Design of phase-modulated broadband refocusing pulses

Broadband linear-phase refocusing pulses were designed with the Shinnar-Le Roux (SLR) transformation and verified experimentally. The design works in several steps: initially, a linear-phase B polynomial is created with the Parks-McClellan/Remez exchange algorithm. The complementary A polynomial required for the SLR transformation is generated with the Hilbert transformation, yielding the minimum-phase response. The phase response of the A polynomial is altered by zero-flipping, which changes the overall pulse shape while retaining its refocusing profile. Optimal pulses in terms of minimal B1max and hence broadest bandwidth were found with non-linear optimisation of the zero-flipping pattern. These pulses are generally phase modulated with a time-symmetric amplitude and anti-symmetric phase modulation. In this work, a whole range of pulses were designed to demonstrate the underlying relationships. Five exemplary pulses were implemented into a PRESS sequence and validated by acquiring images of a water-oil phantom and lactate spectra at TE = 144 ms.