Said again because it's the main point in a difficult subject: 10 bits can contain numeric values representing 4 times the number of steps of tones that 8 bits can, and 12 bits can contain 16 times the number of steps that 8 bits can. We will show below how more steps can extend the range into deeper darker areas, ASSUMING the scanner CCD can do its part to somehow actually sample data in those dark reaches. There are more possibilities of unique shades of tone at the dark end, where data is otherwise quite sparse. The improvement is in the ability to differentiate deep black tones (in positives, but highlights in images from negatives). At least it could if such CCD data were actually present.
Our human eye responds to brightness logarithmically, that's why we measure density logarithmically. The scanner's analog CCD cells operate more linearly than our eye, but the intensity of the reflected or transmitted light in the image is proportional to the logarithmic density of the image.
Courtesy © Eastman Kodak Company, 1995
Above is a sample of that logarithmic density curve from Kodak's Optimizing Photo CD Scans for Prepress and Publishing, page 11 (an Adobe Acrobat .pdf file, 376K bytes).
The graph shows the non-linear aspect of the problem. It charts on semi-log paper the image intensity across the bottom, left to right from lightest to darkest, and image density going up. Note especially at the white end, how large horizontal changes in image intensity make almost no difference in density. And the opposite effect at the black end, where tiny changes in intensity require huge changes in density. Tiny changes in density at the black end are often lost altogether. Data is often very sparse at the black end.
It is interesting that Kodak shows the maximum density capability of a drum scanner as 3.7, the best film transparency as 3.2, their Photo CD scanners to be 2.8, and reflective photographic prints at 2.0 maximum density. This reference is dated, and the Kodak Photo CD scanners are improved today, but notice the small difference in the darkest tones possible between scans with 3.2 and 2.8 dynamic range. This subject was of great importance when 4-bit scanners made B&W images with 16 shades of gray, and still is very important for slides, but is of less concern if scanning prints. Prints have relatively little dynamic range to capture, 2.0 is quite black.
An interesting mathematical curiosity is the absolute theoretical maximum density range shown in the chart below for the various numbers of bits. No scanner is involved, we are only discussing numbers now. Log 10 can be computed with the Windows calculator. 8 bits can store a numerical value 0 to 255. And then for example, the Log base 10 of 255 is 2.4. Log 10 of 1 is 0 (log is only defined >0). The difference is 2.4.
|Maximum values possible
in this number of bits
|Log 10 of the
|4||2 to the power of 4 = 16||Log 10 of 15 = 1.2|
|5||2 to the power of 5 = 32||Log 10 of 31 = 1.5|
We instantly recognize these numbers as being familiar...
Scanners typically advertise dynamic range specifications this way:
24 bit scanners - specifications near 2.4
30 bit scanners - specifications near 3.0
36 bit scanners - specifications near 3.6
42 bit scanners - specifications near 4.2
48 bit scanners - specifications near 4.8
Scanners of those bit depths usually do boast similar dynamic range, per the same calculation. However that is only the size of the container, it is not about the contents. It merely counts bits instead of measuring the data contents or capability. If comparing a 4.8 spec with 4.2, don't believe all you read, neither value is achievable in any CCD scanner.
The most optimistic number I have seen Kodak claim for slide film is 3.4. If scanners could actually do 3.4, there would be no problem. A 3.6 or 4.2 scanner specification is not a measured value, it is only describing the theoretical size of the 12 or 14 bits, without concern about measuring scanner CCD performance. The inherent noise level is only one factor always preventing achieving the theoretical maximum. Isn't it odd that these scanners seem miraculously able to always achieve it?
16 bits are indeed required to store the size of numbers representing dynamic range of 4.8, but 16 bits do not ensure the CCD delivers 4.8 range data (as marketing leads us to believe). We are seriously kidding ourselves if we think CCD performance approaches the limit of the A/D bit depth. It only means that 16 bit A/D chips are inexpensive now, but high quality low-noise CCDs are the problem. High-end scanners do help performance, but price is a more meaningful specification than this number.
This concept of bit depth allows construction of the table shown below. It is an idealistic theoretical case, ignoring that DMin cannot be zero, due to bleeding and other factors. In particular, the chart ignores noise too, but noise is a big problem in the real world.
CCD intensity values are charted with brightest white at density 0, and each step is 1/2 the previous value. Photographers know that one f-stop varies the light by a factor of two, so each step here represents one photographic f-stop. The first f-stop uses half of the total values, and each subsequent step uses half of the remaining total values, etc. You can see that the possible values are extremely sparse at the black end. But even density 2.0 is pretty near black, printed on paper.
The logarithm of that 2X factor is 0.30 (log 10 of 2 is 0.3), so the density intervals are 2X steps too. However, the steps are just numbers that don't say anything about the scanner's CCD or noise level or capability. The steps are not necessarily all useful if the data is noisy or absent. I can trivially make the chart go as low as I wish, I can use 16 bits and just type a few more values, it's easy. I hope you can appreciate that is rather different than actually manufacturing a scanner that is capable of producing real data differentiating unique dark tones that dark (zero-signal level, in the noise).
|2X Intensity Values|
|8 bit||10 bit||12 bit||14 bit||16 bit|
Let me emphasize that this is NOT showing how 48 bit scanners deliver 4.8 dynamic range. 16 f-stops of range is simply not possible (we struggle with 10 or 11 f-stops). This is instead showing how marketing specifications create that number. It only shows how 16 bit A/D chips could represent the numbers for this range, IF the scanner's CCD could somehow magically produce that data (it cannot, and nothing here suggests that it can). This shows how bit count is NOT the same as measured scanner performance (this measured no scanner). It shows how the false scanner dynamic range specifications are created, how they only describe A/D bit count, instead of CCD measured dynamic range. This shows one reason why 30 bit film scanners were insufficient for slides. But today the usual number of bits has surpassed scanner CCD performance. Obviously, if scanner CCDs could actually do 3.4 dynamic range (to match the slide film), there would be no problem, and this subject would hold little interest.
The gray bars show typical specifications, but there is no way real scanner CCDs can actually dig that deep into the zero-signal noise levels. The noise is far from zero, much more than one bit. You can see this by examining your own images.
Are the new film scanners good? You bet, better than ever before, and I don't suggest otherwise. Can they actually do 4.2 dynamic range? No way. Film goes to 3.4, and the CCD scanners cannot quite reach that. The marketing claim of "Dynamic range 4.2" only means "14 bits". Does marketing want you to choose their scanner based on that false specification? It would sure seem so.
There are no standards for defining or advertising this number, and as practiced, it has no meaning. In fairness, all brands must make the same absurd claims now that others do it, because we do seem determined to buy based on this phony number. The 4.8 maximum for 16 bit scanners or 4.2 for 14 bit scanners is simply not possible, it is not even imaginable. Some brands reason that at least one bit must be noise, so they compute a theoretical value 0.3 less (one bit less). However, it would be a mistake to rate them lower simply because they don't claim the same hype. It would also be a mistake to rate them higher, it's still hype, and not measured performance. Buy by brand, buy by reputation, buy by results, buy by price, but don't buy based on this phony marketing number. It's a pity that life is like that.
Don't take marketing scanner dynamic range numbers seriously. Dynamic range is indeed very important, at least especially for slides, but it simply is not possible to do what is claimed today. Normally, price is a better criteria of performance, but of course, exceptions can always exist.