Diffraction effects from giant segmented mirror telescopes

Ultra-high contrast imaging with giant segmented mirror telescopes will involve light levels of order 10^-6 times that of the central diffraction spike or less. At these levels it is important to quantify accurately a variety of diffraction effects, including segmentation geometry, intersegment gaps, obscuration by the secondary mirror and its supports, and segment alignment and figure errors, among others. We describe an accurate method for performing such calculations and present preliminary results in the context of the California Extremely Large Telescope.