Narrow gradient-pulse approximation

Fig. 5.4.5 Definition of q space in terms of position-change NMR. (a) Initial and final positions are encoded by fci and fea in the narrow gradient-pulse approximation. The transformation to a coordinate system where the difference wave number q defines one of the axes corresponds to a right-handed 45° rotation of the coordinate system (cf. eqn (5.4.21)). The perpendicular variable is proportional to the wave number k which encodes position, (b) 2D Fourier transformation of such a 2D position-change data set produces the displacement coordinate in a coordinate frame rotated by 45° on one axis and the space coordinate r on the other axis.

An ingenious approach to the treatment of finite gradient pulse width effects has been provided by Wang et al. (1995). They demonstrate that it is possible to approximate the temporal behavior of any gradient pulse by a sum of impulses, each being in the narrow gradient pulse limit. By this means one can derive an analytical solution to the echo attenuation. 

The large diffusion coefficient of gases result in significant spin motion during the application of gradient pulses that typically last a few milliseconds in most NMR experiments. In restricted environments, such as the lung, this rapid gas diffusion can lead to violation of the narrow pulse approximation, a basic assumption of the standard Stejskal-Tanner method of diffusion measurements. Mair et therefore investigated the effect of a common,... 

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