Magnification through a lens at various diameters

[Ken Van Cleave]

We have a high power plus lens of known front curve, index, and center thickness and have placed a known diameter circular target at a known distance behind the lens. Observing the circular target through the lens we compute the ratio between the diameter of the original circular target behind the lens and the measured target diameter as viewed through the lens on the other side.

Using a very small target, the focal length and power of the lens can be calculated fairly accurately using this magnification ratio along with the distance from the back of the lens to the target. The problem is that the ratio changes significantly when a larger target size is used even though the lens power is the same.

Why does this happen? Are there any formula(s) that can compensate for this so the power can still be predicted as accurately as when a very small target size is used?

 

[B0b-A]

... The problem is that the ratio changes significantly when a larger target size is used even though the lens power is the same. Why does this happen? ...

I think what you are describing is radial distortion ... http://en.wikipedia.org/wiki/Distortion_(optics)#Radial_distortion