Schematic view of the NZ vortex phase-retrieval process. It consists of using the real input coronagraphic images, corresponding to l_p = 0, ± 2 (the l_p =  ± 2 images are provided by polarization splitting, while the unpolarized image (l_p = 0) is directly given by the sum of the two polarized images) projected on aberrations templates, and finding the unknown coefficients by resolving a system of linear equations. Left: the three images needed for the full aberration analysis. Center: linear systems to retrieve the and the f⁽¹⁾ terms. Right: the predictor-corrector approach to evaluate the quadratic correction .