[Leica] Diffraction and all that

[imx <imxputs@knoware.nl>]

There is some confusion when discussing diffraction and the optimum aperture
of a lens. Diffraction is a physical phenomenon, that bends light rays at
small openings, when geometrical optics would like to have straight lines.
Diffraction limits the maximum resolution. An image point is never a true
point, but a patch of light with a certain intensity distribution. For an
aberration free system, the distribution pattern is a small central disc of
high intensity and a series of annular rings of ever diminishing intensity
(or amplitude). As diffraction is related to the diameter of the aperture,
it is best to use a wide aperture when you wish to have the highest possible
resolution. 
A lens that is described as diffraction limited, has a very high level of
optical correction such that the normal aberrations are reduced to such a
small level that the size of the spot approaches the theoretically
calculated (predicted) size and resolution is at its best. The notion of a
diffraction limited lens applies always to the maximum aperture of course.
In most photographic lenses, the geometrical aberrations are quite lage
(relatively speaking). These optical aberrations generate a "point" that is
much larger than the one you get when only diffraction is effective, and
optical aberrations become less effective when stopping down. When you stop
down, you reduce the effect of the optical aberrations (get a smaller patch
of light with a more even illumination distribution), but the effects of
diffraction (due to the small opening) increase. if the lens is moderately
well corrected, the size of the patch is so large, that the effects of
diffraction due to a small aparture will not be detected. Older Leica lenses
can be stopped down to 8 or 11 and you will see at every smaller aperture a
better image quality, "better' that is related to the maximum aperture. More
recent leica lenses have a higher level of abertion correction and now the
size of the spot at medium apertures (like 5.6) is so small, that
diffraction effects will be detected (loss of resolution, loss of contrast).
Most recent leica lenses, specifically the apochromatically corrected ones,
like the R-2/180, and 4/280 are at full aperture already corrected so well
that they approach the theoretical limit, when stopping down a bit and so
may be described as diffraction limited at 5.6, (that is: geometrical
aberrations are reduced the a very small level). With such a lens, stopping
down always degrades the image because of diffraction effects.
So we have three categories of lenses: moderately well corrected lenses,
that only show diffraction effects at the smallest apertures. Well corrected
lenses that show diffraction effects at medium to small apertures (5.6 and
smaller). Such a lens is not to be described as diffraction limited at 5.6
or smaller. At these apertures the lens is not even close to the maximum
(theoretical) resolution, required for the diffraction limit.
True diffraction limited lenses, that show diffraction effects when stopping
down a bit already. Here the resolution is close to the diffraction limited
case. 
To give an example. The R-2/180 at 5.6 resolves 540 lines/mm (270 lp/mm) and
is diffraction limited as the theoretial resolution is close to this value.
The Summicron 2/35 at 5.6 resolves around 100 lp/mm and so is not even
remotely close to the theoretical value and cannot be described as
diffraction limited at 5.6. (but the diffraction effects are visible in a
lower contrast). So do not confuse diffraction limited at 5.6. with the fact
that diffraction effects are visible at 5.6.

Erwin