Systems and methods in accordance with embodiments of the invention implement one-dimensional array cameras, as well as modular array cameras using sub-array modules. In one embodiment, a 1×N array camera module includes: a 1×N arrangement of focal planes, where N is greater than or equal to 2, each focal plane includes a plurality of rows of pixels that also form a plurality of columns of pixels, and each focal plane not including pixels from another focal plane; and a 1×N arrangement of lens stacks, the arrangement of lens stacks being disposed relative to the arrangement of focal planes so as to form a 1×N arrangement of cameras, each configured to independently capture an image of a scene, where each lens stack has a field of view that is shifted with respect to that of each other lens stack so that each shift includes a sub-pixel shifted view of the scene.