Delayed-focus pulses optimized using simulated annealing

Unlike prefocused pulses and shaped pulses based on the linear response theory, delayed-focus pulses (X.-L. Wu et al., 1991, Magn. Reson. Med. 20, 165--170) produce a selective spin echo after a predefined short delay without using a pi refocusing pulse. In this paper, a series of delayed-focus pulses of different flip angles are proposed based on optimization using Fourier series representation and simulated annealing. The resistance of these delayed-focus pulses to T(2) relaxation is also demonstrated using numerical simulation of Bloch equations.