Similar laterally sliding lens ideas were investigated a few times by the optical folks in the department of RARDE / DERA / DSLT / QinetiQ that I worked for. I suspect at least once for every incarnation! One of several hardy chestnut ideas from "management" types needing regular debunking.
The theory works fine for a very small field of view and very small collecting optics. Think of two arrays of insect eye like elements moved so as to bring different pairs into alignment immediately in front of the eye. With the rest of the field of view blacked out.
That idea actually has been used for switchable fields of view / magnification on things like weapons sights, infra red imagers and the like. Basic design is a true flat field, parallel light in parallel light out, telescope with a selection of lenses on the back. Simple enough for small fields of view but the design gets hairy fast if you want a large one.
For glasses the optical surface curvatures needed to bring the whole field of view into focus at the right plane regardless of the angle you are looking through them rapidly become impossibly complex in both design and manufacture. In the limit an infinite number of infinitesimally small lenses that can be assembled into an infinite number of pairs all having the same back focal length. Four sets of surfaces. There is no linear equation solution to give acceptable optical quality. There are approximations that can be found quite easily but none good enough.
Obviously not symmetrical as the effects due to sliding is different for vertical and horizontal planes.
Because the instantaneous field of view of the eye is small and because the human brain has a huge amount of processing power to generate useful images from the eyes "signal output" they can apparently sort of work. But the eye is shifting focus every time it moves and the processing applied changes too to get some sort of image. No wonder attempting to use them is a strain. Don't forget that the human eye is always moving to generate a useful image. The true, in focus, field of view is very small.
The cheapy "con trick" ones will at best be lightly parabolic modifications of spherical surfaces.
I think "Buzz' Busselle said that a pair of fresnel lenses rotating about offset centres might get you close! Of course fresnel lenses and glasses don't mix. Shame, life would be so much easier.
The oil filled lens idea mentioned by Mike is impractical. It requires the "bag" material to have physically impossible stress / strain variation with extension curves to create optically viable surfaces over any useful range. I was given a 3 ft diameter concave mirror made on such principles to test. Interferometric results were "interesting" demonstrating that the the theory of design was inadequate. Probably solvable for infra red wavelengths over a short range by manipulating the material thickness but no good for optics.
Clive
Edited By Clive Foster on 02/12/2020 11:37:25