Rate of Change of Phase
CORRECT. A rate of change of phase is a frequency. This is as simple a statement as saying that the rate of change of velocity is acceleration.
Consider the following. If two movements or oscillations are moving at slightly different rates, they will move in and out of phase with each other (like the ticking of a fast and slow clock—they change between ticking together and ticking alternately). If the slower clock is gradually speeded up, the time between the clocks ticking together (in phase) and ticking alternately (out of phase) will change. At first there will be a short time between the in-phase and out-of-phase moments, until eventually the clocks will be in a constant phase relationship as they tick at the same rate (which may be in phase, out of phase, or in between). The rate at which the clock is gradually speeded up produces a rate of change of phase. Importantly, a rate of change of phase is a frequency. This fact is used to pseudo-frequency encode in the last direction in the image slice. This is called phase encoding.
To create a single MRI image, the same signal measurement is recorded over and over again, but different phase relationships between different rows of voxels are introduced for each measurement. If all the measurements taken are then compared, the rate of change of phase for each row is then different. The Fourier transform can separate out frequencies (or in this case, rates-of-change of phase which are equivalent) and signal intensity information can be deduced for pixels in the phase encoding direction.
Different amounts of phase encoding for each measurement may be easily introduced, by temporarily turning on a magnetic field gradient in the phase encoding direction. Just like the other gradients used in MRI (slice selection and frequency encoding), the phase encoding gradient simply changes the Larmor frequency across the patient in that direction. Whilst the gradient is switched on, spins precessing faster at one end of the gradient will start to "get ahead" of the rest. Spins at the other end of the gradient will begin to "lag behind". After the gradient is switched off, the Larmor frequencies in the phase encoding direction return to their original values (all the same) but a phase difference between the spins on that direction will have been introduced. By simply varying the strength of the magnetic field gradient in the phase encoding direction for subsequent measurements, different phase relationships may be established.
Phase requires two oscillations to be compared, and so a rate of change of phase descibes the changing phase between two oscillations. What is this equivalent to?
Phase describes the difference between oscillations and rotations in a repeated cycle. So what is a rate of change of phase?