What gradient waveform could you use as an acceleration compensation pulse?

Suppose a point object is moving along the x-axis with the following trajectory: x(t) = xo + vt.

(a) Calculate the phase shift that is induced in the transverse magnetization after the application of the gradient waveform shown in Figure P13.2.

Figure P13.2 See Problem 13.8(a).

(b) Calculate the phase shift induced by the waveform shown in Figure P13.3. This is called a flow compensation pulse.

Figure P13.3 See Problem 13.8(b)

(c) Repeat the calculations for the above two waveforms for the trajectory given by x(t) = xo + vt + .

(d) What gradient waveform could you use as an acceleration compensation pulse?

(e) Is it possible to design a gradient waveform that will produce phase shifts that are independent of acceleration but are dependent on the velocity? Explain.

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