The research described in this report resulted from my participation in the design study for the Phased-Array Imaging Telescope. To maintain high transmission, a practical system should contain a minimum number of components. This consideration leads to the concept of shared symmetries between the subtelescope and final collector. This report presents an approach to the design of such arrays, and examines the implications of including aspheric correction for the telescope array. As expected, the number of elements in this correction design concept seems to work well. Four array systems based on this concept are presented; each uses only one spherical mirror as the beam collector. The effects of changing the primary mirror's relative aperture, and of changing the system length, on the symmetry and order of aberrations arising from the use of an eccentric aspheric, are explained in this report. The subtle limitations of techniques for adding special surfaces for decentered aspheric correction to optical design programs are discussed as well. Two additional design concepts are examined and compared. A preliminary tolerancing analysis is performed, and error budgets developed. An adaptive element is considered for relaxing the alignment and fabrication tolerances.
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