A wide-angle Fourier migrator is proposed to more accurately image complex media with strong lateral velocity contrasts. The broadband wave-equation migrator is developed based on the pseudo-Pad & x00E9; approximation, where the Pad & x00E9; coefficients are independent of spatial coordinates, leading to a pure Fourier transform-based matching solution for one-way wavefield extrapolation. We use genetic algorithms to estimate the constant Pad & x00E9; coefficients more accurately than is feasible with conventional least-squares methods. Because of the global features of pure Fourier migrators, we present an angle-partitioning optimization scheme with dip focusing to improve the performance of the Fourier migrator for super-wide-angle waves and strong velocity contrasts. The wavefield gradient is used to calculate propagation angles during dual-domain wavefield extrapolation. Particular attention is paid to the first-order optimized pseudo-Pad & x00E9; Fourier (OPF1) migrator, which significantly improves the split-step Fourier (SSF) method for strong lateral variations at the cost of one additional Fourier transform in each step. Wavefield extrapolation based on the OPF1 method actually constitutes linear interpolation in the wavenumber domain between two split-step terms. We benchmark the OPF1 migrator with other typical migrators based on the exact dispersion equation. Numerical experiments with impulse responses, the SEG/EAGE salt model and 3D field data demonstrate the excellent performance and efficiency of seismic imaging with the OPF1 migrator.