Described are imaging devices that employ patchworks of diffractive structures as focusing optics. Each diffractive structure best focuses light over a relatively narrow cone of incident angles, and provides suboptimal focusing for incident angles outside that cone. Different diffractive structures best focus different angular ranges, with the patchwork thus providing an overall focusable response for the relatively broad range of angles required to image a scene. Images can be captured without a lens, and cameras can be made smaller than those that are reliant on lenses and ray-optical focusing.