PIAACMC optical layout. The top figures show the simulated components designed for MagAO-X, and the bottom figures show the simulated pupil or focal plane images at different positions in the system, for an on-axis source. Top figures from left to right: (1) MagAO-X’s binary aperture stop used for coronagraphic observations (‘bump mask’); (2) forward PIAA0, the first aspheric PIAA lens of the forward set; (3) forward PIAA1, the second aspheric PIAA lens of the forward set; (4) phase-shifting focal plane mask, a transmissive optical component to suppress on-axis light; (5) MagAO-X’s Lyot stop for PIAA observations, a binary mask to block the light diffracted by the focal plane mask, modelled on the apodised pupil shape; (6) inverse PIAA1, the first aspheric PIAA lens of the inverse set. It is the same as foward PIAA1 but flipped; (7) inverse PIAA0, the second aspheric PIAA lens of the inverse set. It is the same as forward PIAA0 but flipped. Bottom figures from left to right: (A) light distribution at the MagAO-X aperture; (B) light distribution after the forward PIAA lenses set; (C) the MagAO-X point spread function (PSF) on the focal plane; (D) PSF after the focal plane mask. It doesn’t change in intensity because the focal plane mask is transmissive and only acts on the phase of the light; (E) light in the pupil plane that is diffracted by the focal plane mask; (F) residual light in the pupil plane after the Lyot stop; (G) residual light in the pupil plane after de-apodisation by the inverse PIAA lenses set; (H) residual light in the science plane.