Imaging with high angular resolution requires large apertures and long focal lengths. This has prevented the integration of telephoto lenses into thin devices such as modern mobile phones. We report a camera module employing multiple rotated rectangular apertures and folding of the optical system into the plane of the camera, enabling an order-of-magnitude reduction in depth compared to traditional telephoto lenses. Multiple images are fused in the frequency domain to yield a single high-resolution image equivalent to that yielded by a single circular aperture. The diameter of this equivalent aperture may be several times wider than the depth of the camera module. We propose two architectures and present illustrative optical designs to demonstrate the concept. Simulations of raytraced image acquisition and computational image reconstruction demonstrate the potential for high-quality, high-resolution imaging from thin, flat lens modules.