The on-sky, open-loop power spectral density of the x-centroids is shown on the left plot, when the modal modulation is applied: it can be seen to be about an order of magnitude above the level of the atmospheric turbulence, which has a slope of f^−5/3 at low frequencies, which turns into f^−17/3 at high frequencies when the turbulence is averaged within the subapertures (﹩f\gt \bar{v}/d﹩). The middle plot shows the same PSD in closed loop (but with a low loop gain, which explains why the low frequency part of the spectrum is similar to the open loop). However, in closed loop, the modulation is around 2 orders of magnitude above the corrected turbulence as can be seen on the PSD of the commands (in modal coefficient space, shown in the right plot).