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



On Wed, 15 May 2002 09:19:41 -0400, Austin Franklin wrote:
>Hi Mike,
>
>>>But, one thing that is VERY important is there is a difference between
>>>sampling sine waves and square waves.  These test patterns are
>>square waves.
>>>Though at Nyquist, you guarantee detecting the frequency, you do not
>>>guarantee full amplitude.
>>>
>>>To sample square waves, and GUARANTEE getting at least ONE "sensor"
>>>that
>>>contains full amplitude, you MUST sample at 4x f (or 2x the
>>line width, NOT
>>>line pair width)...and in the case of an image, f really
>>doesn't matter, but
>>>the thickness of the line (which would be 2f).
>>
>>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 ;-)

Austin,

The Fourier series of a square wave consists of the fundamental frequency
and odd harmonics only.  I don't understand where the '4f' comes from.  4x
sampling won't get the 'amplitude' of the square wave(test pattern) much
better than Nyquist sampling.   You pick up the third harmonic, but how
high you sample depends on the error you are willing to live with.   I'm
more familiar with signal processing than image processing, but it seems
that in this dialog there is much  confusion and information lost when
going between the spatial and frequency domains.

Jon





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