(NMR) Nuclear Magnetic Resonance is a physical phenomenon of the magnetic property of nuclei, which have a positive nuclear spin quantum number.
Under the influence of an external static magnetic field this nuclei will precess about the direction of the magnetic field with an angular frequency (Larmor frequency). Through absorption and emission of RF energy (gradients, RF coils) at the resonance frequency (Larmor equation) and the processing of this raw data by the Fourier transformation - physical, chemical, electronic, and structural information about molecules can be obtained (NMR Magnetic Resonance Spectroscopy, Magnetic Resonance Imaging).

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.

A technique that uses RF pulses and Fourier transformation of the MR signal; have largely replaced the older continuous wave techniques.

Quadrature detection is used in magnetic resonance imaging as well as in Doppler ultrasound and is also called quadrature demodulation or phase quadrature technique.
With this phase sensitive demodulation technique the complex demodulated signal is separated into two components. One is called the real channel; the second part is called the imaginary channel and is located 90° away from the real channel. The signals from both channels are combined to produce a single set of quadrature detected real and imaginary spectra. In MRI, the parts of the demodulated MR signal are further processed by Fourier transformation analysis. All information on the MR signal components e.g. amplitude, phase, and frequency is given by this quadrature detection combined with Fourier analysis.

A real number is a component of a complex number. In MRI, complex data are used for example in the Fourier transforms.