Continues from Larmor precession. M already walks around B0 at ω₀.

A coil along z hears nothing from M precessing around z. You have to tip M off z so a piece of it sits in xy and keeps rotating. The tip is an RF pulse: a small field B1 in the xy plane, oscillating at ω₀. Same frequency as the walk. That matching is resonance. Push a swing at its natural period. Off-frequency B1 mostly misses.

In the frame that rotates at ω₀, B0 drops out and B1 looks still. M then precesses around B1 instead of around B0. How far it tips is the flip angle. For a constant-amplitude pulse of duration t_p:

α = γ B1 t_p

Rotating-frame axes with B1 along x-prime and magnetization tipping from z by flip angle alpha.
In the rotating frame B1 looks still. M precesses around it. The tip is the flip angle α = γ B1 t_p.

A 90° pulse parks M in xy. A 180° pulse sends it to −z. The scanner talks in α, not in B1.

If B1 is off-resonance, M sees an effective field that is not B1, so the tip is smaller and the axis is wrong. Slice selection later uses a gradient so only one slab is on-resonance. That is a later note. What the coil actually records is the rotating xy component, not Mz.

Next note: T1 and T2 relaxation.

中文

接拉莫爾進動。M 已經在 ω₀ 繞 B0 走。

線圈沿 z 放,聽不到 M 繞 z 進動;得把 M 從 z 推開,讓一塊待在 xy 裡繼續轉。這一推是 RF pulse:xy 平面上一個小磁場 B1,以 ω₀ 振盪,跟走路的頻率一樣,對上就是共振;盪鞦韆要照它自己的週期推,頻率不對的 B1 多半推空。

在以 ω₀ 轉的座標系裡,B0 消失,B1 看起來是靜的;M 改繞 B1 進動,不再繞 B0。推多遠是 flip angle;振幅固定、長度 t_p 的 pulse:

α = γ B1 t_p

90° pulse 把 M 停在 xy,180° pulse 把它送到 −z;掃描器講的是 α,不是 B1。

B1 偏離共振時,M 看到的有效場不是 B1,所以推得比較小,軸也不對;後面選層會用梯度,只讓一層在共振上,那是後面的筆記。線圈真正記到的是轉著的 xy 分量,不是 Mz。

下一則:T1 和 T2 弛緩