A coil is a large inductor with a considerable dimension and a defined wavelength, commonly used in configurations for MR imaging. The frequency of the radio frequency coil is defined by the Larmor relationship.
The MRI image quality depends on the signal to noise ratio (SNR) of the acquired signal from the patient. Several MR imaging coils are necessary to handle the diversity of applications. Large coils have a large measurement field, but low signal intensity and vice versa (see also coil diameter). The closer the coil to the object, the stronger the signal - the smaller the volume, the higher the SNR. SNR is very important in obtaining clear images of the human body. The shape of the coil depends on the image sampling. The best available homogeneity can be reached by choice of the appropriate coil type and correct coil positioning. Orientation is critical to the sensitivity of the RF coil and therefore the coil should be perpendicular to the static magnetic field.

RF coils can be differentiated by there function into three general categories:
The RF signal is in the range of 10 to 100 MHz. During a typical set of clinical image measurements, the entire frequency spectrum of interest is of the order 10 kHz, which is an extremely narrow band, considering that the center frequency is about 100 MHz. This allows the use of single-frequency matching techniques for coils because their inherent bandwidth always exceeds the image bandwidth. The multi turn solenoid, bird cage coil, single turn solenoid, and saddle coil are typically operated as the transmitter and receiver of RF energy. The surface and phased array coils are typically operated as a receive only coil.

See also the related poll result: '3rd party coils are better than the original manufacturer coils'

(RFOV) A different field of view (the scanned region) in the frequency and phase encoding directions that means the data acquisition with fewer measurement lines. Because there are fewer rows than columns, a rectangular image is obtained. To reduce the FOV in phase encoding direction (foldover direction) saves scan time by decreasing signal but invariable spatial resolution.
Also called HFI or undersampling.

If the scanned object is oval, e.g. head or abdomen, a rectangular FOV is an easy to use scan parameter to reduce the scan time without loss of resolution.

(SNR or S/N) The signal to noise ratio is used in MRI to describe the relative contributions to a detected signal of the true signal and random superimposed signals ('background noise') - a criterion for image quality.
One common method to increase the SNR is to average several measurements of the signal, on the expectation that random contributions will tend to cancel out. The SNR can also be improved by sampling larger volumes (increasing the field of view and slice thickness with a corresponding loss of spatial resolution) or, within limits, by increasing the strength of the magnetic field used. Surface coils can also be used to improve local signal intensity. The SNR will depend, in part, on the electrical properties of the sample or patient being studied. The SNR increases in proportion to voxel volume (1/resolution), the square root of the number of acquisitions (NEX), and the square root of the number of scans (phase encodings). SNR decreases with the field of view squared (FOV2) and wider bandwidths. See also Signal Intensity and Spin Density.

Measuring SNR:
Record the mean value of a small ROI placed in the most homogeneous area of tissue with high signal intensity (e.g. white matter in thalamus). Calculate the standard deviation for the largest possible ROI placed outside the object in the image background (avoid ghosting/aliasing or eye movement artifact regions).
The SNR is then:
Mean Signal/Standard Deviation of Background Noise

The overall width in hertz needed to observe a particular NMR spectrum. This width is generally set using the Nyquist limit; namely, that the temporal sampling rate must be equal to twice the maximum spread in frequencies.

(N) The SI units is moles/m³.
Definition: The concentration of nuclei in tissue processing at the Larmor frequency in a given region; one of the principal determinants of the strength of the NMR signal from the region.
For water, there are about 1.1 x 105 moles of hydrogen per m³, or 0.11 moles of hydrogen/cm³.
The signal intensity measured is related to the square of the xy-magnetization, which in a SE pulse sequence is given by
Mxy = Mxy0(1-exp(-TR/T1)) exp(-TE/T2)
where Mxy0 = Mz0 is proportional to the proton or spin density, and corresponds to the z-magnetization present at zero time of the experiment when it is tilted into the xy-plane.
True spin density is not imaged directly, but must be calculated from signals received with different interpulse times. The spin density contrast can be generated by using a long TR and sampling the data immediately after the RF pulse (with a TE as short as possible).