A Fonnalism for Generating Multiparametric Encoding Gradients in NMR Tomography

A general mathematical formalism for generating multiparametric NMR image encoding gradients is introduced. The new schematic approach enables one to construct any desired encoding gradient which may be used in an imaging sequence. Basic gradient waveforms which can be used as building blocks of the desired encoding gradients are presented. A matrix operator for obtaining the encoding gradient for any kind of phase encoding is derived. Specific examples illustrating how to obtain "pure" spatial, velocity, or acceleration encoding gradients for moving spins are presented.