Edge of field performance

Lets say you had 2 refractors. One was a 6" f/8 and the other a 3" f/8. The true field size in the 3" scope would be 2x larger than the 6" scope with the same eyepiece. What is the best way to compare the edge of field performance of the objective. With the same eyepiece in the scopes or with different eyepieces in each scope of the same design(Nagler)that would show the same true field.

Mark

Most lenses are designed to have zero coma. They will have off-axis astigmatism and field curvature. The field curvature will cause off-axis stars to be out of focus, and the astigmatism will show the stars as ovals on a flat field and small cross shapes at best focus off-axis.

Field curvature of a lens, where all elements are up front, will be approximately 0.35 times the focal length. It will be inward curving. A short lens will have a steeper curvature than a long lens. Double the focal length, double the radius of curvature.

Now take these and do a bit of geometry to figure out what the off-axis star image will look like.

Rolando

This comparison between the 3" and 6" does not make much sense
unless you are trying to attain the same true field of view
in the eyepiece for some purpose, like observing the
entire moon. For example, using a 15mm eyepiece in the 3"
and a 30mm eyepiece in the 6". Otherwise it begins to be
comparing apples and oranges.

As Roland says, for a simple doublet the field radius
of curvature is about 1/3 of the focal length. So the
3" will tend to have twice the curvature at a given
linear distance from the field center. This would
be important if you were imaging with a certain
detector size, and only cared about how the images
looked at the detector corners (ignoring the
different true field sizes).