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In other words, can a photograph (or any other printed image) be scanned and the output yield a file that can be used to print a copy with the same resolution/sharpness as the scanned material?

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    Is this a theoretical question or are you trying to solve an actual problem? There is a point of diminishing returns. It depends on what your intended output file is. If you just want to reproduce a 4x6inch photo as a 4x6inch photo, that is of course very easy to achieve. On the other hand are you wondering if you can achieve an exact 100% copy without any image quality loss whatsoever(imperceptible or not by the human eye)? – dpollitt Jan 3 '14 at 4:17
  • Yes, see my answer below. However, this might be rather costly, depending on your requirements. Do not consider ink printers! :-) – TFuto Jan 3 '14 at 15:34
  • I dont want to print the photo myself. I want to scan a picture that has been printed in photosensitive paper, (not with ink printer),take the file to a photo print shop and they will use chemical photosensitive paper to print it. – angel rojas Jan 4 '14 at 15:20
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No, it can't.

A reason for that is quite simple to understand. Printer splits an ink in dots pattern where some of the dots are larger, some are smaller, and some overlap. See the macro image of printed page:

Print

Meanwhile computer images work on a basis of pixels - where each "dot" is square (not round), equal in size and doesn't overlap any other, nor there are any spaces between them. So if you scan such a printed image - there's inevitable loss of details due to the way image is printed out.

Therefore you always will have a loss of image sharpness, resolution, as well as quality of colors (reasons for that are much more complicated than just raster printers use - quality of an ink, paper, used processing, number of inks, coatings, and other things make a huge difference to how the colors look like on an image, not to mention further difficulties with scanning).

  • There are better printers than inkjet printers... :-) – TFuto Jan 3 '14 at 15:35
  • I'm not sure I agree with the logic here. If the dots are much smaller than the pixels of the original print, and if the scanner also can scan at a fine enough resolution, it shouldn't be hard to produce a duplicate print which is as sharp and detailed in all meaningful practical senses. Getting the color to match is a different story, but that's probably limited by the gamut of the original print anyway. – mattdm Jan 3 '14 at 15:51
  • I dont want to print the photo myself. I want to scan a photo and take the file to a photo print shop and use chemical photosensitive paper to print it. – angel rojas Jan 4 '14 at 15:17
  • mattdm - it's perfect theory if you assume that all of the pixels on a print can be automatically mapped to their perfect representation of the pixels on a final image. As I tried to point out - that's not possible. Old rule from the University of Technology that applies to everything: "every measurement includes some uncertainty" - in that case: measurement is scanning, uncertainty is imperfections of scanned image. – MarcinWolny Jan 9 '14 at 14:33
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In theory:

Yes, as perfectly described in sampling theory, in the Nyquist rule.

If you know the grain size of the photograph, or the point size of the the printout, you have to use at least a double resolution using scanning. Meaning: a grain or dot on the photograph has to be at least perfectly covered by two scanlines and two scanner sensor pixels, or whatever it is called.

You also have to make sure that there is no internal image processing, so you end up with a raw image interpretation.

In practice:

The photo grain is not a perfect square. So that should be considered.

Also, the scanner's lens or edge will already alter the image a bit (it is not sampling a perfect square, but something similar). This works as a low-pass filter, and also can work as some kind of a convolution filter.

The printer you want to use to reproduce your image will also emit dots, instead of emitting perfect squares. This is also a kind of 2-dimensional filter.

Also, scanner mechanical elements do a bit of jitter in sampling, but that can be eliminated, too, with a bit of postprocessing, if needed.

However, if you go well beyond the Nyquist frequency, these will have very limited effect.

I Suggest:

Get the smallest grain size on your photo, divide by 2 => that is Nyquist. Divide that by 8-10 to oversample. And that will be the needed scanning and printing resolution.

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    You are right in terms of spatial resolution and your approach is scientifically sound. Yet, there is another aspect not to be forgotten: COLOR! Color is something so relative to the device and medium that even when using international standards (sRGB etc) none can really guarantee true duplication of the same color. So again, as you stated, one must apply the same rule for sampling color (in terms of bits per pixel)... So it turns up that the problem is actually 3-dimensional (actually 5-or-6-dimensional if you have RGB or CMYK scanning-printing) including x-y resolution and color resolution. – sepdek Jan 3 '14 at 15:45
  • @sepdek: you are definitely right. However, the OP did not specify an actual equipment, and his requirements. There are scanners that can scan in the entire Lab gamut! Also, the human eye also has a color resolution limit of its own. These could be also considered. – TFuto Jan 3 '14 at 15:54
  • @sepdek: Actually he asked: same resolution/sharpness! No words about color reproduction... :-) – TFuto Jan 3 '14 at 15:57
  • yes, he did not ask about color, but people often believe this is included...many years in this field made me eager to add to your answer though, for completeness... As for the scanners you mention, it is not only about them, as it is also about matching them with software for processing and devices for printing. The problem is very old; dates back to the early scanning and printing systems, but as you correctly stated is a matter of Nyquist limits. – sepdek Jan 3 '14 at 20:07
  • I dont want to print the photo myself. I want to take the file to a photo print shop and use chemical photosensitive paper to print it. – angel rojas Jan 4 '14 at 15:17
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It depends on the relative quality of a lot of things. If the quality of the printer and scanner far exceed the quality of the original source, then it is quite possible there will be minimal loss as both the printing and scanning would effectively create multiple similar points for every point of the original image. This would allow for random error to be strongly reduced by downscaling the image and combining the multiple samples back together. That said, this would still only get a very close approximation of the original. There is always some amount of generational loss in any analog transfer. You can reduce the impact by using much higher qualities than otherwise necessary, but some small degree of loss still occurs.

In other cases however, if the print quality is close to the quality of the original photo, then a large amount of information is lost because of the difference in how the pixels are rendered. In a print, small dots of ink or pigment are applied to the paper in a pattern that dithers to produce the actual colors we see as the image. They are microscopically small, but if the print resolution and image resolution are close, there won't be a good way to reliably reverse the dithering to get the original pixel colors and thus a much higher resolution scan that captures all the points being dithered is necessary, but the image is then significantly different. You can also similarly downscale again after the capture, but it will result in a lot of information being taken from originally neighboring pixels based on the spread of the dots. To the human eye, it would probably still be rather close, but it wouldn't be nearly the same as the original if you did a digital comparison.

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No, each transfert from one media to another one is working with tolerance due to captor/probe/output device. so at least you could have the same in perfect world but you only have partial in real world. Transfert is loosing part of the information with the physical limitation of each device not like a digital copy of a file on computer that copy each simple info exactly the same on the new support (in reality there is also tolerance but there is a auto correction info that could be assimilate to exact copy)

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I will try to explain using an example from earlier days when music was still recorded using analog technology.

Maybe you remember the times when music was recorded using tapes. Even with high-quality equipment it was impossible to avoid quality loss. Maybe making a good enough copy was entirely possible, but lossless, no.

The exact same applies to scanning a printed photo today. Repeating the scanning and printing process will always reduce quality.

As a side note, I always have big difficulties in getting dust out of my scans of photo prints, so I leave that to professional services.

  • The entire science of Digital Signal Processing guarantees that with the proper method, your analog-to-digital transfer is lossless for music. – TFuto Jan 3 '14 at 15:36

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