How to set focus on top item?

Is it possible to make images that look like they are in focus when the optics of the viewer are not set to a focal distance equal to the image's distance from the optics?

• Normally, an object is "in focus" when the focal distance of the optics are set to the object's distance. Can you create an image that would be out of focus when your focal distance is at the object's distance, but in focus at a different focal distance? Can we design images so that people with lesser eyesight see them clear without using glasses? Can we print a book so that myopic readers can read it without having to use glasses or aids of any kind?

• Answer:

  I assume by image you mean an image captured in a photo or something similar. The process of undoing a blur is called http://en.wikipedia.org/wiki/Deconvolution. From a purely mathematical perspective, assuming perfectly measured light intensities, blurring can be undone, or you can get close to undoing it. However, in practice these kinds of problems are very sensitive to error so that any imperfection in the blurred image leads to big errors in your attempt to undo the blur. This makes the method much less useful than you'd like. An old technique is http://en.wikipedia.org/wiki/Unsharp_masking where the image to be blurred is itself blurred and then subtracted. I think it does more to give an illusion of sharpness rather than actually removing the blur. Another popular method is http://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution and that can sometimes bring back features that were apparently lost by blurring. There are plenty of more sophisticated methods too. With many of these methods you pay a price. You may get an improvement in sharpness but you also get http://en.wikipedia.org/wiki/Ringing_artifacts around edges. These can quickly look worse than the blurring you're trying to fix. There are special kinds of blurs that can be removed. This is the basis of http://en.wikipedia.org/wiki/Coded_aperture photography. I'm not really sure what the state of the art is but people have built cameras that allow you to change focus after you took the photograph. But you can't do this with a photo taken with an ordinary camera. TL;DR It's hard but you can generally make a little bit of improvement to the image.