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Re: [OM] resolution limits (long)

Subject: Re: [OM] resolution limits (long)
From: "Mark Hammons" <astair@xxxxxxxxxxxxx>
Date: Sun, 27 Sep 1998 09:26:52 -0500
>That's because of the way multiple systems interact.  If you have a lens
>focused perfectly on the film without vibrations or other interference,
>so you are only seeing the effects of lens aerial resolution and
>film resolution, the combined resolution on-film is approximated
>by a Gaussian error accumulation, or:
>
>1/R = 1/Rl + 1/Rf
>
>where R = resulting on-film resolution
>
>     Rl = aerial resolution of the lens
>
>     Rf = on-film resolution
>
>
>note that this is an approximation only, but is representative of what
>is going on.



I understand the basic theory but your equation is at variance (no pun with
mean, standard deviation and variance) with John Petrush's equation of:

(1/R)**2 = (1/Rl)**2 + (1/Rf)**2

John's equation gives you more "encouraging" results, as I will demonstrate
on some of your examples below:

( By the way, I swithced the ordering of Joseph's equation so that lens
resolution is listed first then film resolution -- to coincide with the ordering
in his examples).

>So, if a lens has aerial resolution of 300 lp/mm, and a film can resolve
>up to 100 lp/mm you might see a combined on-film resolution when the
>two are used together of about:
>
>R = 1/(1/300 + 1/100) = 75 lp/mm on-film


Or:
 R = 1/SQRT( (1/300)**2 + (1/100)**2) = 95 lp/mm

>
>But if the lens only resolved 200 lp/mm in its aerial image, then the
>on-film resolution would be approximately:
>
>R = 1/(1/200 + 1/100) = 67 lp/mm


Or:
  R = 1/SQRT( (1/200)**2 + (1/100)**2) = 89 lp/mm

>Keep in mind this is just a reasonable approximation and also assumes a
>perfect world of no shutter vibration, perfectly accurate focus etc.
>Of course, the real world isn't quite that friendly, and this will reduce
>the on-film resolution a bit more.  It is quite tough to get 100 lp/mm
>on film because there isn't much head room in the maximum resolution
>of the film for the other errors to accumulate in without lowering
>the numbers, hence we see 50-100 lp/mm as typical on-film resolutions.
>Most films are up in the 125-160 lp/mm range for high contrast subject
>matter, and down in the 50-80 lp/mm for low contrast subject matter,
>by the way.


Does there exist a web page somewhere that lists the resolution of
several films, BTW?

>Too see why it isn't worth the extra money normally to build a lens with
>an aerial resolution of 500 lp/mm, let's do the calculation for that assuming
>a film capable of 100 lp/mm:
>
>R = 1/(1/500 + 1/100) = 83 lp/mm.
>

Or:
   R: 1/SQRT( (1/500)**2 + (1/100)**2) = 98 lp/mm

>So, (and again this is just a back of the envelope approximation, but it
>is a good rule of thumb or guideline) going from a 300 lp/mm aerial
>resolution to 500 lp/mm aerial resolution the on-film resolution
>might only jump from 75 lp/mm to 83 lp/mm, about a 10 0ncrease
>(ie you can enlarge 10% more) but the price of the lens might go
>up 4x or more, hence would not be a very profitable venture.


Or, in the case of John's equation it goes from 95 lp/mm to 98 lp/mm.
Which is even LESS of percentage improvement but neverthless it
shows that the system resolution is BETTER in both cases than
the equation that Joseph used.

Where things would really shine is IF the film resolution is better
than 100 lp/mm.  As I stated earlier, I didn't know about typical values
of film resolution, but apparently Velvia is around 160 lp/mm.  So
lets do one brief example with Velvia, using a 50mm F1.8 Zuiko which
has say 90 lp/mm resolution and a "Super" lens that has a resolution
of 300 lp/mm:

F(50mm F1.8 Zuiko @ F1.8) = 1/SQRT ( (1/90)**2 + (1/160)**2) = 78 lp/mm  (not
bad!)

F(50mm F2.0 Super @ F2.0) = 1/SQRT ( (1/300)**2 + (1/160)**2) = 141 lp/mm
(YIKES!)

As you can see, whereas the lens was the limiting factor by a huge margin in the
first case, the film becomes the limiting factor in the second case.  It is more
dramatic
in John's equation than Joseph's because of the fact that the inverse components
are squared, which heightens the weight of the lower resolution component
with respect to the higher resolution component in the resulting answer.

I think what this boils down to is that having a lens of say 2x the resolution
of
the best film resolution would be very nice.  It would allow for the system
resolution
to be only slightly below the film's resolution ( at least at maximum aperture).
I'm not really complaining about the resolution of the various lines of lenses
but
just pointing out what is technically possible.


Mark Hammons




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