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RE: [APML] need suggestions on how to use a reducer with a Taurus TIII
Hi Wei-Hao,
These are such great questions! They drive straight to the heart of optical design.
Astigmatism! Yes thanks for reminding me...it's so intertwined with field curvature in this kind of design problem that it's easy to forget you are also correcting for it as well. Kind of hard to describe the impression....it's kind of like hanging out with a married couple. You hang out with one and you automatically hang out with the other. Like a package deal. :)
>From what I remember of talking to Taurus Tech and from seeing on their website, their reducer is optimized for the field curvature of an SCT. So, in the case of using it for the refractor, the field would be overcorrected (ie bends outward or the edges of the field go away from the objective)...to what degree depends on the difference between SCT's and the refractor's curvature of field. This doesn't necessarily mean you should reject it for use with a refractor: This same overcorrected field is handy when it comes to correcting for astigmatism.
Astigmatism results from the tangential (like surface of a wheel) and sagittal (like spokes of a wheel) fields not coinciding with each other...they simply see different amounts of power for the same reason you see different dimensions when you hold a circular disc at an angle..the outline then looks like an eclipse. In a system with no field curvature, the sagittal field lies in the paraxial focus plane (ie sagittal field is flat). For a positive lens like the refractor objective, you will have undercorrected astigmatism. The sagittal focal surface curves inward (ie towards the objective), and the tangential focal surface curves inward even farther. For a lens system with no field curvature (for example, the refractor with a reducer that corrects for its field curvature), the sagittal focal surface is flat but the tangential surface still curves inward. So, what you really want to do when you also have astigmatism is overcorrect the field curvature to give a little bit of overcorrection of astigmatism as well. This creates a sagittal field that curves outward, and a tangential field that curves inward by the same amount. The result on film is nice sharp stars at center, and while they may bloat a little towards the edge, they are still round well-focused images that are pleasing to the eye. Note this doesn't make the tangential or sagittal fields coincide any more than they already are...it simply adjusts their location to give pleasing results.
There's really not a lot more you can do when it comes to astigmatism...actually reducing astigmatism will almost always increase coma in the lens design. This usually isn't a good idea. I'd rather have astigmatism I could balance out later than have coma which I can't do anything about after the system has been built. So when the Tak reducer corrects for astigmatism, it really is balancing it out rather than reducing it (that is, adjusting the locations of the tangential and sagittal focal surfaces rather than bringing them closer together). Note that doing this overcorrects field curvature. See how astigmatism and field curvature and the ways you correct them are so related? Unless the Tak reducer is doing something really really wierd, but I don't think it is. :)
So in our example of a reducer used to correct field curvature in an SCT, when it is used on the refractor it ends up overcorrecting the refractor's field curvature...which is what we want anyways to balance astigmatism. It's neat how that works...it's things like that and all the other ways the different aberrations interact that I find so fascinating. Anyways, again, how well it balances astigmatism depends on the differences between the system the reducer was designed for and the system you are actually using. And since astigmatism is balanced the same way field curvature is corrected, distance again really isn't a big player except to tweak the radius of curvature on the lens surfaces. So with the example of the Tak reducer in a different spot, the correction isn't optimal but I don't think it's very sensitive.
Hope this helps,
Jason
P.S.: If you can find a copy of "Telescope Optics" by Rutten & van Venrooij, they have a great description of this in Ch. 4 (which I used as a reference here) and a whole two chapters (14 & 15) dedicated to the design of reducers and field correctors. This is a really good book.
Another great book is "Intro to Lens Design w/ Practical Zemax Examples" by Joseph Geary. This book is based on lecture notes from a graduate level course he teaches at the University of Alabama - Huntsville. It's a really good book because it shows you how to design optics using Zemax, which is one of the 4 major optical design packages used in industry (it also happens to be the design package I use at work). It's based on his syllabus so it's got homework problems and a mid-term and final exam as well. :)
-----Original Message-----
From: astro-photo-bounces@seds.org
[mailto:astro-photo-bounces@seds.org]On Behalf Of Wei-Hao Wang
Sent: Tuesday, February 15, 2005 5:55 PM
To: Discussion of Film Astrophotography
Subject: Re: [APML] need suggestions on how to use a reducer with a
Taurus TIII
Hi Jason,
Thank you very much for the explanation. This clears some of my questions
but also arises some others.
First, as you explained, the Taurus reducer sits inside the guider and there
is no distance problem. But is the Taurus reducer optimized for Tak FS?
If not, then the distance doesn't really matter because it's not optimized
anyway. On the other hand, if I want to use an optimized reducer (like the
one made by Tak), then there might be a distance problem after adding in
a guider between the camera and the reducer.
The second question is, is it true that all the reducer do is to correct for
its own color and field curvature? As I know, APOs like the Tak FS has
significant astigmatism. Doesn't the reducer also correct for this? How
sensitive to the distance do you think the astigmatism correction is?
Wei-Hao
--
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Wei-Hao Wang :)
Institute for Astronomy at University of Hawaii
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2680 Woodlawn Drive Personal Website:
Honolulu, HI 96822 http://www.ifa.hawaii.edu/~wang
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