Simulation of a 14-mode Zernike cMWS (modes Z₃−Z₁₆) combined with an APP optimised for a 10^-6 dark hole with a 180° opening angle. Left: multiplexed pupil-plane phase design Ψ_cMWS containing the high spatial frequency HMWS binary grating overlaid on the smoother APP design. Right: corresponding focal-plane PSF: positively and negatively biased PSF copies are located in the top and bottom half of the image respectively, separated by the white dashed lines. Two example pairs are labelled (defocus, Z₃ and 45° astigmatism, Z₅), illustrating the symmetry of the ± 1 orders about the zeroth order PSF.