as the mask size increases, pupil geometry has a larger impact on performance, as the range of pupil plane spatial frequencies accessed by the focal plane mask begins to overlap with the low spatial frequency components of the pupil geometry (central obstruction, large segments, thick spider vanes). This difference is most noticeable between the GMT pupil with few large segments and the TMT or EELT geometries with numerous small segments.

Selected examples of apodization functions and Lyot plane intensity images are shown in Figure \[fig:APCMLCexamples\]. In each case, the apodization function is smooth and free of high spatial frequencies, and no light is left within the geometric pupil in the Lyot pupil plane, as all residual starlight is diffracted outside of the pupil and in the gaps between segments.

![image](fig03.eps)

Table \[tab:APCMLC\] gives for several APCMLC designs the key design parameters (focal plane mask size $a$, focal plane mask transmission) as well as the coronagraph performance (throughput and IWA). For each pupil shape considered, the first design (design \# 1) is the most aggressive in IWA, with a nearly fully transmissive focal plane mask. This aggressive design is also the one with the highest throughput, as the apodization strength needs 