I've read the various websites on aliasing and grain aliasing, especially
<http://www.photoscientia.co.uk/Grain.htm>, but feel that they all miss the
point, being more concerned with CCD aliasing, and not really knowing what
causes grain aliasing, despite all the fancy math
The purpose of this email is to present my theory of grain aliasing.
The question that nagged me while I was reading was simple: Given that film
grain is totally random, why would scanning (sampling at some number of pixels
per inch) cause grain to be affected more than anything else in the image?
Random is random, so the scanner pitch (number of pixels per inch) shouldn't
matter one bit. And the grain is far too fine for even the pro scanners to
resolve. Yet, it seems to matter. Why?
The key is in the assumption "totally random". While it's true that the film
grain is random, it doesn't follow that grain clumping follows the same
randomness rule. In fact, it cannot, because granularity does not look like
grain to the eye, when magnified to the same visual size.
The word "random" has a lot behind it. There are many different kinds of
random, and for each kind there is a probability distribution, such as
Gaussian, Poisson, Exponential, Geometric, etc.
Film grain is probably a Poisson process, which means that the probability of
each grain forming is independent of all other grains. (The average
probability of a grain forming will increase with increased illumination of the
film area in question, but each grain makes its own decision without consulting
its neighbors.) One consequence of this is that if one plots the probability
density (average number of developed grains per unit area) as a function of
distance from a randomly-chosen grain in the image, the plot will show a
constant. That is, the probability density does not vary with distance from
the chosen grain, and no distance is more important than any other. The
distribution is uniform with respect to position. (Unitil we get to the size
scale of the clumps.)
Film granularity (grain clumping) is most likely *not* a Poisson Process, from
the look of the sample photos one sees. I don't know the physical cause of
clumping, but the implication is that the grains in a clump do somehow talk to
one another (to form the clump), and that the clumps are not uniformly
distributed. If one plots the probability density of clumps as a function of
distance from a randomly-chosen clump in the image, the plot will show a peak
somewhere. That is, the density varies with distance, and one particular
distance (to the peak) is more important than any other. This distance is the
average distance between clumps. The distribution is non-uniform with respect
to position.
Now, we can see where the grain aliasing comes from. First of all, it's really
granularity aliasing; the grains are too small for any non-research scanner to
see. And (unlike the grain) the granularity has a built-in characteristic
distance, the average spacing between granules, and if the scanner's sampling
pitch is about the same as the average spacing between clumps, the effect of
the granularity will be greatly enhanced, and may become wierd as well.
What to do? Films designed to be scanned will have somehow abolished the
peak, so there is no characteristic average distance, or moved the
characteristic distance well away from typical scanner pitches, probably by
making the characteristic distance far smaller the the scanner pitch. If one
has existing film to be scanned, the only solution is to change the scanner
pitch (optical, not interpolated) to avoid the peak.
If my theory is correct, making the scanner optical pitch larger or smaller
will work equally well, though one's instinct is to go for finer. It will all
depend on the actual probability density versus distance function, which may
not have just one peak.
Joe Gwinn
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