text: The Shinnar–Le Roux (SLR) algorithm is a mathematical tool for generating frequency-selective radio frequency (RF) pulses in magnetic resonance imaging (MRI). Frequency selective pulses are used in MRI to isolate a slice through the subject for excitation, inversion and saturation.
  Given a desired magnetization profile, determining the RF pulse that produces it is generally nonlinear, due to the non-linearity of the Bloch equations. At low tip angles, the RF excitation waveform can be approximated by the inverse Fourier Transform of the desired frequency profile, using the excitation kspace analysis. The small tip angle approximation continues to hold well for tip angles on the order of 90 degree. However, for tip angles greater than 90 degree, a different approach must be used.
  A direct solution to the pulse design problem was independently proposed by Shinnar  and Le Roux  based on a discrete approximation to the spin domain version of the Bloch equations.