Firstly I just want to say "thank you" to Ray for the great write-up and discussion. I've never had access to astronomy software to do any form of deconvolution but I think you've convinced me that I should plonk down some cash for PixInsight.
Secondly, if it hasn't been made clear already, I'd like to say that iterative deconvolution is a process of separating the observed from a model of the noise in the image - in our case the atmosphere. Of course the atmosphere is ever-changing and we take many images over long time periods so the blurring effect that we see will vary slightly over the image frame, so _yes_ it will never be perfect. Even if it never changed we will also come up against losses of precision in our computers and this will cause some loss of accuracy.
By comparison, sharpening is a (generally) simple matrix math function which shifts affects contrasts based upon their surroundings in a way that we decide. There is often a considerable loss of information from this process (as information from higher orders is concentrated in lower orders). Personally I think the only place for sharpening is as a final, mild step to make an image "contrasty" for its final medium - on screen or in print.
Cheers,
Cam
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