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Alignment Constraints For Phased, Diffraction-Limited Multiple Aperture Optical Systems

A crucial parameter for an optical phased array is the sensitivity of the system performance to alignment and phasing errors among the telescopes. For an array of telescopes to be coherently phased, the focal planes of each telescope must be exactly superposed. This paper presents mathematical derivations of all the conditions needed to achieve the required degree of superposition. These conditions are derived by analytically computing the point spread function for a combined aperture system (i.e., all apertures are included). The conditions for ideal superposition cause this function to be constant over an extended field-of-view. The sensitivity of a phased array system to single-or multiple-telescope deviations can thus be quantitatively evaluated, for monochromatic or broadband light.