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Generally speaking, CA is caused by different colours focusing to different points, a doublet will focus 2 colours to the same point, a triplet, 3. (simply speaking) Are there downsides to using a cheap refractor, a mono CCD, colour filters and refocusing for each colour? Is it simply too difficult to achieve critical focus with the different filters? I strongly suspect I'm missing something, but can somebody please tell me what.
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Think of light colour as a countinum (not discreete R G and B) and you will see what you are missing. For example, look at the images I took on this page with R G and B filters.
http://deepspaceplace.com/ed127.php
Look closely at the one with the blue filter. The blue filter has a 'passband' - a range of frequencies if you like - that this scope is unable to bring to perfect focus. So you are still going to get bigger stars when you use the blue filter, and still get some blue halos when you combine into the final R+G+B images. In fact the point where the green filter ends and the blue filter starts, the light is focused to almost the same point. So there isn't much benefit in refocusing between images at all.
Narrowband filters (such as Ha) have a very narrow passband, so this is a slightly different story.
I hope this makes sense!
James