This dissertation derives and demonstrates a new approach to the design of wide-field interferometric telescopes. The first part of this dissertation is a tutorial on multiple aperture systems. Design basics such as PSF and OTF, fill factors, resolution, and temporal coherence are investigated. We show that the perfect image for a multiple aperture system is the sum of an image from each aperture and a set of fringes from each pair of apertures. Four example systems are designed by applying the derived design rules. The first system is a rotationally-symmetric Paul system that is then segmented to make a four-aperture system. The low-order design rules in this system are shown to be automatically satisfied. The second system is an array of four afocal telescopes that share a three-mirror combining telescope. Fold flats are used in the inner two arms to satisfy the requirement that the axial pathlengths should match. Linear piston errors are eliminated by forcing the beam configuration into the combiner to be a scaled version of the afocal array. The angles of the fold flats are chosen to eliminate any constant tilt errors. As a third example, the design of a beam combiner for the Large Binocular telescope is explored. By applying the design rules, coherent imaging with a 1 arcminute field of view is achieved with just three reflections. Linear defocus errors appear, but are minimized by bringing the beams to focus as closely together as possible. The sine condition is satisfied for the axial rays so that the linear piston errors are zero. As a fourth example, a space telescope design is presented that utilizes a flat gossamer mirror technology. The system would consist of a primary array of flats, a shared secondary mirror, and a tertiary array with one mirror corresponding to each of the primary flats. Each branch of the system consists of a primary flat, the shared secondary, and a tertiary that brings the beam to the correct image point. The position of the tertiary is chosen to eliminate axial pathlength errors. The RMS wavefront error is calculated as a function of the system parameters. This gives an efficient method for exploring design space for the gossamer systems. The performance of a system of five flats is explored in this way. A few specific five-flat systems are modeled with full interferometric raytraces, and the results show good agreement with the Strehl values predicted by calculation of the RMS wavefront errors. (Abstract shortened by UMI.)
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