Recalled echoes in NMR imaging
A method of encoding NMR free induction signals with information on the spatial distribution of spins is discussed. Modulation of one magnetic field gradient can be used to form a train of echoes (recalled echoes). Each echo is encoded with one dimensional spatial information. A second, orthogonal, gradient can be used to encode the echo train with information in a second dimension. The technique may therefore be used to form a 2D image from a single free induction signal in tens of milliseconds. A simple model of the behaviour of the spins under the imaging pulse sequence is developed and it is shown that a 2D Fourier transform will yield an image of spin distribution. Echoes produced during alternate phases of the modulated gradient are time reversed and failure to take this into account will lead to considerable aliasing in the image. A simple method of correcting for this without loss of resolution is proposed. Resolution and field of view are discussed. The effects of relaxation and magnetic field inhomogeneities are discussed in terms of the model. It is predicted that practically achievable resolution will be limited by image distortion caused by inhomogeneities. The relationship between signal to noise ratio and resolution is discussed and the efficiency of the system compared with that of other Fourier transform techniques. Aspects of instrumentation are discussed, particulary signal bandwidth requirements (gradient production and data collection) and main field measurement (shimming). 2D images supporting the qualitative predictions of the model are presented. Recalled echoes may also be used in conjunction with another encoding technique to give a simultaneous 3D imaging technique. Images produced by one such combination are presented.