T2* · field maps · reversible loss

Dephasing in Three Dimensions

A field gradient across the sample, a fan of phases, and a signal that dies far faster than T₂ alone would allow.

What this figure is for

The field is not uniform across the lattice: spins on one side sit a little higher in field and run ahead, spins on the other side lag. Switch on Shade spheres by field offset to see the map that is driving it, then watch the phase colours sort themselves along that same axis.

Two decays, one signal. The measured envelope is T₂*, and it is always faster than T₂: 1/T2* = 1/T2 + 1/T2', where T₂′ comes from the static field spread. The dashed grey curve is the T₂ part alone, so the gap between the curves is the reversible loss.
Reversible means recoverable. Hit the 180° button part-way through the decay. The phase fan mirrors, the fast spins are suddenly behind the slow ones, and the sum rebuilds itself into an echo that touches the dashed T₂ curve. Nothing was lost, only reordered.
Where it comes from in practice. Imperfect shim, the air cavities behind the sinuses and ear canals, a metal restoration, the deoxyhaemoglobin in a draining vein. The last one is the signal source for BOLD fMRI, which is why functional imaging uses T₂*-weighted gradient echoes and deliberately does not refocus with a 180°.

Try this in class: park the inhomogeneity at 8 Hz and run the spin echo button. Then set it to 0 Hz and run it again. In the second case there is no echo to form, because there was never any reversible dephasing to undo.