Stereo imaging is routinely used in Simultaneous Localization and Mapping (SLAM) systems for the navigation and control of autonomous spacecraft proximity operations, advanced robotics, and robotic mapping and surveying applications. A key step (and generally the most computationally expensive step) in the generation of high fidelity geometric environment models from image data is the solution of the dense stereo correspondence problem. A novel method for solving the stereo correspondence problem to sub-pixel accuracy in the Fourier frequency domain by exploiting the Convolution Theorem is developed. The method is tailored to challenging aerospace applications by incorporation of correction factors for common error sources. Error-checking metrics verify correspondence matches to ensure high quality depth reconstructions are generated. The effect of geometric foreshortening caused by the baseline displacement of the cameras is modeled and corrected, drastically improving correspondence matching on highly off-normal surfaces. A metric for quantifying the strength of correspondence matches is developed and implemented to recognize and reject weak correspondences, and a separate cross-check verification provides a final defense against erroneous matches. The core components of this phase based dense stereo algorithm are implemented and optimized in the Compute Uni ed Device Architecture (CUDA) parallel computation environment onboard an NVIDIA Graphics Processing Unit (GPU). Accurate dense stereo correspondence matching is performed on stereo image pairs at a rate of nearly 10Hz.