POAM diversity principle. The optical propagation is more complicated for a coronagraphic phase-mask. Indeed, this scheme presents three different polar propagations with the same entrance aberrated pupil, which is presented in the classical phase diversity system. The first polar Fourier transform is the same as for classical imaging (PFT[P(ρ,θ)]), but after the phase-mask coronagraph, the inverse polar Fourier transform including the VVC POAM properties becomes PFT^l_p, − 1[U(r,φ)]. In the coronagraphic pupil plane P_c(ρ,θ), the main part of stellar photons are rejected at the edge of the pupil and some of the remaining photons inside the pupil possess an added POAM  ± l_p. The final polar propagation PFT^l_p[P_c(ρ,θ)] gives the final attenuated coronagraphic image. An optical polarizing system (quarter waveplates and Wollaston) located after the Lyot stop (the circular dashed circle in the coronagraphic pupil) allows us to separate the two circular polarizations and then the two POAMs. This mathematical development gives a complete set of modal functions .