Systems and methods in accordance with embodiments of the invention implement modular array cameras using sub-array modules. In one embodiment, an X×Y sub-array module includes: an X×Y arrangement of focal planes, where X and Y are each greater than or equal to 1; and an X×Y arrangement of lens stacks, the X×Y arrangement of lens stacks being disposed relative to the X×Y arrangement of focal planes so as to form an X×Y arrangement of cameras, where each lens stack has a field of view that is shifted with respect to the field-of-views of each other lens stack so that each shift includes a sub-pixel shifted view of the scene; and image data output circuitry that is configured to output image data from the X×Y sub-array module that can be aggregated with image data from other sub-array modules so that an image of the scene can be constructed.