0.825 $\lambda/D$ & 99.85% & 54.26% & 0.93 $\lambda/D$\
E-ELT APCMLC \#2 & 0.9 $\lambda/D$ & 78.76% & 49.92% & 1.00 $\lambda/D$\
E-ELT APCMLC \#3 & 1.2 $\lambda/D$ & 50.56% & 38.43% & 1.29 $\lambda/D$\

Apodized pupil complex mask Lyot Coronagraph (APCMLC) for apertures of arbitrary shape {#sec:APCMLC}
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Principle {#ssec:APCMLCprinc}
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In this section, it is shown that the APCMLC is compatible with non-circular apertures, as illustrated in Figure \[fig:APCMLCprinciple\], and a description of how it can be designed for arbitrarily shaped pupils is provided. While the APCMLC description provided here remains qualitative and focused on aspects relevant to non-circular apertures, a more complete analytical description is provided in [@2010ApJS..190..220G] for circular unobstructed apertures. We describe the APCMLC by following how electric field (also refered to as complex amplitude in this paper) from an on-axis point source propagates through the coronagraph system.

The APCMLC, illustrated in Figure \[fig:APCMLCprinciple\], uses a circular focal plane mask to partially transmit and phase shift the on-axis point spread function (PSF) core (complex amplitude B on Figure \[fig:APCMLCprinciple\]). The transmission and phase shift are uniform within the mask radius, and the mask is fully transmissive, with no phase shift, outside this radius. This produces 