Either the phase due to an applied field or field inhomogeneity and generated during the time between two RF pulses, or the phase change of the RF pulse from one pulse to the next.

The phase angle f is in turn affected by resonance offsets due to magnetic field inhomogeneity. If f varies throughout the image, the result will be inhomogeneous signal intensity (shading).

Quick Overview
Please note that there are different common names for this artifact.

During frequency encoding, fat protons precess slower than water protons in the same slice because of their magnetic shielding. Through the difference in resonance frequency between water and fat, protons at the same location are misregistrated (dislocated) by the Fourier transformation, when converting MRI signals from frequency to spatial domain. This chemical shift misregistration cause accentuation of any fat-water interfaces along the frequency axis and may be mistaken for pathology. Where fat and water are in the same location, this artifact can be seen as a bright or dark band at the edge of the anatomy.
Protons in fat and water molecules are separated by a chemical shift of about 3.5 ppm. The actual shift in Hertz (Hz) depends on the magnetic field strength of the magnet being used. Higher field strength increases the misregistration, while in contrast a higher gradient strength has a positive effect. For a 0.3 T system operating at 12.8 MHz the shift will be 44.8 Hz compared with a 223.6 Hz shift for a 1.5 T system operating at 63.9 MHz.

For artifact reduction helps a smaller water fat shift (higher bandwidth), a higher matrix, an in phase TE or a spin echo technique. Since the misregistration offset is present in the read out axis the patient may be rescanned with this axis parallel to the fat-water interface. Steeper gradient may be employed to reduce the chemical shift offset in mm. Another strategy is to employ specialized pulse sequences such as fat saturation or inversion recovery imaging. Fat suppression techniques eliminate chemical shift artifacts caused by the lack of fat signal.

See also Black Boundary Artifact and Magnetic Resonance Spectroscopy.

(MTC) This MRI method increases the contrast by removing a portion of the total signal in tissue. An off resonance radio frequency (RF) pulse saturates macromolecular protons to make them invisible (caused by their ultra-short T2* relaxation times). The MRI signal from semi-solid tissue like brain parenchyma is reduced, and the signal from a more fluid component like blood is retained.
E.g., saturation of broad spectral lines may produce decreases in intensity of lines not directly saturated, through exchange of magnetization between the corresponding states; more closely coupled states will show a greater resulting intensity change. Magnetization transfer techniques make demyelinated brain or spine lesions (as seen e.g. in multiple sclerosis) better visible on T2 weighted images as well as on gadolinium contrast enhanced T1 weighted images.
Off resonance makes use of a selection gradient during an off resonance MTC pulse. The gradient has a negative offset frequency on the arterial side of the imaging volume (caudally more off resonant and cranially less off resonant). The net effect of this type of pulse is that the arterial blood outside the imaging volume will retain more of its longitudinal magnetization, with more vascular signal when it enters the imaging volume. Off resonance MTC saturates the venous blood, leaving the arterial blood untouched.
On resonance has no effect on the free water pool but will saturate the bound water pool and is the difference in T2 between the pools. Special binomial pulses are transmitted causing the magnetization of the free protons to remain unchanged. The z-magnetization returns to its original value. The spins of the bound pool with a short T2 experience decay, resulting in a destroyed magnetization after the on resonance pulse.

See also Magnetization Transfer.

(PE) The partial echo technique (also called fractional echo) is used to shorten the minimum echo time. By the acquisition of only a part of k-space data this technique benefits (like all partial Fourier techniques) from the complex conjugate symmetry between the k-space halves (this is called Hermitian symmetry).
The dephasing gradient in the frequency direction is reduced, and the duration of the readout gradient and the data acquisition window are shortened. Partial echo gives a better SNR at a given TE when a smaller FOV or thinner slices are selected, allows a longer sampling time, and a larger water fat shift (WFS, see also bandwidth) due to a lower gradient amplitude. The resolution is not affected. This is often used in gradient echo sequences (e.g. FLASH, Contrast Enhanced Magnetic Resonance Angiography) to reduce the echo time and yields a lower gradient moment. The disadvantage of using a partial echo can be a lower SNR, although this may be partly offset by the reduced echo time.
Also called Fractional Echo, Read Conjugate Symmetry, Single Side View.

See also Partial Fourier Technique and acronyms for 'partial echo' from different manufacturers.