>From: Richard Schaetzl <Richard.Schaetzl@xxxxxxxxxxxxxxxxxxxx>
...
>A line needs at least a row of two pixel for his representation.
...
>Because it is unlikely that an (real life) grid of 42 lines/mm will be
>projected in a way it fits exactly on the CCD array you need an higher
>resolution to represent this or your usable resolution will be reduced
>further.
Well, this is not strictly false, but it isn't quite accurate, either.
>I think this is a phenomenon, a man called Shanon (sp?) has discribed
>(Shanons theorem). Acording to this theory you need at least double the
>resolution (frequency) you want to represent.
Although Shannon is considered the father of information theory, the 2x
rule is actually known as the "Nyquist Limit," after another pioneer of
information theory.
The problem with your first statement is that it makes some faulty
assumptions. Sampling orientation has nothing to do with required
resolution. Actually, to perfectly represent ANY orientation of ANY "step
function" -- in other words, alternating black and white lines with perfect
edges and maximum contrast -- would require an INFINITE number of samples!
According to theory, sampling at twice the highest line frequency will
perfectly reproduce a SINE function -- one in which the change from white
to black progresses through various shades of gray in the manner of a sine
wave. Fourier (another information theory pioneer) said that any periodic
function can be represented by an array of sine and cosine functions, and
the Nyquist Limit is where the sampling frequency limits the representation
to a single sine wave.
But let's compare digital samples to film grain. Unlike digital samples,
film grain has random shape, which tends to look more pleasing to the eye
than pixellated digital output. (This is why I recommend Genuine Fractals
for up-sampling, because like film grain, it produces random artifacts.)
But no matter how many lines per mm you can sample, if your sampling
resolution is greater than the film grain, you aren't going to improve
things by increasing the sampling frequency.
In my experience with the Nikon LS-2000, I can "sample the grain" in film
of about ASA 400 and above, therefore more samples aren't going to improve
the output of such scans one bit. In fact, because the edges are softer as
you approach the Nyquist Limit (because a step function looks more like a
sine wave), it actually looks better to sample below the grain frequency,
because it softens and blurs the grain.
Again, my "ASA 400 Rule" is a rule-of-thumb, not an absolute, and will vary
depending on film type, lighting, optical resolution, etc.
: Jan Steinman <mailto:jans@xxxxxxxxxxx>
: 19280 Rydman Court, West Linn, OR 97068-1331 USA
: +1.503.635.3229
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