to increase for larger focal plane mask sizes. The APCMLC throughput never exceeds 70% due to the need for a pupil apodization. Transmission curves are given in Figure \[fig:APCMLCtransm\] for the APCMLC designs listed in Table \[tab:APCMLC\].

Phase Induced Amplitude Apodization Complex Mask Coronagraph (PIAACMC) for apertures of arbitrary shape {#sec:PIAACMC}
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Lossless Phase-Induced Amplitude Apodization (PIAA)
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![image](fig04s.eps)

While the APCMLC described in Section \[sec:APCMLC\] achieves full on-axis coronagraphic extinction for almost any pupil shape, its throughput is limited by the entrance apodization required to achieve perfect destructive interference in the output pupil plane. The system throughput decreases as the focal plane mask size increases, with a maximum throughput equal to 72% for a 0.64 $\lambda/D$ radius purely phase-shifting transparent mask on a circular unobstructed aperture. Throughput, and consequently angular resolution, degrade rapidly with increased focal plane mask size: it is 18% for a 2 $\lambda/D$ radius mask. The results obtained in Section \[ssec:APCMLCdesigns\] also show that the APCMLC maximum throughput (achieved for the designs with the most aggressive IWA) is lower on segmented pupils than it is for an unobstructed circular pupil (“Throughput” column of Table \[tab:APCMLC\]). Moreover, throughput, angular resolution and IWA are significantly degraded when the 