[Leica] diffraction limited lens: the theory

[Erwin Puts <imxputs@knoware.nl>]

>Uh , I was under the impression that all lenses are diffraction
>limited.   A matter of physics as I remember. The reason many
>manufacturers don't include f/22 or f/32 apertures on their lenses is
>the quality level suffers too much from diffraction at those apertures.
> When you read lens tests they will often tell you that a lens reaches
>it's optimum at 5.6 or f 8.  I've always been under the impression the
>reason the lens did not improve after that point was that it was
>limited by diffraction.

First some theory. The phenomenon of diffraction: if a wave encounters a
barrier that has an opening of dimensions similar to the wavelength, then
the wave will flare out into the region behind the barrier. The first thing
to notice here is the fact that the diffraction is wavelength-dependent.
The diffraction for red is different from green or blue. The second thing
to notice is that we talk about openings of a diameter similar to the
wavelength itself. F/22 is a huge hole in the universe when compared to the
"length" of a wave.
When diffraction is applied to some real world phenomena as taking pictures
of point-light sources (like distant stars) we note that such a point is
represented as a circular disk with a series of rings of diminishing light
intensity. When we examine distant point objects whose angular separation
is small we will note that the diffraction patterns overlap to such an
extent that we do not seen two objects but only one. We then need Rayleighs
criterion to estabish the minimum separation betwen the two objects to be
resolvable. Smaller diffraction patterns are possible when using a lens
with a large diameter and/or light of shorter wavelenghts.
The diffraction equation than only gives a solution for the minimum
distance between two objects to be seen as two separate objects.It is a
measure for the theoretical maximum resolution of a lens.
An example: a 50mm lens focused at infinity and with a diaphragm of 2.8 can
resolve points with a diameter of 4/1000 of a mm. In resolution
terminology:250 lines/mm or more scientific 125 linepairs/mm (cycles/mm).
In a diffraction limited lens further stopping down will naturally decrease
the resolution figure , but the degradation is *only* the result of the
diffraction effect. In a normal lens the degradation will be much more as
the impact of some optical aberrations will increase when stopped down. On
the other hand some other optical effects decrease when stopped down, but
unfortunately these effects are less important.
So generally the effective resolution is lower than the theoretical
resolution because the effects of optical aberrations are more destructive
than the diffraction effects, even at smaller apertures!!
The diffraction effect is lower when the aperture is wide (2,0 or larger).
So if we have a lens with very high corrections at full aperture (like the
2,0/180) and we can reduce the negative effects of these optical
aberrations that increase when stopped down, then the only limiting factor
on resolution is the diffraction effect.
A diffraction limited lens then is a lens that is as fully corrected as
nowadays possible for the 'normal' geometrical optical aberrations. Only in
this case can we state that the image degradation when stopping down  can
only be attributed to diffraction effects.
We must note however that resolution is the least interesting aspect of a
lens' behaviour, micro contrast at the 20lp/mm limit is much more important.
As a general rule it is indeed true that highly corrected lenses (with
apertures of 2,0 or larger) are at their optimum at 4 or at most 5.6.
Lesser lenses (or with lower maximum apertures) sometimes need 8 or 11 to
balance the several kinds of aberrations.
Erwin