We present a single-shot computational imaging system employing pupil phase engineering to extend the field of view (FOV) beyond the physical sensor limit. Our approach uses a point spread function in the form of a multiple-point impulse response (MPIR). Unlike the traditional point-to-point imaging model used by most traditional optical imaging systems, the proposed MPIR model can collect information from within and outside the sensor boundary. The detected raw image despite being scrambled can be decoded via a sparse optimization algorithm to get extended FOV imaging performance. We provide a thorough analysis of MPIR design regarding the number of impulses and their spatial extent. Increasing the number of impulses in MPIR of a given spatial extent leads to better information gathering within the detector region; however, it also reduces contrast in the raw data. Therefore, a trade-off between increasing the information and keeping adequate contrast in the detected data is necessary to achieve high-quality reconstruction. We first illustrate this trade-off with a simulation study and present experimental results on a suitably designed extended FOV imaging system. We demonstrate reconstructed images with a 4× gain in pixels over the native detection area without loss of spatial resolution. The proposed system design considerations are generic and can be applied to various imaging systems for extended FOV performance.