I've done a little more experimentation. I scanned a Tmax 100 negative and selected 8 bit gray scale for the storage mode. The scanner was a canon fs4000us in 4000 dpi mode. The image was the leader part of the film, including exposed and unexposed parts of the leader. It's very dusty because there's not much point in protecting a leader from dust, but this fact is irrelevant to the demo. Here's what the scanned slide looks like. It shows the crop window that I used for subsequent operations.
All of the following images are from the cropped area. The first image below shows the cropped rectangle with no operations performed on the scan.
In the image above I'm showing a histogram adjustment window, but no adjustments have been made, as indicated in the percentage boxes. Note that there is a very subtle gradient in the image.
I then did the following adjustments in 8 bit mode using photoline software. First I did a 5 pixel Gaussian blur, followed by a histogram using the limits of 31% to 41% for the histogram, as seen in the histogram window. This workflow was intended to show that banding can occur if an image is scanned in 8 bit mode followed by the wrong workflow. As you can see, this workflow did produce a lot of banding.
Then I did a slightly different workflow. For this one I started with the same cropped 8 bit image, but this time I first did a conversion to 16 bits. Then I smoothed with a 5 pixel radius followed by a 31% to 41% histogram. This is exactly what I did in the other workflow except that I started by converting the 8 bit image to 16 bits. As you can see, there is pixelation because it's a small crop window, but there is no banding. The gradients are nice and smooth.
I think this pretty convincingly shows that the workflow I proposed worked like a charm to eliminate banding, even though the scan was only 8 bits. It also demonstrates the risk of using the wrong workflow.
I did some other things with this, but to avoid posting too many images I'm just going to describe the results. First, small crops of both the unexposed and exposed portions of the leader had distributions that were several bits wide. This is the condition that assures that banding does not occur.
Second, If I zoom in on a histogram to look at the distribution the histogram looks the same, regardless of whether it was an 8 bit histogram or a converted 16 bit histogram. There are the same number of peaks and they have the same magnitude relationships. Note, the peaks are one bit wide in either case. However, the peaks in the 16 bit converted image, while still one bit wide, are separated by runs of bits containing zeros. This is as it should be from theoretical considerations.
Third, I used Tmax 100 film for this because it is the finest grained film that I have available, and fine grain provides the most severe test of what I am claiming.
Fourth, I did this test on a negative with the most extreme regions because it provides the most severe test, and in particular it shows that gamma encoding of the saved image did not invalidate the concept. Gamma encoding is going to be most likely to over-ride my assertions in one of the density extremes. It doesn't really matter which one because I tested both extremes.
Fifth, It is highly unlikely that intermediate densities is going to give a different result.
Sixth, I also looked at histograms of crops from the film holder of the scanner, which showed up in the scans because I set the scan window large enough to include the frame of the film holder. These crops should be perfectly black, but they were not, and they also showed distributions that were several bits wide. I don't have a definitive explanation for this, but it is probably some combination of scattered light inside of the scanner, ambient light leaking into the scanner, and electronic noise in the scanner. It is worth mentioning that one of the advantages that some users have seen when comparing the Canon scanner to a Nikon scanner is slightly more noise in the high density part of a film when scanning with the Nikon. Otherwise they have basically the same scan quality, although the Canon scanner is much slower.
Seventh, scanning in 16 bit mode did not result in any improvement over scanning it 8 bit mode, provided that the correct work flow is followed. In particular, for practical purposes there was no improvement in dynamic range because dynamic range is limited by noise in the images, not the bit depth of the word used to store the results. Also, dynamic range depends on the effective size of the viewing window. In particular if the viewer's vision does not resolve the individual pixels then an effective signal averaging effect occurs such that the effective dynamic range is greater than that of the individual pixels. This is actually very well known. It's why half-tone printing works, even though at a fine level the paper is either black or white, which is effectively one bit of dynamic range at the small spatial scale.
I also did an experiment on a different piece of film leader. Part of the scan was dense film and part was just scanning air. The light part (i.e. air) showed a little bit of streakiness. This is not going to affect a film scan because even in an unexposed region the film is dense enough and grainy enough that the streaks won't be seen. I'm not sure what the origin of the streakiness is, but likely it has something to do with slight mismatches in the dark current of the sensor elements, such as different amounts of dark current.
Please, other interested users of Photrio, do some experiments and post the results. As I have already mentioned, I am prepared to have my assertion proven wrong by actual experimental results, but the experiments must follow the correct work flow. Otherwise the experiments would be testing an assertion that I did not make.