Light-curve comparisons for Schwarzschild space-time with a slowly rotating spherical star (R = 12 km, M = 1.6 M_⊙, ν = 1 Hz, i = 60°, θ_s = 50°, ρ = 1°, and T_eff = 2 keV) emitting according to a blackbody or Hopf profile with a spot size of either 1 or 30 degrees. The black solid line shows the pulse profiles computed using the S+D approximation (forward-in-time method; see text), and the red dashed line is a profile computed with the code presented here. Lower panel: residuals as Δ = (model_S+D∕model − 1) × 100%.