Velocity q space

Because the measurement of displacement takes some time A, the measured quantity can also be considered to be displacement over time, that is average velocity v = R/A during the time lag A. The Fourier-conjugate variable to displacement R has been given 

The analogy between diffraction signals from scattering experiments and the loss of phase information in NMR imaging is illu.strated in Fig. 5.4.3 [Blii4. The magnitude square of the NMR signal k ) measured in A space from a more or less 

In one dimension this relationship is expres.sed by the following calculation The signal V (k) measured in an imaging experiment is expressed in terms of the associated image 5 (r) by inverse Fourier transformation, 

Formation of the magnitude square of s k) eventually introduces the displacement R. For the purpose of conformity with subsequent calculations, the following approach is taken in computing the magnitude square of 

With these substitutions the magnitude square of the measured signal s k) can be expressed as 

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