# Why is 180 degree pulse applied after half echo time (TE) in Spin Echo sequence?

The definition of Echo Time from Radiopaedia:

The echo time (TE) refers to the time between the application of the radiofrequency excitation pulse and the peak of the signal induced in the coil. It is measured in milliseconds. The amount of T2 relaxation is controlled by the TE.

Why do we apply the 180 degree pulse at TE/2 in a Spin Echo sequence in order to refocus spins (that are dephased by magnetic field dishomogeneties) ?

The effect of the refocusing pulse is to reverse the phase of the excited spins. If a spin experiences a static magnetic field that is slightly different from the main magnetic field then it will precess at a slightly different Larmor frequency. Call the difference in frequency $$\Delta f$$, the off-resonance frequency. Since field is static, $$\Delta f$$ is constant, so the spin accumulates phase at a constant rate $$d \phi/dt= 2\pi \ \Delta f$$.

Now, immediately after excitation, all spins have $$\phi(0)=0$$ phase. After a time $$\tau$$ then each spin has a phase $$\phi (\tau_-)=\tau \ 2\pi \ \Delta f$$. If we then apply a refocusing pulse each spin will have a phase $$\phi (\tau_+)=-\tau \ 2 \pi \ \Delta f$$. After another time $$\tau$$ then the spin will accumulate phase at the same rate bringing the phase to $$\phi(2\tau)=0$$

So, regardless of $$\Delta f$$ and $$\tau$$ if you apply a refocusing pulse at time $$\tau$$ you get your phase to return to $$0$$ at time $$2\tau$$. We call the condition of all spins returning to $$0$$ an “echo” and therefore the “echo time” is $$TE=2\tau$$

• Thanks for your answer ! However, why is the duration of dephasing equal to TE/2 ? Jan 14 at 11:47
• @HelpNeederStudent because once you apply the refocusing pulse it stops dephasing and starts rephasing. I will add a few sentences to the answer
– Dale
Jan 14 at 17:36
• Sorry... I can not understand yet. So in your practical example, TE/2 is 15 ms ? Jan 16 at 14:46
• @HelpNeederStudent yes
– Dale
Jan 16 at 18:09
• I apologize... the concept of rephasing at some rate is now clear, however I don't understand why this rephasing has to be applied at TE/2 instead, for example, of TE. Could you explain it using a time course diagram of Spin Echo pulse sequence ? Jan 17 at 8:06