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Residual misalignments of the Keck Telescope primary mirror segments: classification of modes and implications for adaptive optics

Because of limitations in the alignment process resulting from the telescope active control system and from atmospheric turbulence, the segments of the Keck Telescope primary mirror are never perfectly aligned. We describe a scheme for classifying these misalignments in terms of modes of the primary mirror. We describe these modes in terms of noise propagation, symmetry (specifically their resemblance to Zernike polynomials), and how discontinuous they are. Modal spectra of typical mirror misalignments are presented. The edge discontinuities which result from these misalignments are significantly smaller than what one would expect from random, uncorrelated tip/tilt errors of the same size, a fact which may have important implications for adaptive optics systems on segmented mirror telescopes.