I have a similar setup to yours (microscopic examination of the aerial
image). However, you are making a BIG mistake if you assume that the fact
you can see, say 450 lp/mm with an f4 lens, means that it is diffraction
limited. All it means is that the MTF at 450 lp/mm is greater than zero.
It says nothing at all about the MTF at 100, 200, 300 or 400 lp/mm.
In fact the MTF at some lower spatial frequency could be ZERO, or
even negative (phase reversal). You can get lenses with fairly
severe amounts of spherical aberration and even defocusing, and
STILL get the same MTF near the spatial frequency limit as a perfect
lens. However the MTF at lower frequencies can be very poor indeed,
though still greater than zero everywhere.

The effect of aberrations on lens MTF (which equates to resolution
on film) is absolutely non-intuitive, i.e. you have to calculate
it. It is rarely, if ever, simply an overall drop in MTF and
a proportional drop in ultimate resolution. Things just don't
work that way in wave optics.

A diffraction limited lens has the maximum theoretical MTF value at
ALL spatial frequencies. You cannot measure that with visual examination
of the aerial image by eye. You can get a good idea, if you have enough
experience though. Ultimate resolution numbers (450 lp/mm for an f4 lens)
are NOT a good test of anything, other than ultimate resolution.
Ultimate resolution says nothing about the performance of the lens
photographically and nothing about whether it is "diffraction limited".
I have myself seen lenses that would resolve right out to the diffraction
limit, yet which were quite average in performance on film, due to
low MTF at frequencies *below* the thoretical diffraction limit.

One example I could give would be to take a perfect lens and measure
the ultimate resolution, say 450 lp/mm for an f4 lens. Then put a
stop (obstruction), 1/2 the diameter of the front element, in the
center of the front element. You should still see 450 lp/mm. In fact
the MTF at around 400 lp/mm will go *UP*. However, at lower spatial
frequences there will be a huge drop in MTF, and the photographic
performance of the lens will be poor. You can do the same thing by
taking a lens and adding, say, 1/2 wave of spherical aberration.
The only difference in this case will be that nowhere will the MTF
go up. It will stay the same at the high limit, but drop everywhere
else.

Hope this clears up any confusion. I think it illustrates that you can
mislead yourself if you don't look closely at all the factors involved
in evaluating lenses.


Bob Atkins
AT&T BEll Labs, Murray Hill, NJ Email: rma@clockwise.att.com
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