Estimating phase errors from pupil discontinuities from simulated on sky data: examples with VLT and Keck

International audience; We propose and apply two methods for estimating phase discontinuities for two realistic scenarios on VLT and Keck. The methods use both phase diversity and a form of image sharpening. For the case of VLT, we simulate the `low wind effect' (LWE) which is responsible for focal plane errors in low wind and good seeing conditions. We successfully estimate the LWE using both methods, and show that using both methods both independently and together yields promising results. We also show the use of single image phase diversity in the LWE estimation, and show that it too yields promising results. Finally, we simulate segmented piston effects on Keck/NIRC2 images and successfully recover the induced phase errors using single image phase diversity. We also show that on Keck we can estimate both the segmented piston errors and any Zernike modes affiliated with the non-common path.