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Gradient Echo

With the method that has been described so far $k$ only takes positive values during the measurement. If the effective spin density is real, then by making use of the characteristics of the Fourier transform, it may be enough for reconstruction, but in practice this is often not satisfied. (The effective spin density can be complex due to several factors; e.g. if the sensitivity of the detector coil is inhomogeneous, or if the initial phase of the spin system is not zero.) The negative regions of the $k$ axis can also be covered, if a high negative gradient is applied before data collection; afterwards, data are collected by applying a positive phase encoding gradient. The signal is rapidly defocused by the negative gradient; after that, as a result of the frequency encoding gradient the phase differences in the sample will decrease and the signal will reappear: an echo can be observed. This is called gradient echo. As opposed to the spin echo, the gradient echo does not eliminate the coherence loss caused by the static inhomogeneities; thus, relaxation is determined by $T_{2}^{*}$. Of course, the spin echo can be combined with a gradient echo, thus the negative values of $k$ can be mapped in this case as well.

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