Spatial maps of travel-time shifts Δτ(x,y) (top) and wave packet amplitudes A(x,y) (bottom) with respect to the quiet Sun. From left to right are results for wave packets p₁, p₂, p₃, and p₄. Waves propagate from L (red lines) in the + x direction. The black circles denote the outer boundary of the penumbra of the sunspot. The parabolic curves (white lines with equation (y/R)² + x/(x_F + λ/8) = 1) depict the boundaries of the first plane-wave Fresnel zones with focus at (x,y) = (x_F,0), chosen such that the sunspot fills the width of the Fresnel zone. The focus position x_F depends on radial order and is taken from Table 1. We do not display the results in the near fields (gray regions where distances from L are less than 3λ).