Linear Sweeps Generate Extreme Echoes: Explanation, Generalization

Patrick H. Le Roux¹, Brice Fernandez²

When a train of RF pulses with constant nutation is modulated in phase according to a periodic quadratic law, a refocusing for all the three components of magnetization (Extreme Echo) is generated at the end of the modulation or after two periods if the period is odd. This was first observed experimentally and also demonstrated mathematically . But that demonstration lacks any physical meaning. We propose here a simple geometrical explanation in which the symmetries of the echo to echo rotation plays an essential role. This remark leads to more general phase modulation having the same property.