I'm frustrated by the notion that the only way to deal with field flatteners, other than those designed to mate with a specific optical design, is to buy it, mess with various spacings, and see how it does.
It seems to me that there ought to be a way to establish the field curvature of the telescope in a reasonably accurate way, and then what I think of as the anti-curve of the field flattener, and figure out where to put the silly thing in the image chain. This is just based on intuition and what little I know of optics so far.
I think I follow the notions of a basic flattener: the goal of a plano-convex at the image plane is to "delay" the wavefront more in the center and less at the edges, to bring the overall wavefront to a plane. I'm not sure I follow what's going on when the field flattern design is more complex and distant; they seem to be at least two elements, and they want to be placed at some distance from the image plane. The same sort of thing must be happening, but it's acting at a distance. Somehow.
I have also been exposed to the notion that the field curvature is primarily a function of the strongest element in the optical design, so, for example, you can find a reducer that has been designed with field flattening in it, somehow, and not require a separate flattener. And that Roland Christen seems to think it's best to design a different flattener for each objective design, though some of them apparently cover more than one telescope. And that most vendors suggest that their "generic" flattener will cover a range of focal lengths, with a suggested chart for what the spacing should be for each of them.
Then there is a gap in my understanding, and we leap to the pragmatic approach of "buy one of them, get some extension tube adjustabiliy in some way, and start tinkering until it works best."
My questions are like so:
Could I theoretically use a sensor, perhaps with a custom-machined off-axis gizmo that puts the optical axis near one corner of the sensor so that the other corner of the sensor covers a longer radius, combined with automated focusing to try and nail down the best point of focus at the center and out on the radius?
Is there a way to measure the radius of the field flattener, to characterize its optical characteristics such that I can compute the right spacing from the objective focus?
Or for that matter, what would the typical flattener's design parameters be based on? Is it simply a matter of focal lengths and curvatures? Or is the curvature correction going to be a function of focal ratio? And/or what else would affect how it performs with a particular telescope?
There HAS to be at something better than "buy it and try it" -- maybe not a fully derived technical solution, but... something.