[Leica] Nyquist again (was scanning)

[Johnny Deadman <john@pinkheadedbug.com>]

on 7/25/01 3:46 PM, Mxsmanic at mxsmanic@hotmail.com wrote:

[to Austin]

> Your posts consist almost exclusively of personal attacks; mine consist of
> information and discussion relating to the topic at hand.  I'll leave the
> evaluation of the relative utilities of our posts as an exercise for the
> reader.

the original dispute was about this I think:

Austin insists:

>>> Which means you need a scanner of 5400 SPI
>>> to reliably detect your 53 lp/mm...

Mxsmanic drones: 
>> 
>> Nope.  53 lp/mm times two = 106 lp/mm, or 2692 dpi.

This is all about Nyquist frequency in the end. The Nyquist frequency is the
bandwidth of a sampled signal, and is equal to half the sampling frequency
of that signal. In the case of a signal consisting of a continuous range of
frequencies, the Nyquist frequency is the highest frequency that the sampled
signal can unambiguously represent.

In the case you guys are locking horns about, you require the sampled signal
to unambiuously represent a frequency of 53 lp/mm. We refer to line pairs
rather than lines because a black line needs another white line beside it to
qualify as a line. So one 'cycle' is a black line followed by a white line.

The Nyquist criterion says that we need to sample this at 106 lp/mm, or 2692
dpi.

However all this tells you is that a sampling frequency of 2692 dpi is
sufficient to *represent* 53 lp/mm. However, it does NOT guarantee to
reliably *detect* the 53 lp/mm in all cases. This is where the confusion in
this case arises.

In the case in question, as Austin points out, it is perfectly possible to
position the sensors so you get a uniform gray. Therefore you need to
oversample considerably in order to guarantee any kind of *resolution* of
those lines. But it is not as simple as just doubling up: any increase in
sampling frequency over the Nyquist threshold will increase the resolution.

In order to prevent aliasing (whereby a, say, 106 lp/mm grid shows up as a
53 lp/mm grid because the sampling frequency is too low) you would normally
put a low-pass filter before the sensor, to cut off all frequencies above
the Nyquist frequency. Scanners of course, don't do this (though as Jim
points out, digital cameras *do*). Some people argue that the result is
'grain aliasing', where film shows up looking a lot grainier on a scan than
it does in real life (tm).

hth



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John Brownlow

http://www.pinkheadedbug.com

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