Analytic diffraction analysis of a 32-m telescope with hexagonal segments for high-contrast imaging

Large segmented telescopes cannot be modeled accurately with fast-Fourier-transform techniques since small features such as gaps between the segments will be inadequately sampled. An analytic Fourier-transform method can be used to model any pupil configuration with straight edges, including tolerance analysis and some types of apodization. We analytically investigated a 32-m segmented primary with 18 hexagonal segments for high-contrast imaging. There are significant regions in the image in which extrasolar planets could be detected. However, the hexagonal profile of the pupil was not as useful as expected. The gaps between the segments, the secondary obscuration, and the secondary spiders must be as small as possible and their edges must be apodized. Apodizing the edges of the individual segments reduced the useful regions in the image since the gaps appeared to be wider.