Physics, Techniques and Procedures

Frequency encoding

method for localization of MR signals in MR imaging (see spatial encoding). Once the spins have been excited by a radiofrequency RF pulse, they reradiate radio waves at a frequency which according to the Larmor equation is proportional to the local magnetic field strength. If during signal recording in an MR pulse sequence a magnetic gradient field, the so-called frequency encoding gradient, is switched on along an arbitrary direction, the signals radiated from different positions along this direction will have different frequencies (Fig.1), i. e. frequencies will vary from lower to higher from the left side to the right side of the body. A Fourier transformation FT of the recorded signal will yield signal amplitudes at different frequencies which correspond to the signal from the pixel columns in the example shown in Fig. 1. Thus localization is accomplished in one spatial dimension. As the frequency encoding direction can be chosen arbitrarily, the MR operator can decide whether the "rows" or "columns" of the image are at the same frequency. Viewed in k space, the constant readout gradient used in frequency encoding causes the position in k-space during signal acquisition to advance at a constant speed in one direction. Thus, all the data points acquired during the readout are equally spaced along one line in k-space. A preparatory gradient (which could be called a pre-phasing or dephasing gradient), is used to centre the line containing the collected k-space samples.

Spatial resolution in the frequency encoding direction is determined by the temporal width of the acquisition window (which determines the resolution in frequency), the strength of the frequency encoding gradient and the gyromagnetic ratio which define the proportionality constant between position in the frequency encoding direction and temporal frequency. The field of view FOV is proportional to the product of the amplitude of the frequency encoding gradient, the gyromagnetic ratio, and the readout bandwidth.

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