Imaging revisited


We want to measure some spatial magnetization distribution Mxy(r) present after excitation, weighting or other preparation.

The Fourier theorem
Any function can be written as a weighted sum of phase rolls:



Note: This decomposition is purely conceptual.
no gradients are applied so far.

Now, how can the amount () of a specific phase roll be measured?

Easy! We refocus it with a gradient. 

The signal will then be proportional to  before the refocusing.

Refocusing can be done by applying a gradient G moving from k to k=0.