Warning long boring engineering stuff follows, no OM content.
Jan@xxxxxxxxxxxxxx writes:
<<
>>... To sample and reconstruct
>>a grating of lines (a square wave) and produce sharp high contrast
>>edges (not turn them into a lower contrast sine wave) you need a whole
>>lot more.
>I think we're comparing apples with oranges here. Correct me if I'm
>wrong, but "resolving line per millimeter" means that one can discern
l>ines, not that they have sharp edges. In that respect, the result of
>a visual test of lpmm is not unlike scanning near the Nyquist limit
> -- fuzzy things one can just discern as lines.
Jan,
In general I agree with you here except that just discerning lines
would be defined in a test criteria something like "the contrast of the black
to white has dropped to 700f its low frequency (low lpmm) value. In normal
electronics this would be analagous to something like the half power or -3dB
point. (the 70 0.000000e+00xample is an arbitrary value , I don't remember what
is
commonly used for lens tests and it may depend on the application. For
example in astro work lpmm, is not used but a similar but not identical
criterion: the ability to resolve two adjacent points (stars) with some very
low contrast between the peaks). We can continue resolving lines at a much
lower contrast out to significantly higher resolution (lpmm) than the lpmm
limit quoted in a test. This is analagous to an amplifier where the amplifier
still passes signals well beyond the -3dB point albeit at a reduced level.
Thus your point about MTFF is well taken. I tried to make this point in my
original post by saying there is a contrast criterion.
> Also, the sensor cell size performs inherent low-pass filtering of
> the result. For aliasing artifacts to be visible, the sampled area
> would have to approach a point. This is why scans can all stand a
> little careful sharpening.
The first point about low pass filtering is true but being sampled data the
filter has
rather different characteristics than a pure analog filter. It has a sinc
(sin X/X) characteristic that drops rather slowly with frequency (lpmm) with
lots of notches at frequency multiples of the pixel width. The slow cut-off
means it is a rather poor anti-aliasing filter except at the narrow notch
frequencies. I am not so sure about your second point, for aliasing to occur
the picture must just have features seperated by spacing closer than the
pixel spacing.(sample frequency). The scanner manufacturer can do things to
reduce aliasing noise by for example analog filtering the serial ccd signal
before digitizing or by defocusing the optics! This of course reduces
resolution (lpmm) to much below the Nyquist criterion. Ideally you need to
use more samples and have a good antialaising filter ahead of the digitizer
to achieve your actual desired resolution but pixels cost money and scan time.
>(BTW: my rule-of-thumb is ten times the base frequency to reproduce a
>square wave. Thus a 100 lpmm grid requires 50,800 samples per inch to
>reproduce with sharp, square edges.) >>
The 10 samples makes sense because a square wave has only odd harmonics
(1,3,5 .. etc) and most of the energy is in the first three harmonics. So to
resolve the first three harmonics requires you to sample at, at least twice
the 5 th harmonic or 10 (using the Nyquist criterion).
Another way of looking at it :To hope to reliably resolve any square edge
content *at all* requires sampling at at least 6 pixels (3 rd harmonic x2)
per lpmm desired resolution.
Jan, really not too much disagreement here.
Regards,
Tim Hughes
Hi100@xxxxxxx
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