Frank,

Let me explain where I got the numbers. 3200 ppi is about 126 pixels per mm. Digital sampling theory says that if you collect 126 pixels per mm, then the most you can resolve in line pairs per mm is half of that, which is what is usually called the Nyquist limit. Roughly speaking, you need two pixels for each line pair. But the digital theory is actually much more complicated, and despite several attempts, I don't claim to have mastered it yet, but I am still working on it. It invovles some advanced mathematical techniques like Fourier analysis, which fortunately, like any well trained mathematician, I do understand. But there are many other subtleties, and the texts on the subject tend to not to be models of exposition. Personally, I find that naive attempts to understand it via simple intuitive models seldom work for me until I understand the actual theory. The problem is that there are numerous ways to construct simple intutitive models, and they give different answers, so one can argue interminably about which is right. When all is said and done, you have to go to real digital theory, confirmed by observation, and done by experts. Then you can get a better understanding by an appropriate intutitive model. I don't know just how the shape of the sampling elements and the fact that it is stepped in half steps and anything else may affect the results, but I am doubtful that one can work it out by such a naive model.

As an example, one point I didn't mention is aliasing. Any complex signal can in principle be decomposed into periodic signals of different frequencies. Frequencies above the Nyquist limits are aliased to lower frequencies and create artifacts which can degrade the image. So scanners sometimes have methods to filter out frequencies higher than the Nyquist limit. The Epson scanners actually use a staggered set of sensor elements, each half the nominal scanning frequency, and this supposedly reduces aliasing. But how it might modify the "true" sampling frequency, I don't know.

I hadn't seen a Nyquist limit referring to the shape of the sensors that you refer to. Can you give me a reference?

P.S. My name is spelled "EVENS".

## Bookmarks