Principle of Fourier NMR

Here the inhomogeneous polarizing magnetic field points in z direction, and the spatial inhomogeneity in x direction has been expanded into a Taylor series and truncated after the second term. The first term of this series is the homogeneous field B(), the second one is the field gradient Gx = dBJdx)x=0 in x direction. 

The quantity x t) denotes the position of a magnetisation component on the x axis. For flowing and moving objects the position is a function of time. For short times also x(t) is expanded into a Taylor series and arbitrarily truncated after the third term, 

The expansion coefficients are initial position x0, initial velocity vx0, and initial acceleration ax0 in x direction. Combination of equations (1) and (2) yields  

Thus by suitable modulation of Gx(t) the signal phase can be made dependent on position, velocity, or acceleration. The effect of a distribution in frequency is handled either by 

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