Evolution with respect to the magnitude of the guide star of the residual phase due to noise in open loop for a SHWFS with LGS for a 16 m telescope. The solid lines correspond to the residual phase variance due to RON (red line), photon noise (green line), and the sum of both (blue line), as predicted by the model. The markers correspond to the mean of 200 end-to-end iterations, with the errorbar the standard deviation of the residual variance. For reference, at 1 kHz and magnitude 10, N_ph = 1.8 × 10⁵ photons on the full pupil.