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Why not just use random phases?

"If the goal of RF spoiling is just to scramble the phase of the transverse magnetization, why do we use this specific formula, ϕn=ϕ0n(n+1)2\phi_n = \phi_0 \frac{n(n+1)}{2}, instead of a random number generator?"

a student, in class

It’s a good question, and the answer isn’t obvious. A random phase does scramble the transverse magnetization. On average it even does a slightly better job than the quadratic scheme. What it does badly is let the sequence reach a steady state.

How to use this book

Each page builds on the previous one, from a handful of spins up to a full image. All figures are interactive: hover for values, use the sliders to change the flip angle, click legend entries to hide or show curves, and drag to zoom.

  1. Why the quadratic formula works covers the SPGR sequence, why gradient spoiling alone is not enough, and why the quadratic formula produces a steady state (and random phases don’t).

  2. A few spins shows the RF phase schedules, a few isochromats in a voxel, and the voxel signal in the complex plane.

  3. Steady state (or not) compares signal over time, signal against flip angle, and the effect of the choice of ϕ0\phi_0.

  4. A full image shows what each scheme does to a full image.

  5. Takeaways summarizes the results and gives discussion questions for class.

RF spoiling: why not just use random phases?
Theory