Figure 5.

Results of composite pulse optimizations interpolated across the 2D parameter space of sub-pulse duration (Δt_s) and the number of sub-pulses (N_s) with sub-figures (a), (b), (c), and (d) corresponding respectively to α₀ values of 30°, 60°, 90°, and 180°. Color scale indicates the minimized function value (δ_α); black contours give corresponding minimum repetition times (T_R,min) in milliseconds; solid, dashed, and dotted white lines are isocontours of total pulse duration (ΔT) at 5, 10, and 20 ms, respectively. Black asterisks indicate the values of N_s and Δt_s for the optimized pulses specifically compared to block and BIR-4 pulses in Figs. 6, 7, and 8 and Table 1. Data indicate that the lowest values of δ_α migrate toward the top right corner of the parameter space with increasing α₀—thus reflecting increased power requirements. At lower α₀, δ_α minima tend to be found in the upper left, suggesting that the maximum number of short-duration sub-pulses yields the best performance given that a certain power threshold is satisfied.