The process of locating a MR signal by altering the phase of spins in one dimension with a pulsed magnetic field gradient along that dimension prior to the acquisition of the signal.
If a gradient field is briefly switched on and then off again at the beginning of the pulse sequence right after the radio frequency pulse, the magnetization of the external voxels will either precess faster or slower relative to those of the central voxels.
During readout of the signal, the phase of the xy-magnetization vector in different columns will thus systematically differ. When the x- or y- component of the signal is plotted as a function of the phase encoding step number n and thus of time n TR, it varies sinusoidally, fast at the left and right edges and slow at the center of the image. Voxels at the image edges along the phase encoding direction are thus characterized by a higher 'frequency' of rotation of their magnetization vectors than those towards the center.
As each signal component has experienced a different phase encoding gradient pulse, its exact spatial reconstruction can be specifically and precisely located by the Fourier transformation analysis. Spatial resolution is directly related to the number of phase encoding levels (gradients) used. The phase encoding direction can be chosen, e.g. whenever oblique MR images are acquired or when exchanging frequency and phase encoding directions to control wrap around artifacts.

The temporal order in which the phase encoding gradient pulses are applied. The order can be sequential, centric, reverse centric, random, etc.

A strategy for incrementing the position of the k-space trajectory of an echo planar imaging (EPI) pulse sequence.
Echo planar imaging (EPI) uses a constant gradient amplitude in one direction. This, combined with an oscillating gradient system in the frequency encoding direction, produces a zigzag trajectory in k-space. In the blipped phase encoding variant of EPI, the k-space position in the phase encoded direction is incremented by gradient 'blips' of the appropriate area. These, when timed to occur during the reversals of the read-out gradient, produce a rectilinear path in k-space.
The artifacts in an EPI image can arise from both hardware and sample imperfections. These are most easily understandable from examination of the k-space trajectory involved, which is either a zigzag form (when using a constant phase encoding gradient) or a rastered zigzag (when the phase encoding is performed with small gradients at the end of each scan line, so-called 'blipped' EPI).

(Gφ) The phase encoding gradient is a magnetic field gradient that allows the encoding of the spatial signal location along a second dimension by different spin phases. The phase encoding gradient is applied after slice selection and excitation (before the frequency encoding gradient), orthogonally to the other two gradients. The spatial resolution is directly related to the number of phase encoding steps (gradients).

(PEAR) Each phase of the respiratory cycle coincides with the collection of phase encoded data. The low order phase encoded data, with is highly sensitive to motion, is collected towards the end of exhalation and beginning of inspiration. The high order data, which is less sensitive, is collected over the remaining part of each respiratory cycle.