a destructive interference within the geometric pupil, between the light that passes around the focal plane mask disk and the phase-shifted light passing through the focal plane phase-shifting disk. With a Lyot mask (Lmask) selecting only the geometric pupil, a coronagraphic effect is achieved. The concept is thus an intermediate point between the conventional Lyot coronagraph or Apodized Pupil Lyot Coronagraph (APLC) [@2003AA...397.1161S], which use a large fully opaque focal plane mask, and the phase mask coronagraph [@1997PASP..109..815R; @2000SPIE.4006..377G; @1999PASP..111.1321G; @2010AA...509A...8N] which uses a small size fully transmissive phase-shifting focal plane mask. In the APCMLC, the focal plane mask size can be chosen anywhere between these two extremes, and defines the ratio between the amount of light within the circular mask and outside the mask. As the focal plane mask radius decreases, a smaller fraction of the light is within the mask radius, and its transmission must increase to maintain the flux balance between the “inside focal plane mask” (corresponding to low spatial frequencies in the pupil) and “outside focal plane mask” (high spatial frequencies in the pupil) components, a necessary condition to achieve destructive interference.

Full destructive interference within the geometric pupil also requires that the two components are 