At 13:34 7/20/01, Paul Wallich wrote:
At 12:34 AM -0500 7/20/01, Mark Hammons wrote:
Diffraction limiting from small apertures seems to kick in sooner and with
greater prominence with the shorter focal lengths than with the longer ones.
-- John
Actually, I believe it is strictly a function of the F-ratio.
Assume you have a 50mm Lens at F50. You have a 1mm aperture
hole and the L/A angle is whatever milliradians and the light has to
travel 50mm to the film so you have the spot size as (2*L/A*50)mm =
(100*L/A)mm.
If you now go to a 100mm lens at F50 your aperture is now 2mm.
Call this A'. Well A' = 2A (the aperture size of the 50mm lens at F50).
And the total spot size is (2*L/A'*100)mm = (200*L/A')mm =
(200*L/2A)mm = (100*L/A)mm, which is the same spot size on the
film as the 50mm F50 lens.
So the smaller angle of diffraction by going to a longer focal LENGTH
lens of the same focal RATIO is exactly offset by the longer DISTANCE
the light has to travel to the film plane. Thus, the spot size is a function
of the focal ratio.
I had been wondering about this for a while, because while it seems
sensible it also doesn't always seem to be the case. My guess is that
you get some kind complicated effect as a result of the fact that the
physical distance between film and diaphragm isn't the same as the focal
length. In particular, most short lenses are retrofocus designs (to clear
the mirror) and most long lenses are telephoto (to reduce total length
and weight).
Obviously all of the glass involved makes the problem more complicated
than just the physical position of the aperture, but it seems to me from
a first cut at the problem that the back elements wouldn't/couldn't/shouldn't
(if they're acting properly on light coming through at larger apertures)
completely compensate for the difference between physical aperture placement
and focal length.
paul wishing for that old copy of mathematica
--
Paul Wallich pw@xxxxxxxxx
My thinking was about short and long compound lenses wherein the ratio of
entrance and exit pupils are not equal to one. In this respect I'm very
rusty about exactly what should happen theoretically. Many simpler
equations for understanding principles about practical compound lenses
assume the ratio of the entrance and exit pupil is one. This is the
apparent diameter of the aperture as viewed from outside the lens from
front and rear. Not true in many practical camera lenses. Take a 24mm or
shorter SLR lens and stop it down to about f/11 and then compare what the
diameter looks like from front and rear. Now take a 135mm or longer SLR
lens and do the same thing. With most SLR lenses you will see different
apparent diameters of the aperture from the front and rear.
Obviously, when diffraction limiting kicks in *is* confounded by specific
lens design as witnessed by remarks made by Gary Reese about observing it
with his lens tests over normal aperture ranges, at least as a "second
order" effect. Stop any lens down far enough and you _will_ hit
diffraction limiting.
-- John
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