The effect of this lensing increases linearly as the viewing angle decreses. You say you want me to teach you math, but this is simply high school level trig that you can easily look up online.

I know that it MUST increase linearly, in order for it to counter perspective. Yes, I can do the math in order to come up with the necessary magnification based on distance. That's not the point.

Mathematically, I know what this lens NEEDS to do. I just don't know of any type of lens that is ABLE to do it. You need to show that there is a type of lens that is capable of producing this effect, either mathematically or empirically. This lens must be able to:

1. Increase magnification linearly with distance.

2. Produce this effect no matter where you are on the day-side of earth.

3. Produce this effect regardless of weather, as long as the sun is visible.