Quote:
|
Originally Posted by Don Pensack
... Linear diameter of coma is 3r/(4N)^2 where r=off axis distance in mm, and N=focal ratio. No mention of focal length is made.
|
Don, I think there is a bit of confusion about what Bratislav was trying to get across. He was not arguing that the
amount of coma will be different for different focal lengths, but that the optics needed to correct it will need to be designed for a particular focal length, and independent of f-ratio (once you have chosen the fastest f-ratio you want the corrector to still work in).
Thinking about the problem in my simple-minded way (having no experience with designing optics), this seems to be correct, for two reasons.
1) If a corrector is matched to a fast mirror of some focal length, then it also must be a match for all slower mirrors of the same focal length, because the fast mirror can be split into a slow inner mirror and a fast periphery. The corrector must work on both slow inner and fast outer halves of the mirror if it is to work on the mirror as a whole. So you cannot have a corrector designed for fast mirror that will not work just as well on an arbirtrarily slow mirror of the same focal length.
2) If you think about scaling up a fixed f-ratio mirror (increase f.l. but keep f-ratio constant), the amount of coma at some point in the focal plane will increase linearly with size of the mirror. But so will the distance
r of that point from the optical axis. Combine this with the fact that for any given mirror, the amount of coma is a linear function of
r, it follows that the amount coma will indeed be the same for any given
r independent of the focal length, as we all seem to agree. However, when you scale up the optics, the field curvature will change. A scaled up field will have less curvature, i.e., for the same
r, you are closer to the focal plane in a long focal length mirror. (e.g., think of circular arc of fixed length as you blow up the circle.) So a small fast mirror will have a more strongly curved field than a large mirror of the same f-ratio.
Because of #1, the coma corrector cannot be specific to any f-ratio.
Because of #2, it makes sense that the corrector must be specific to focal length, because while the amount of coma at a given distance from the optical axis is independent of FL, its distance from to the ideal flat focal plane is not, with field curvature getting stronger as the FL gets shorter.
From this I would conclude that there will be an ideal focal length where Paracorr works best, and there is a range of focal lengths above and below this where it works well. I expect there would probably only be an issue with small mirrors, as the field is practically flat once mirrors get large enough, so a corrector designed for a flat or nearly flat field will work well with arbitrarily large mirrors. However, I would not be surprised if the Paracorr did not work with a 4" f/4, for example. Anyone care to check?