The field curvature of a Newtonian is equal to it's focal length.
Field curvature is a function of the square of the linear distance off axis so it quickly diminishes as magnification is increased and the field narrows.
It is linear,,, and then in a subsequent statement you say it falls off
as the square??
The second statement seems to be talking about the actual deviation,
not the 2nd derivative, curvature..
You are probably talking about two things and calling them by the same name.
#2 seems closer to what is really going on with this trouble, though...
The eyepiece wants to see a flat flocal plane.
Unfortunately, it sees a focal sphere section instead,
and if you focus on the center, the outer parts are not at the correct distance.
...and start to blur.
The effect is observable and undeniable.
Somehow, we both must be talking about the "Petzval Surface":
There is a nifty example of how the Kepler space telescope has
a grid of sensors laid out on a curved surface.
Each sensor will experience only the curvature-caused deviation of focal points
of a flat facet that is 1/5th of the cell mount width,
so, roughly....1/25th of the deviation...
That z-positions look like your second definition of "curvature", the deviation from a plane.
The radius of the curved mount seems to fit your first definition of "curvature".
When the smoke clears, though, the layout of the sensors for the Kepler
on a curved surface demonstrates exactly what an eyepiece is up against..
The focal points at the edge are not where the eyepiece wants them to be.
And a little "curvature"(math and physics definition) adds up to an obvious deviation.
I was wrong about higher power making the edges more out of focus, though.
I have edited that out.
The higher power means an eyepiece with a smaller field stop...
so it all cancels out: hi and low power see the see the same field trouble.
I have edited that error out..
Edited by MartinPond, 16 September 2019 - 09:03 PM.