A security device for projecting a collection of synthetic images as well as a computer-implemented method for producing such a security device are provided. The synthetic images may represent different viewpoints of a target object or image that change from one viewpoint image to another viewpoint image as the location of the observer changes relative to the device. The nature of each synthetic image can, however, be completely arbitrary, much like the images that are provided by a display device such as a television or computer monitor. In an exemplary embodiment, a special symmetry is used to generate the synthetic images, which allows the device to be manufactured without regard for registration.