[Wavytone]

Casstony,

The field curvature is a function of the telescope design and isn't just a function of the curvature of the secondary mirror.

For example, take several different cassegrain designs having primaries and secondaries of similar radii - the classical cass, Dall-Kirkham, Meade/Celestron SCT, A Gregory maksutov, the RuMak, and the ones that have a corrector at the secondary mirror - all will have quite different field curvatures - some negative, some positive and it is even possible to come up with an aplanatic solution (flat).

There are some optical formulae for analysing two-mirror designs that use conic sections (A.E. Conrady) to determine the curvature to third-order but these don't work for surfaces with complex shapes such as the SCT corrector. The best way is to ray-trace the design to calculate the curvature precisely.

While it is possible to calculate the field curvature for common telescope designs, in some respects it is most unfortunate that eyepiece manufacturers never state what the field curvature of the eyepiece is (or was designed for), consequently finding the best eyepiece to give sharp focus across the whole field (ie to match a specific scope) is frankly trial-and-error - as we all know. The problem mainly affects low and medium power eyepieces - not a big deal for high power ones.

The result is that an eyepiece that works well in an f/5 Newtonian (curved focal plane) may be disappointing in f/7 aplanatic refractor designed for imaging (aplanatic = flat focal plane, to suit a flat sensor).