Hollow optical elements that derive optical power from compound-curved reflective surfaces to produce a desired composite optical power. The reflective surfaces in combination with polarization control, can produce a triple-pass arrangement that determines the optical power. Two functional films, one or both of which are formed (e.g., thermoformed), can be joined at the perimeter to form units that are mechanically robust and therefore preserve optical performance under mechanical load. The air-spaced cavity formed between the two layers is free of birefringence concerns, where polarization control is crucial to contrast. These optical elements can be installed in frames or headsets to form lightweight wearable magnifiers, wide-angle collimators, tele-photo lenses, or for any application requiring optical power. They may be most appropriate for applications where light efficiency is not critical, such as well-lit environments, where the insertion-loss of 1 to 2 stops is not problematic.