APPARATUS AND METHOD FOR SPATIALLY ORDERED PHASE EAPPARATUS AND METHOD FOR SPATIALLY ORDERED PHASE ENCODING AND FOR DETERMINING COMPLEX PERMITTIVITY INCODING AND FOR DETERMINING COMPLEX PERMITTIVITY IN MAGNETIC RESONANACE BY USING SUPERIMPOSED TIME-VN MAGNETIC RESONANACE BY USING SUPERIMPOSED TIME-VARYING ELECTRIC FIELDS ARYING ELECTRIC FIELDS

摘要

An MRI apparatus comprises a magnet system producing a homogeneous magnetic field along the z axis. A plurality of wire conductors arranged in a "bird cage" configuration are supplied with a circularly rotating RF field centered near the Larmor frequency &ohgr;. sub.o. The wire conductors receive a voltage source V.sub.p having a frequency &ohgr;. sub.p, which is less than the Larmor frequency. The voltage source V.sub. p rotates about the wire conductors at a frequency of &ohgr;.sub.s, which is much less than the frequency &ohgr;.sub.p, to successively apply the voltage V.sub.p to each pair of diametrically opposed wire conductors in a manner which is ordered as a spatial cylindrical harmonic rotating at a frequency &ohgr;.sub.s. The voltage source V.sub.p produces electric fields in the object which generate linear magnetic field gradients in the object. The voltage source V.sub.p phase encodes the detected signals which thereby enables a transverse magnetization at each point within the object to be rapidly mapped back by projection techniques. Alternately, the transverse magnetization can be mapped back by an inverse transformation of a complex plane extending from the measured region by analytic continuation or by a linear transformation utilizing the solutions to Sommerfeld's Integral. The complex permittivity or ionic mobility may be continuously measured through its effect on the transverse magnetization for analysis or process control. The apparatus rapidly and continuously produces an image of the object without requiring conventional gradient field coils or any mechanical moving parts.