The basic building block of the spin-echo sequence, shown in Fig. A readout gradient pulse is centered on the echo center. A (slice-selective) 180° pulse at time t = 2x causes the appearance of a spin-echo at t = x. The phase-encoding gradient can be applied immediately afterward simultaneously, a "dephasing" gradient pulse can be applied along the readout axis. A single encoding step starts with a slice-selective 90° pulse. In a spin-echo imaging sequence, the readout gradient is applied during the formation and decay of a spin-echo. In this example, only the transverse component of the magnetization is shown as vectors, aligned initially with the horizontal axis, after application of a radiofrequency pulse. An array of magnetic moments stacked up along the horizontal axis. The phase encodings are repeated N times to achieve a spatial resolution in the direction of the phase-encoding gradient of Ax = L/2N.įig. The spin density distribution p(x) can be reconstructed if the phase encodings are repeated for a range of kx values to sample the spin density distribution at different length scales or spatial frequencies. L denotes the spatial extent of the object to be imaged that is, p(x) = 0 when |x| > L. St is the ith Fourier component of the spin density distribution p(x). The index i is a label for the phase-encoding pulse. 6, the signal that is recorded after a phase encoding can be represented as a sum or integral, with each contribution weighted by a phase factor to account for the phase warp produced by a phase encoding gradient: We refer to the variation of the magnetization phase as phase warp.įor a 1D distribution of spins, as in the example of Fig. The quantity kx is the spatial frequency at which the x and y components of the transverse magnetization (Mx and My) are modulated by application of the phase-encoding gradient in the x direction. The tails of the radiofrequency waveform were attenuated with a Hanning windowing function to avoid "ringing" artifacts in the slice profile.įig. The radiofrequency pulse in this example has the shape of a sinc function to excite a rectangular profile. Gradient waveforms usually have trapezoidal shapes that is, they rapidly ramp up, maintain constant amplitude for a well-defined duration, and then ramp down. To avoid this complexity in pulse sequence diagrams, the waveforms for the "logical" gradient channels, as shown here, are typical. The gradient channels are typically given logical names, such as "slice-select" and "readout." The direction for the slice selection gradient can be arbitrary and is achieved by using three equivalent gradient coil sets for gradients in the x, y, and z directions and applying a combination of waveforms on all three gradient channels according to the desired slice orientation. Waveforms that are applied along the radiofrequency (R.F.) and one gradient channel during a slice-selective radiofrequency excitation.
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