See Aliasing Artifact.

Quick Overview

A moiré pattern is an interference pattern created for example when two grids are overlaid at an angle, or when they have slightly different mesh sizes. The human visual system creates an imaginary pattern of roughly horizontal dark and light bands, the moiré pattern that appears to be superimposed on the lines.
In MRI, the appearance of moiré fringes can be caused by a variety of reasons e.g., inhomogeneity of the main magnetic field caused by a defect shielding (interference with RF pulses), interferences produced by aliasing, and interferences of echoes from different excitation modes (with different echo times).

Take spin echo-based techniques, or a surface coil. This artifact is often sensitive to shimming or susceptibility gradients.

According to Shannon's sampling theorem, the sampling frequency should be twice the frequency being sampled. The maximum measurable frequency is therefore equal to one half the sampling rate. This is the so-called Nyquist limit. When the frequency is higher than the Nyquist limit, aliasing occurs.

(PCA) With this method images of the blood flow-velocity (or any other movement of tissue) are produced. The MRI signal contains both amplitude and phase information. The phase information can be used with subtraction of images with and without a velocity encoding gradient. The signal will be directly proportional to the velocity because of the relation between blood flow-velocity and signal intensity.
This is the strength of PCA, complete suppression of stationary tissue (no velocity - no signal), the direct velocity of flow is being imaged, while in TOF (Inflow) angiography, tissue with short T1 (fat or methaemoglobin) might be visualized.
The strength of the gradient determines the sensitivity to flow. It is set by setting the aliasing or encoding velocity (VENC). Unfortunately, phase sensitization can only be acquired along one axis at a time. Therefore, phase contrast angiographic techniques tend to be 4 times slower than TOF techniques with the same matrix.

See also Phase Contrast Sequence, Magnetic Resonance Angiography, Contrast Enhanced Magnetic Resonance Angiography, Flow Effects and Flow Quantification.

The data acquisition beyond the FOV in phase encoding direction, with doubling the number of acquisitions and the scan time.

See also Oversampling and Aliasing Artifact.