the signal between echoes vanishes sooner, and the echo peaks stay exactly where they were. That independence is the entire point of the spin echo, and it is why spin-echo T₂ values are reproducible across scanners while T₂* values are not.
Why TE controls contrast. Set T₂ to 300 ms and then 1500 ms, and compare the height of the last echo. Long-T₂ tissue such as CSF still has signal at a long TE while short-T₂ tissue has none. That difference is T₂ weighting.

Careful with the cartoon: the isochromats here keep a constant frequency, so refocusing is perfect. Real spins diffuse between regions of different field and molecular tumbling randomises their phase. That randomness is precisely T₂, and it is what stops the echo train from going on forever.