ABSTRACT
In the previous chapter spin–warp imaging was introduced and discussed. It was shown how a constant gradient in the presence of a band-limited radio frequency pulse can be used to select a particular anatomical slice for excitation, and the received signal (after the readout gradient is turned on) becomes the projection of the object on the frequency encoding axis. It was proved mathematically that on each spatial location along the x axis, the composite signal is the summation of all the signal sources in columns perpendicular to that location. Mathematically, to be able to extract both the amplitudes and the locations of the signal sources along the orthogonal axis, a separate set of measurements needs to be carried out. Similar to frequency encoding, phase encoding is applied by imparting phase shifts on the spins along the y direction, depending on their position. Following simple linear algebra notation, the solution to decoding all amplitudes and spatial locations arises from pulsation of the phase encoding gradient at m steps, providing independent measurements that allow solution of the set of equations.
