To the best of my recollection the problem with small apertures is the
changing ratio of the circumference of the aperture vs. the area of the
aperture.
I will clarify by noting that the circumference of the aperture is
formed by the diaphragm blades. The diaphragem blades are edges and
whenever a light beam passes nearby an edge it is diffracted. That is,
it is bent away from its intended course and the diffraction contributes
to loss of sharpness and lowered contrast.
The glass area defined by the aperture, however, is a clear area with no
edges. Light passing through here should hit the lens designer's
intended target (more or less). If we have a very large clear aperture
area relative to the linear length of the edges the edges will
contribute relatively less to the image formation. The clear aperture
area will prevail by providing an overwhelming number of properly
obedient light rays.
The problem is that, as the size of the aperture decreases, the ratio of
the circumference of the aperture to the area of the aperture increases.
For example, lets take a 50mm lens at f/8 and f/16. At f/8 the diameter
of the aperture is 6.25 mm and the circumference is 19.64 mm. The area
of the aperture is 30.68 square mm. and the value of the area is 1.56
times larger than the circumference. At f/16 the diameter of the
aperture is 3.125 mm and the circumference is 9.82 mm. The area of the
aperture is 7.67 square mm. But now the value of the area is only 0.78
times the circumference.
In short, the smaller the aperture, the larger the relative size of the
diffracting edge of the circumfenence to the unobstructed glass area.
As the relative amount of diffraction continues to increase so does the
quality of the image deteriorate. This is why we see 50mm lenses
generally giving up on small apertures at about f/16 and shorter focal
length lenses at even larger focal ratios.
Chuck Norcutt
om2@xxxxxxxxxxxxxxxx wrote:
> In fact, many high performance designs start to degrade even at f/8, which
> is usually the sweet spot for most lenses. I speak particularly of Leica
> lenses, which are usually best between f/4 and f/8.
>
> Also, in general the longer the focal length, the smaller the minimum
> aperture can be. Is that because of the more telecentric light rays?
> Anyone? This is evidenced by Large Format lenses for 4x5, which routinely
> go to f/45, and 8x10 or 11x14 lenses, which can go to f/128.
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