ROC curves of T_E (green), T_NP (blue), and T_B (orange). Theoretical ROC curves for T_NP and T_E plotted using Eqs. (17) and (24), for a companion at ρ = 200 mas, c = 1200, and θ = 45° off the vertical. Dashed lines correspond to theoretical ROCs, while solid lines represent ROCs obtained by Monte-Carlo simulations. The closer a curve is to the black line on the diagonal, the less powerful the corresponding test. The higher flux regime is represented in the top panel, and the lower flux regime in the bottom panel. The performance of T_NP and T_E are accurately described by the theoretical expressions in Eqs. (17) and (24). The test T_NP presents the highest performance. T_B is the next-best-performing test and T_E has the lowest performance of the three. We see a clear improvement of the power of all tests as the flux (and thus the S/N) increases.