Optical interferometry is a technique which can be used to obtain high-resolution imagery of a distant target by interfering light collected by multiple telescopes. Image restoration from interferometric measurements poses a unique set of challenges. The first challenge is that the measurement set provides only a sparse-sampling of the objects Fourier Transform and hence image formation from these measurements is an inherently ill-posed inverse problem. Secondly, atmospheric turbulence causes severe distortion of the phase of the measured Fourier samples. We develop array design conditions for unique recovery of the true Fourier phase in the presence of this distortion, as well as a comprehensive algorithmic framework based on the notion of redundant-spaced-calibration (RSC), which together achieve reliable image reconstruction in spite of these challenges.