Continuing the discussion of 8 bit vs. 16 bit mode, the issue of dynamic range has come up, so let's explore that a little deeper.
The most important thing to understand is that having a ADC converter with more bits does not necessarily mean that the dynamic range of a given system is greater than if you have an ADC converter with fewer bits. The reason is that there are at least two things that can limit the dynamic range. The first is how many bits are in the ADC. However, if the signal source is a noisy one, then at some point noise is the limiting factor, not the number of bits in the ADC. This is well-known in signal processing theory.
Since the Epson scanner has come up in the discussion let's explore the question of whether noise is the limiting factor. Here's the experiment. Using my Epson V/750 scanner. I made a scan with half of the image that transmits 100% (i.e. air, with no film) and the other half of the image where the light is perfectly blocked. I did this by laying a thick piece of black paper on the scanners glass. I placed it on the glass instead of the focal plane of the scanner to make sure that there is no texture captured in the image. Above the paper is a standard 35mm multi-frame film holder. Above that I placed a book. There will be no light penetrating through the book and the black paper. All scans were done in 6400 dpi mode.
I selected a crop area and scanned it twice, once saving the scan in 8 bit mode, and the other saving the scan in 16 bit mode. As you can see in the attached photo I included part of the film holder frame, so the light area is actually less than 50% of the image. (Please note. This is actually a image I snipped from a screen shot. It is not the original file, which was too large to upload. In fact, all images shown in this post are screen shots of displayed results, not the original scanned files. However, all work was done on the original files themselves.)
From the 8 bit scan I cropped a small piece from the lower left hand part of the image, containing roughly 9000 pixels. In this region of the image light is not just blocked by the paper and the book, but also the frame of the film holder. Note: this is a snipped image from a screen shot, as are all of the images I am showing.
Then I did a histogram correction. I selected the 2.5% from the left hand side of the histogram correction (the dark end), so one can see the histogram structure in the dark region cropped from the image. Here's what it looks like There are just a few peaks. The spacings of these peaks correspond to one step of an 8 bit word. In addition to the graph I am showing the resulting image of the histogram correction. It's noisy.
This is already a strong hint that 8 bits is more than enough dynamic range to capture the noisy signal. In a scan of film the scanner noise and the film grain will combine to make a scan even noisier, but just the scanner noise alone, without even considering film grain, is sufficient to imply that 8 bits is plenty to capture the dynamic range possible in a scan. Otherwise we would not see multiple peaks in this histogram.
We can make this a little more quantitative by treating the histogram plot as if it were a probability distribution, i.e. normalizing the set of peaks to a sum of 1. The standard deviation of the peak cluster turned out be be 0.55, where 1 is the step size of the digitization. (Note: in the figure the distance between the peaks is 40 arbitrary units of the horizontal axis. The standard deviation in these arbitrary units was 22, but I then renormalized the spacing of the horizontal axis to unit increments, so the normalized standard deviation is 0.55 of the digitization step size.)
Although 0.55 is an important number, it is not to be taken directly as determining the dynamic range limit. A more reasonable number is three sigma. This is the criterion used by analytical chemists to specify a detection limit, which is the value that can just barely be said to be reliably distinguished from a blank. Using this criterion one can say that the 0.55times 3 or .65 digitization steps (out of an 8 bit word size) is where we can just barely say that the image is not quite dark. This means that the dynamic range of the Epson scanner is 155 to 1.
What about if I do the same analysis to scan saved in 16 bit mode? Here's the image of the histogram for that case. This is after we have selected the darks side of the histogram.
Note there are more peaks present because 16 bits can hold more discrete numbers than 8 bits. Of course they are also closer together for the same reason. However, the width of the distribution is comparable to that of the 8 bit scan. (Note: the horizontal axis is of the same relative length the 8 bit and 16 bit histograms.) In fact, if I go through the entire calculation, treating the peak cluster as a probability distribution, calculating the standard deviation, and determining the dynamic range, it works out to a dynamic range of 113 to 1, which is a bit worse than the 8 bit scan. However, I consider this to be within experimental error, meaning that the dynamic range for the 8 bit and 16 bit scans are basically the same.
Just for fun I also took the 16 bit scan and converted it to 8 bits. (These manipulations were all done in photoline, as were all manipulations done in this post.) Here's the result.
Note this result is qualitatively very similar to the 8 bit scan. When I go through the calculation I get a dynamic range of 121 to one. Why did it get a little better after I converted the 16 bit scan to 8 bits? I don't have a full answer to that. However, I suspect that it may be due to the data being in gamma corrected format. Mathematically speaking, this is a non-linear process, and sometimes non-intuitive things can happen when non-linear operations are done on data, and this can be especially true when there is the possibility of roundoff error.
The conclusion from this is that from the point of view of dynamic range there is no advantage to saving scans in 8 bits vs. 16 bits on the Epson scanner because the dynamic range is limited by scanner noise, not by the bit depth of the word used to store the result. If film is scanned this is even more the case because film grain will provide an additional level of effective dithering.
Next comes something very important. The dynamic range discussed above is the single-pixel dynamic range. The effective dynamic range of a full scene can be (and virtually always is) higher than the single pixel dynamic range. This is because when we look at a picture we normally don't see the individual pixels. In fact, our eyes cannot resolve single pixels of most images at ordinary viewing distances. We can think of our visual acuity as sampling an effective patch size in the image. For a given point in the scene our eyes effectively average the result over the pixels in the patch. The dynamic range improves as the square root of this patch area, which means that it improves linearly with the linear patch dimension. For example, if a patch is two times larger in linear dimension it is four times larger in area, and the dynamic range averaged over a patch of this size is twice as high as the single pixel dynamic range. If this were not true then, for example, half-tone printing would not work.
There is also the fact that the film has a gamma associated with it, so when converting the film's gamma to a more linear scale and inverting and adjusting the image, the scene-referred dynamic range is expanded still further.
And as a final comment, although I am not a signal processing engineer, I have spent a good fraction of my profession career as a PhD chemist dealing with the problem of extracting useful information from data having experimental uncertainty, including noise, and along the way I have studied and learned quite a bit about digitization of signals as well, both from an engineering perspective (for example, knowing the difference between a successive approximation ADC vs. a flash ADC, or what's the difference between a pulse counting system and an ADC based system data acquisition system), as well as a theoretical perspective, and an analytical perspective. So if you want to question my credentials to discuss this topic please feel free to do so. I can't stop you, nor do I believe I should stop you. However, I am personally confident of know as much as or more about this topic than 90% or maybe even 99.9% of the people who are likely to be reading this. And I don't know if anyone has noticed, this, but for my part I don't recall having questioned the credentials of any specific persons posting on this topic. I generally believe in a principle of more or less free speech when it comes to scientific or technical matters, especially in the context of informal public forums, and I prefer not to question the credentials of others. It would be nice to give me the same courtesy. I don't want this thread to turn into a battle of credentials.
