Methods

1. Gradient spoiling
The gradient echo sequence includes the RF-pulse, the dephasing gradient and the rephasing gradient. The parameters are selected in a way to ensure, that the phase difference is  between the spins at the opposite ends of the voxel:

where n is an integer (in our case n=1),  is the applied gradient ( ) and  the gyromagnetic ratio. Under this condition it is ensured for each repetition cycle that the transverse magnetization is dephased to zero:

The negative and the positive gradients, which are actually used in order to create the echo, are skipped in our considerations, because the "net-area" under this gradient is zero (figure 1)

Figure 1: Gradient echo sequence (figures: grad_echo.jpg and grad_no_echo.jpg.)

2. RF spoiling
To eliminate this constructive refocusing, the phases of the transversal magnetization need to be scrambled in such a manner that they add together in a destructive way, and thus do not contribute to the signal following the RF pulse. This phase scrambling is achieved by making the resonance offset angle  a function of RF pulse number n and the phase increment :