In a message dated 6/16/2003 3:48:46 AM Pacific Daylight Time,
DigitalBlackandWhiteThePrint@yahoogroups.com writes:
> Yes, electronically, 100 ohms in parallel with 100 ohms does give you 50
> ohms, but electronics are not the same as optics and film. Film records the
> data just like a CCD array does, using discrete elements. If the photons
> being "measured" happen to fall right on the sensing area, it will record at
> that resolution, if it happens to straddle two sensing areas, it'll record
> half that resolution. What you will get are values from %50 gray on two
> adjacent sensing areas, to one %100 white and one %100 black (if you are
> using a test pattern that is). Of course, film grain size is random, but
> still within a rather narrow size band.
>
> It's more than a formula, it's an understanding.
>
> Austin
>
The electronic analogy was merely to point out the classic formula used to
figure out system MTF between lenses and film. The "understanding" that you
outline concerning "straddling" two sensing areas is precisely what is taken into
account with the formula.
The classic U.S. Air Force LPPMM test target contains hard edged lines on
Kodalith to represent, as best as possible 0% and 100% modulation (which would
averge out to 50 mathematically). This is not what happens in a continuous tone
image, but gives an extreme tonal contrast with which to efficiently judge an
optical system. So when we make a contact print of the test target using an
enlarger as a collimated light source onto a particular film, we remove the
influence of optics and their aberrations from the light path. This give us pure
film MTF to work with. Now if we test a lens separately in the same manner we
also isolate the performance of the lens without the influence of film
anomalies. If the best we get by looking at the arial image from the Lens under test
with high power optics is 100 LPPMM also, we need to combine the two.
The accepted formula for doing so, in all literature I have ever come across
is to invert the sum of their inverses. So, 1/100 is 0.01 for the film and
lens. If we add 0.01 + 0.01 = 0.02. Now taking the inverse of 0.02 (1/.02), we
get 50. This is the BEST possible performance we can expect with a high
contrast subject, with the lens and film working together. If either one of them is
slightly lower (usually the lens), then the system drops to less than 50 LPPMM.
If we only happen to get 60 LPPMM from the lens at a certain aperture, then
the system MTF drops to 37.5 LPPMM.
This is why, historially, larger formats have always won the sharpness
contest, as the gains are much greater by adding more Millimeters to throw the
image onto rather than trying to cram more line pairs into the same millimeters
(which solid state imagers do better than color film for a given number of
millimeters). But that is beyond the scope of this text.
Your reasoning sounds good, but it doesn't appear to be congruous with the
traditional formulas cited above.
Claude
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