Spatial Encoding and Reconstruction in MRI with Quadratic Phase Profiles

Application of a slice‐selective frequency modulated radio‐frequency excitation pulse in a magnetic resonance (MR) imaging experiment creates a quadratic phase profile along the direction of slice selection. This quadratic phase profile inherently localizes the signal contribution to its vertex, which can be shifted with the application of a linear magnetic field gradient. Different methods for reconstruction of the spatial profile are discussed. The point spread functions of these reconstructions are similar to that of conventional Fourier transforms; one important difference is the elimination of aliasing at the expense of MR signal amplitude when performing ‘local,’ or limited, reconstruction. Limited reconstruction together with spatially limited excitation combines some of the advantages of both three‐dimensional phase‐encoded and two‐dimensional multislice techniques in appropriate situations. Applications discussed are three‐dimensional gradient echo experiments applied to time of flight MR angiography and T₂‐weighted data collection.