Field maps · T2* · refocusing

Dephasing & Rephasing Across the Sample

Looking straight down the bore at a slice of tissue. Each cell precesses at the rate its own local field dictates, and the coil adds them all up.

Press 90° excite to tip everything into the transverse plane.

Cell shading is the field offset at that location; arrow direction and colour are the phase accumulated there.

The same spins redrawn from one origin, with the vector sum in red.

|signal| T₂ envelope

The field map

Linear field gradient A smooth shim error straight across the slice.

Local susceptibility blob A sinus, an ear canal or a metal clip: a big offset over a small region.

T₂ (irreversible) Random molecular-scale dephasing. No pulse can undo this.

τ (half the echo time) The echo lands at TE = 2τ after the 90°.

Grid size Number of cells across the slice.

Playback speed Simulated milliseconds per second.

Shade cells by field offset Show the vector sum

|signal|0.000

T₂ envelope1.000

field range0 Hz

t since 90°0 ms

What this figure is for

The previous figures treat the sample as a single vector. This one insists on the fact that position matters: every cell sits in a slightly different magnetic field, so every cell accumulates phase at a different rate. The coil has no idea which cell is which. It receives one number, the vector sum, and that number collapses as soon as the cells disagree.

Watch the colours, not the arrows. Immediately after the 90° every cell is the same colour. As time passes the hue sweeps across the slice in step with the field map, which is exactly the phase ramp that a frequency-encoding gradient deliberately imposes during readout.
180° versus reverse time. Reverse time is the cheat: it flips the sign of every precession rate, which no experiment can do. The 180° pulse achieves the identical refocusing by flipping the accumulated phase instead and letting the spins keep running forward at the same rates. Both bring the colours back together; only one of them is physics you can buy.
The blob is refocused too. Turn the susceptibility blob up to 30 Hz. Its cells race away from the rest and the signal dies almost at once, but a 180° still recovers the echo. This is why spin-echo EPI keeps signal near the sinuses where gradient-echo EPI drops out.
What is never recovered. Lower T₂ to 200 ms and run the echo. The echo comes back on time but shorter, and it always lands on the dashed T₂ curve. That curve is the ceiling: refocusing buys back the field-map dephasing and nothing else.

Try this in class: set τ to 500 ms, press Run a spin echo, and ask the room to predict where the echo peak will fall before it happens. Then change T₂ and ask them to predict how tall it will be.