[namibj]

The difficulty is actually more with maxing it flat, so the phone can be thin. If you have length to spare and only a chip to record, you can get awesome f/2 optics (diffraction limited) with only a Schmidt corrector and otherwise two spherical surfaces and 3 flat ones (not counting the flat front outside facing of the Schmidt plate) with a field-flattened Schmidt camera. The only strong downside apart from the limit on FOV at around 4 degrees for this simple design (slight better designs should allow for up to about 30 degrees) is that it's twice as long as the focal length. It should still allow ultra-tele shots by resting the tube on the shoulder, without anything to actively compensate rotation shake.