Current carrying coils designed to produce a desired magnetic field gradient (so that the magnetic field will be stronger in some locations than others).
Proper design of the size and configuration of the coils is necessary to produce a controlled and uniform gradient. Three paired orthogonal current-carrying coils located within the magnet that are designed to produce desired gradient magnetic fields, which collectively and sequentially are superimposed on the main magnetic field (B0) so that selective spatial excitation of the imaging volume can occur.
Gradients are also used to apply reversal pulses in some fast imaging techniques. Gradient coils in general vary the main magnetic field, so that each signal can be related to an exact location. The gradientcoil configuration for the z-axis consists of e.g., Helmholtz pair coils, and of paired saddle coils for the x- and y-axis.
A coordinate system, which uses the distance from the coordinate system center and positional angles to identify points in space rather than orthogonal independent unit vectors as in the Cartesian coordinate system. Polar and partly polar (cylindrical) coordinate systems are widely used to describe spin motion in NMR experiments.
It is important to know how to compute the coordinates of a point in the polar coordinate system when they are given in a Cartesian system and vice versa. The length of the vector r pointing from the coordinate origin to a point in 2D space is given as
r = √(x2 + y2).
while the polar or phase angle f is obtained by performing the operation
f = arctan (y/x),
where the arctan function is the inverse of the tangent function.