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I am trying to process an image in good quality to appear blurred to a normal person and good to a person suffering from myopia as seen in this source.

Is it possible that a picture that is blurry will appear normal to a person suffering from myopia (farsightedness)?

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    $\begingroup$ While you can't do this with a physical ("real") image, you can do it with a "virtual" image. Adjust the optics to throw the virtual image plane to a location that the myope can focus on but that 'normal' vision folks cannot. $\endgroup$ – Carl Witthoft Dec 16 '15 at 15:02
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    $\begingroup$ Isn't this a duplicate of "Is it possible to blur an image in such way that a person with sight problems could see it sharp?" $\endgroup$ – Rahul Dec 16 '15 at 17:42
  • $\begingroup$ the only way would be to deform the phase of the light field coming from the picture in a way such that the crystalline lens of the eye now it can produce a good focus on the retina... in other words, spectacles! $\endgroup$ – scrx2 Dec 18 '15 at 15:39
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A quick footnote to Nathaniel's answer:

If an image looks blurred to you it's because you are viewing it in a plane that isn't the focal plane.

Image

If you put a screen where I've drawn the red dotted line then the image on the screen will look blurred.

If you measure the light in the red dotted plane then at every point in that plane the light wave will have an intensity and a relative phase. If you know the intensity and phase then you can reconstruct the in focus image using the Huygens construction, and indeed the process is known as Huygen's deconvolution. The trouble is that when you take a photograph the photographic process only records the light intensity and it loses the phase.

So if you're starting from a photograph you've lost half the information originally present, i.e. the relative phase, and that means it's impossible to reconstruct a perfectly focussed image. A blurred photograph won't look normal to anyone - myopic or otherwise. However it is usually possible to improve the blurred picture to some extent, which is why Huygens deconvolution software is so widely available.

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    $\begingroup$ Are you sure that phase information is needed when dealing with trying to reconstruct a perfectly focussed image from an out-of-focus image the was illuminated with incoherent light? I've seen descriptions of image recovery in which the problem is described as trying to deconvolute an out-of-focus image taken with an (unknown) point-spread function in which there is missing information because of the finite size of the picture. In fact, it seems that those two bits of missing info would still be a serious impediment to image restoration even if one did have full phase information. $\endgroup$ – Samuel Weir Dec 16 '15 at 18:17
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No, it's not possible, sorry. This is because blurring (or more generally, convolution) is a lossy operation, meaning that information is lost when an image is blurred, such that it can never be completely retrieved. While there are ways to sharpen a blurred image, these are either very non-trivial or else they're only approximations - there's no way to sharpen an image such than when it is later blurred it will return to its original appearance.

From a quick skim of the article you linked to, I don't think there's any claim that what you suggest is possible. Could you have misunderstood something perhaps?

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    $\begingroup$ Which is why those CSI episodes where they sharpen the image on a few pixels are just nonsense. $\endgroup$ – PaulMurrayCbr Dec 16 '15 at 8:51
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    $\begingroup$ Not sure about blurring, but the convolution (seen as a mathematical operator) can be reversed or deconvolved, although in real life the result is often scrambled by noise (see Numerical Recipes in C, Cambridge University Press). $\endgroup$ – DarioP Dec 16 '15 at 14:13
  • $\begingroup$ @DarioP it seems you're right - I had assumed that convolution (as a mathematical operation) was non-invertible, but it seems the difficulty of doing deconvolution in practical applications actually stems from not knowing the kernel exactly. But since convolution is linear and its inverse must also be linear, that seems to imply that you can sharpen an image such that it will return to its original appearance when later blurred, as long as you know the exact kernel for the blurring convolution. This might mean my answer is technically wrong. $\endgroup$ – Nathaniel Dec 17 '15 at 1:04
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I think that you can do something like that, but you have to exploit a caveat.

Myopia affected people have the same depth of field of normal-viewing people, with the exception that instead of going from tens of cm to infinity, it goes from few cm to tens of cm. This forces myopics to go close to the objects in order to put them on focus, but also allows them to resolve much more details. It is basically like having the macro turned on in a camera.

So you have to start from an image rich of tiny details which in reality could not be resolved by the human eye at a standard distance of ~30 cm. Then they would appeared blurred to a normal viewing person, while a myopic, being able to go much closer, may see them.

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