Theoretical question

Hi, please excuse me if this is too off-topic but I hope to find some knowledgeable people here.

I have a camera (Panasonic FZ1000) with a fixed zoom lens with a shortest focus length of 25mm (eq. to full format).
Now I have bought a second hand wide angle adapter for a different make of camera. With this I can get to a focus length of 18mm. But the images aren’t sharp near the boundary.

Does anybody know about (references to) mathematical means to correct this.
I wouldn’t mind solving partial differential or integral equations numerically if this should be necessary.
I could even do some inverse computation of parameters of a given model.

Many thanks for any hints or references.

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A wide angle converter will not get you good quality unless it’s matched to the lens, like the Ricoh GR and its GW-3. Plus, the FZ1000 is wider than most to start.

You can only correct certain aberrations after the fact: distortion (lossless, effectively) and lateral chromatic aberration (nearly lossless). Others require deconvolution which amplifies noise and has computational precision issues and has ringing and you have to crop the edge…

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You may be able to improve your images by creating a lens correction profile for you lens combination using Adobe Lens Profile Creator -
https://www.adobe.com/support/downloads/product.jsp?product=193&platform=Windows

it will correct distortion but there is little you can do about lens distortion at the edges. There is a reason why very high quality fish-eye lens can cost tens of thousands of dollars.