TwoEqualPulseSequence

Another useful pulse sequence is the {$\phi -\tau - \phi$} sequence, made of two equal length pulses. It is easy to visualize it for {$\phi=\omega t=2\pi/3$} with the use of the figure. The first pulse nutates the blue arrow, equilibrium magnetization {$\mathbf {M}$} from the z-axis to the red arrow position by 120 degrees. Time evolution for a time interval {$\tau$} will defocus the slow and fast spin precessing components. In the rotating frame slow spin lag behind the resonant spin (red arrow) and the fast spin move forward in the anticlockwise direction, together fanning out into the pale pink conic surface. The second pulse will make the red arrow resonant component to nutate by another 120 degrees to the green arrow position, with fast and slow components following as well. Hence fast spin are now lagging behind in the anticlockwise direction. After evolution for another time interval {$\tau$} the spin echo is refocussed to a maximum. Although the projection in the {$\hat x^\prime$} direction is not the absolute maximum (there is a factor {$\cos 2\pi/3$} reduction), it will be the maximum among all equal pulse durations, as it is easy to convince oneself.