# Phase encoding

Now that we have selected a single slice and a single column within that slice, we need to localise the signal along that column (ie. the row). We do this by applying another gradient in the y-axis.

If we take a single column through the slice (i.e. a single frequency in the read-out direction) and then divide this into sections in the y-axis, each segment will have the same frequency and phase.

We switch on the phase-encoding gradient along the y-axis before the readout gradient. Some sections will precess with a quicker frequency and some with a slower frequency. When we switch off the gradient all the segments return to the same frequency but they are now all out of phase with a phase-shift that depends on the position along the column.

### 2. Repeat cycle With every cycle the amplitude of the phase encoding gradient is changed so that the phase of the MR signal at a certain y-axis position changes each time. If we look at a single point in time along the cycle and look at the amplitude of the wave at that point, it varies with each cycle. If we then plot this amplitude with each cycle we get another wave.

Each point along the segment will have a phase encoding curve with a different frequency. Those at the furthest ends of the gradient will have a greater change in their phases and, therefore, a higher frequency phase encoding curve. The point at the middle of the gradient, the isopoint, will never change its frequency or, therefore, its phase. A Fourier transform is again applied to extract these frequencies and place them in the correct place along the y-axis.

The signal strength (brightness) is given by the maximum amplitude of the phase-shift curve as this corresponds to the maximum amplitude of the original signal.

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Σ  Summary
1. Phase-encoding gradient applied along y-axis
2. The frequencies of each segment in the column are now different
5. However, they are now out of phase
6. The amplitude of the signals is plotted
7. The cycle is repeated with different strengths of phase-encoding gradients producing different phase shifts each time
8. The plot of the amplitude with each phase shift forms a wave with a particular frequency
9. Each area in the column with have a phase-shift wave with a different frequency depending upon its area along the y-axis
10. Fourier transform is applied to separate out the frequencies and slot them into their position along the y-axis

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