>From: AG Schnozz <agschnozz@xxxxxxxxx>
>
>Because Nyquist is not being applied
>to imaging in the same manner as it is applied to audio.
Huh? One doesn't "apply" Nyquist, any more than one "applies" Newton when an
apple bonks you in the head!
Nyquist applies, whether we like it or not, to any sampling system.
>With
>audio it was determined that you needed two samples to define a
>waveform.
No. You need two samples per cycle to re-create any periodic sine waveform.
You're confusing Nyquist with Fourier. For any complex waveform, you'll have to
sample at twice the frequency of the highest frequency sine wave component.
Fourier proved that ANY complex periodic waveform can be represented as a
series of sine and cosine waveforms. Thus, you cannot re-create a 1,000 Hz
square wave by sampling at 2,000 Hz, since a perfectly square wave contains an
infinite number of harmonic components.
>With imaging, it isn't necessary to have the 2:1 sampling to
>define an object. Each pixel stands alone in its ability to
>define a quality and quantity of light striking it.
But to sample a pattern of 100 lines per millimeter, you need to sample at 200
lines per millimeter, since you must sample both the line, and the space in
between lines. Thus, Nyquist holds true for imaging as well as for audio.
In fact, unless the lines are sine-shaped, gradually ramping up to black, then
gradually fading to white, you need much more than 200 samples per millimeter
to guarantee proper re-creation of sharp-edged lines. My rule-of-thumb is that
step responses require 10 times the Nyquist sampling rate.
There is one theoretical case: if your sampling system is phase-locked to the
sampled system, you can make certain assumptions. For example, you can
re-create a 1,000 Hz square wave by sampling at precisely 2,000 Hz. You can
re-create a sharp 100 lpmm pattern by sampling PHASE LOCKED at 200 spmm. But
this has little practical use, and in reality, if either clock is off by the
tiniest bit, you end up with heterodynes (1D signals) or Moires (2D signals).
>Anti-aliasing filters of various forms must be used...
>
>I totally disagree with the assessment that a slightly "off"
>lens yields better digital pictures.
Yet a soft lens is precisely a low-pass filter, which is what an anti-aliasing
filter is!
The idea is to keep frequencies over the Nyquist limit from producing
artifacts, which a suitably soft lens will do, but a razor-sharp lens will not.
--
: Jan Steinman -- nature Transography(TM): <http://www.Bytesmiths.com>
: Bytesmiths -- artists' services: <http://www.Bytesmiths.com/Services>
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