Possible immunities in interferometer end mirrors

It is known that the end mirrors of a Michelson interferometer can be made immune to the effects of tilt or of lateral translation by suitable design. The question arises as to whether both types of immunity can be achieved at once. This paper shows, from elementary considerations, that this is not possible so long as the end mirror assemblies are self-contained systems, and the extent of the immunities conferred by systems which invert or do not invert the wave-front is examined.