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[filmscanners] Re: Film resolution - was: Re: 3 year wait



Austin Franklin wrote:
>
> Hi Mike,
> > When sampling a square wave at the nyquist frequency, the square wave can
> > be perfectly reconstructed from the resulting samples.
>
> As I've pointed out, at Nyquist, when the line is not entirely "seen" by ONE
> sensors, two sensors will only see a reduced part of the line, and therefore
> the detected amplitude of the line will be decreased.  That is NOT
> "perfectly reconstructed", as you say, since you are not reconstructing the
> amplitude accurately.  The ONLY way to guarantee acquiring full amplitude is
> for the sensor spacing to be at least 4f, which guarantees that a line of
> width f will be fully detected by at least one sensor.
>
> Try drawing this out on paper, or do something to visualize it...or heck,
> design a scanner ;-)

Sorry, but what you say isn't true.  As I've mentioned numerous times
(and hopefully this time will be the last), for black and white
stripes, the Nyquist rate is twice infinity -- so to scan at the
Nyquist rate in your example, the spacing between samples is
half of zero distance apart.  When the samples are half of zero
distance apart, it WILL sample correctly.

Mike K.

P.S. - Go get a book on Nyquist and go through the mathematical
       derivations.  I've done so (long time ago) and it all works
       out so long as you apply it correctly.  THE NYQUIST RATE THAT
       ALL BUT MYSELF AND ONE OTHER PERSON USE IS *NOT* THE NYQUIST RATE,
       IT'S WAY BELOW THE NYQUIST RATE WHICH IS WHY IT DOESN'T WORK. The
       Nyquist rate is twice the "repetition" rate (as it is being
       mis-applied) ONLY if the repetition is sinusoidal (or co-sinusoidal :-).
       NOT if there is the least bit of contrast-edge (and in this case,
       sinusoidal in both the vertical and horizontal directions).  One has
       to break down the signal into the frequency domain then take
       twice the highest frequency component -- and for abrupt black white
       edges it is *infinite* frequency (in practice there can't be such a
       perfect edge, when looking at the molecular level, it won't be
       so stark, so the real highest frequency will be lower, but still
       REAL high).

P.P.S. - What I've been doing for the last month is "Signal Integrity
         Analysis" for a design of mine that's now being converted into
         circuit boards by our circuit board dept. I'm analyzing those very 
kind of
         edges where my "black and white" (equivalent) transitions are
         signals that switch state in a few hundred pico-seconds -- and I'm
         trying to make sure they'll do so reliably -- so when my circuit board
         is made it'll work reliably. Even a signal that goes "black and
         white" once a second still has frequency components in the multi
         Giga-hertz range when that once per second change occurs.  So
         in a vague way, "been there, done that", I'm reporting to you
         what happens.  For those who know what I'm talking about, I'm
         using Mentor Graphic's ICX program.

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