Chemical Shift Directions
Surely, seeing as fat and water precess at different frequencies, they acquire a different amount of phase encoding when the phase encoding gradient is applied?
That's true, but think for a moment about what the phase encoding (PE) gradient does. The gradient is no different from the frequency encoding (FE) gradient in terms of what happens to protons in a sample of interest. The PE gradient changes the frequency of precession of the spins just like the FE gradient does! Both are magnetic field gradients, which simply change the field strength and hence also the Larmor frequency. The difference between them is when we use them. The FE gradient is applied as we read out the echo, whereas the PE gradient is turned on for a brief moment and then switched off again before we read out the echo. This brief change in frequency in the PE direction results in a range of phase changes in the phase encoding direction. And, it is true to say that since there is a chemical shift between fat and water, a phase difference between them will evolve. However, as we vary the strength of the PE gradient to fill k-space line by line, the phase difference does not accumulate. It's a new excitation and a new echo each time. The amount of chemical shift between fat and water does not change from one signal to the next, and since phase encoding relies on the rate of change of phase from line to line in the PE direction, no chemical shift artefact is seen.
Further reading on this topic:
Books: Q&A in MRI p126-127