The question of whether Celestron scts were corrected for coma sometimes comes up for discussion. To do so the 2ndry would have to be figured to a prolate profile, the resulting under-correction being balanced by a more strongly aspheric corrector plate.
I've made the equivalent Primary conic constant of an 8'' Dall Kirkham in an F/2/10 arrangement with a back focus of 8'' of 0.712 the relative strength of the corrector when the 2ndry is spherical.
In contrast Rutten and van Venrooij give 0.834 as the relative strength of the corrector in their aplanat version having an aspherical 2ndry.
In both cases the remaining correction is achieved by the 2ndry.
The relative strengths of the corrector affect their positions in the null setup below.
A light source is placed at the focus S of the primary with the beam being transmitted through the plate before and after reflection from the primary and is null tested at the focus of 2nd scope.
The stronger plate of the aplanat will achieve a null closer to S than the plate of the all spherical system. For the 8'' scope I get 0.67 focal length for the aplanat against 0.8 for all spherical.
For the all spherical case the calculation is:
0.712 of total correction for corrector and 0.288 for 2ndry.
0.288/0.712 = 0.404.
The fourth route of 0.404 = 0.8 f.l from S (Spherical aberration varying as the 4th power of the radius)
Assuming the same relative corrector plate position, a 5 fold amplification and the same relative back focus I think these numbers stay the same whatever the aperture. But the back focus gets shorter relatively as the aperture increases which slightly reduces both figures.
A corrector position between these extremes would suggest a part reduction of coma.
Edited by davidc135, 10 June 2022 - 08:07 AM.