Evolution with respect to the magnitude of the guide star of the residual phase variance due to photon noise in open and closed loop for an 8 m telescope with a 4λ/D modulated NGS. The solid line corresponds to the residual phase variance ${\sigma }_{\text{noise }}^2$ using sensitivity analysis from Eqs. (2) and (3), and the markers correspond to the mean of 200 E2E iterations, with the error bar being the standard deviation of the residual variance. For reference, at magnitude 10, N_ph = 4.5 × 10⁴ photons.