1. An array camera, comprising: a plurality of cameras, where each camera includes separate optics, and a plurality of light sensing elements; a processor; wherein the optics of each of the plurality of cameras are configured so that each camera has a field of view that is shifted with respect to the field-of-views of the other cameras and so that each shift includes a sub-pixel shifted view of the scene; wherein the light sensing elements of a given camera in the plurality of cameras have a pixel pitch defining a camera Nyquist frequency, and where the optics of the given camera have a modular transfer function (MTF) such that the optics optically resolve contrast at spatial frequencies higher than the camera Nyquist frequency (Ny); and wherein software directs the processor to: obtain a set of low resolution images from the plurality of cameras, where each of the low resolution images include aliasing patterns; determine disparity between pixels in the set of low resolution images to generate a depth map from a reference viewpoint, where the depth map indicates distances to surfaces of scene objects from the reference viewpoint; synthesize a high resolution image using the set of images and the depth map, where the spatial frequency at which the high resolution image displays contrast is greater than the camera Nyquist frequencies (Ny) of the plurality of cameras and less than the spatial frequencies at which the optics of each camera optically resolve contrast.