24x30 From a 4x5 Scanned On A 4870?

[Leonard Evens]

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".

[Frank Muscroft]

Leonard,

Sorry for misspelling your surname. Getting back to the topic, I must have explained poorly. Firstly, using the shape of the pixel to arrive at a reolution is purely intuitive on my part. To my knowledge CCD sensor specifications are usually given as X by Y pixels and consequently when calculating the number of pixels per mm the result is the number of pixels per mm in the direction of the major or minor axis. Photographs are made up of diagonal lines as well as horizontal and vertical lines and along the direction of the pixel diagonal the dimension of a square pixel is greater than the horizontal or vertical direction by 1.414.., therefore in this direction there are 1.414.. less pixels per mm and the reolution number is therefore effected by a factor of 1.414.... Even if the pixels are not square, there will still be less pixels per mm in the diagonal direction than in the horizontal or vertical direction. Thus, the resolution of example reduces to 48.5 lp/mm in the diagonal direction from 63 lp/mm in the horizontal or vertical direction.

My reference to the Nyquist limit was confusing, the reference to using 10 pixels to resolve 7 lines is actually in reference to aliasing at frequencies above the Nyquist limit. An explanation of this is given in the Schneider white paper "Optics for Digital Photograpy" available on the Schneider web site http://www.schneideroptics.com/info/white_papers/optics_for_digital_photography.pdf .

[byard pidgeon]

A basic rule for scanning to large format printers is: one pixel in the file for each pixel in the output. You can sometimes get away with less, you can use more, but I've seen surprisingly "photographic" results, even on lower resolution older printers, using this rule. Printer manufacturers, like scanner makers, tend to blatantly lie (oh, alright...exaggerate) the resolution capabilities of their devices, because that's what the market is attuned to. The optimum printing resolution is usually a fraction of the advertised resolution...like maybe a fifth or sixth...but as far as I know, only a few large format printer manufacturers will tell you what it is.