runswithsizzers,
More discussion:
The first thing to consider is that film grain is a form of noise, which in this context means that if I photograph a perfectly featureless blank wall with film, then the exact density from two points on the film cannot be perfectly predicted by knowing the exact density at any other point on the film. That uncertainty is perceived by the viewer as film grain, and it arises from the fact that an image on film is actually composed of silver grains in the emulsion. We don't actually see individual grains when we look at a “grainy” piece of film, but we perceive the image as grainy because of the uneven variation in density at different points on the film.
I used the term “points on the film” rather loosely, just to get the conceptual train of thought started. We don't actually see points on the film, but rather (roughly speaking) our visual field is divided into a series of small very regions (ultimately governed by the size of the rods and cones in our eye) that are put together by the brain to compose the picture.
The same goes for a scanner. The scanner sees the image in terms of pixels, each pixel covering a very small area of the film. A single pixel is what I am referring to as a point on the film, not in the sense of a mathematical point (which covers an infinitesimally small area) but simply as a very small area.
If we take two pixels in the scanned image the values of the pixels will vary in a statistical sense, even if the photographed scene was a perfectly blank featureless wall. A large component of this variability comes from film grain, and because the silver particles are placed in a more or less random pattern in the emulsion it is relatively unpredictable and can therefore be characterized as “noise”. I say “relatively unpredictable” because we might know the average density in a region of film, but in any two pixels there is a degree of unpredictability. That degree of unpredictability can be characterized as a standard deviation. (I am assuming that you know what “standard deviation” means. If not it will require some discussion to capture that concept.)
Now, if the standard deviation is, let us say, four units, and if the step size of the analog to digital converter is, let us say, two units, then that is sufficient to capture virtually all of the information present in the image, i.e. using a detection system with a smaller step size(e.g. one unit of step size) doesn't improve things by any noticeable degree. This is true even if gradients are present in the image.
By the way, I wrote this in terms of density, which strictly speaking is not the best way to discuss the problem because density is a logarithmic function and signal acquisition in a scanner is a linear function, but I think it is good enough to capture the basic idea.
I can go into a more extensive discussion if that would be helpful.
