I have recently ordered a Samyang 500 mm/f6.3 mirror lens on eBay, for about £80, largely out of curiosity -- at the very least, it will be an interesting toy and I can always sell it.
Mirror lenses are frequently criticised for many things, but predominantly a perceived lack of sharpness and their 'doughnut' bokeh. This question features an excellent explanation of why central aperture obstructions mask out spatial frequencies and reduce sharpness.
My question is simple -- for a mirror lens, we [or Samyang] know the geometry of the lens pretty exactly, and hence its point spread function. I realise that knowledge of the position for all items in the photograph is required to "correct" for the bokeh (if you wanted to), but I have naïvely thought that we'd be able to work out the PSF analytically or numerically, and then improve contrast by deconvolving images obtained by it.
While I wait for my lens to arrive in the post (I've got more than a week to go!), I've quickly explored this idea using Kamen Kunchev's (Creative Commons licensed) pigeon picture I found on flickr:
I've then estimated the aperture for the camera:
Computed its corresponding point spread function (shown in magnitude on a funny semi-log axis to make the structure visible):
...and used it to perform a maximium-liklihood based, regularised blind deconvolution to obtain the following 'sharpened pigeon':
Now, to my mind, this looks a bit weird. Contrast has definitely been improved, but it isn't entire the step change that one might perhaps naively expect. I've played around with adjusting the filter size -- which obviously makes a huge difference -- and I think it's probably the case that my PSF isn't entirely accurate. Of course, artistically the original is a lot better, and I suspect it always will be, but it strikes me as perhaps odd that we're unable to correct for a known property of the imaging system. What am I doing wrong?
Are there documented examples where people have tried this before? As catadiatropic imaging systems have been used in telescopes for literally centuries, I expect that there's a relatively simple way to up the "contrast" on these interesting devices.
(What happens if you just increase the intensity of the other regions of the image's k-space?)
EDIT: Perhaps I'm just getting my estimate of the aperture wrong. Below is another attempt with a smaller annulus and a smaller obstruction. Are there any Lightroom plugins that let one easily play with these sorts of things, out of curiosity?