Terrestrial exoplanets shine in light reflected from a parent star. Optical spectra are required to provide evidence of a life-supporting environment. Exoplanets are very faint and their optical spectra are contaminated by the spectrum of the parent star. High angular resolution provided by large apertures is needed to distinguish between the spectrum of the exoplanet and its star. Today, large aperture telescopes use segmented primary mirrors that employ close-packed hexagonal segments. The telescope primary mirror is periodically discontinuous with straight lines. These discontinuities scatter unwanted radiation from the much brighter parent star across the field of view to obscure the light from the very faint terrestrial exoplanet. These discontinuities, which mimic a diffraction grating, result in a non-uniform distribution of background light across the image plane. This non-uniformity masks or hides exoplanets from view, to reduce the number of exoplanets that can be observed with a large aperture telescope or to reduce the quality of spectra and thus lead to misinterpretation of data. Here we introduce the concept of the pinwheel pupil whose unique diffraction pattern significantly reduces the non-uniform distribution of background radiation. Diffraction patterns from pinwheel pupils are compared to the monolithic filled aperture, the classical Cassegrain, the 60-degree symmetry of the hexagonal segments (JWST, E-ELT, etc.). Diffraction "spikes" are reduced by at least 10 5. We discuss the "pinwheel pupil" advantages to spectroscopy, image processing, and observatory operations. We show that, segment fabrication of curved-sided mirrors is not more difficult than fabrication of hexagonal mirror segments.. This is the report of quantitative study of Fraunhofer (far field) diffraction patterns produced by three different topologies or architectures of mirror segmentation, when illuminated by a plane wave of monochromatic white-light. A plot, in angular units of the intensity as a function of azimuth, Phi f , within annular rings at different FOVs, centered on the system axis of the diffraction pattern will be presented. The advantages of the segmented pinwheel pupil is discussed.