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Comment by nomel | Hacker News Reader

At one time I wanted to see if I could pre-deconvolve what's shown on a computer screen so that a person with a slight vision problem could use it without having to wear glasses, using their blurry eyes to convolve the images back to the original image. I found a paper/website that did this (can't find it anymore), with some example images of text, and it worked fairly well, but spatial resolution was very limited.

One interesting limitation is that negative brightness is needed to make it work without distortion. Limiting the brightness range of the image, so that black can act as a sort of "darker than possible" level helps.

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That's a super interesting idea and I think should work very well. If it was combined with the use of camera (for tracking the distance away from the monitor / screen) I think it could work very well; especially that noise / quantization / compression is not a problem in such a case.

The paper:

O. Keleş, E. Anarım: Adjustment of Digital Screens to Compensate the Eye Refractive Errors via Deconvolution.

Link to PDF:

https://www.researchgate.net/profile/Emin-Anarim/publication...

Dude. I have... multiple books on my shelf about Deconvolution (though more 1 dimensional than 2 dimensional)... never even heard of this and am tickled pink :D Thanks! (and thanks grandparent for remembering it)

Will 100% post to HN ~should~ when I try implementing it.

I find it very unlikely to work.

Convolution smooths out functions. If you convolve any function with a Gaussian kernel, you get a C^infinity function (a function that has continuous derivatives of arbitrary order).

This anti-blurring effect would attempt to find for a given function f another function g so that g convolved with a Gaussian kernel is f. But if f is discontinuous no such function exists.

This is not just academic. Letters on a screen are discontinuous functions.

You could say that a certain amount of smoothness is tolerated. Or that all signals are discretized anyway, so the whole concept of continuity is mathematical non-sense.

So, what I provided is just heuristics, is not a solid proof. It's still in principle possible to produce such a anti-blurring algorithm, I just find it highly unlikely, I would not invest much time in it.

Look up computer generated holography! It is certainly possible to calculate a hologram of a letter which focuses at some different depth than the screen.

There are issues which arise from restricting the hologram to a real valued grid, like limited FoV and noise, but these are not impossible problems to solve and existing technology is already quite good in terms of image quality.

Maybe it could be used to make VR and AR headsets that have no lenses.

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