Conditions under which two-element variable power lenses can be created. Part 1. Theoretical analysis

The conditions under which a two-element variable power lens can be created are examined. Such a lens is defined as one in which the functional form of the optical effect created does not change as the elements translate with respect to one another--only the magnitude of the effect changes. It is found that only variable power optical effects that can be described by quadratic functions can be formed by laterally translating two-element variable power lenses. In the case of rotationally translating two-element variable power lenses, possible designs are found by mapping possible laterally translating designs from a Cartesian space to the polar coordinate space of the rotationally translating lens.