[Leica] Lens Formulas and Depth of Field (35mm Summicron formulas)

[Erwin Puts <imxputs@knoware.nl>]

Hello Jeff,
You stated:

"Now, I've always heard that depth-of-field is a function of focal
"length, distance and aperture -- optical formula isn't supposed to enter
"into it -- and while at some level this has to be just a convenient
"approximation, since there are optical formulas which are demonstrably
"more sharp than others, what I've seen seems more dramatic than I'd
"expect given the widespread acceptance of the depth-of-field `rules'.
"BUT: there's a potential explanation.  I also noticed that the
"diaphragm-shaped highlights produced by specular reflections in
"out-of-focus areas seemed larger in diameter at the same nominal f-stop
"with the ASPH than with the pre-ASPH.  If the ASPH formula happened to
"transmit light less efficiently than the pre-ASPH, and if the marked
"`f-stops' of the lenses were calibrated to transmittance rather than
"physical aperture size (this would, after all, be the choice with the
"most utility given that people will wish to use external light meters
"and non-TTL flashes and such), then the two lenses could have different
"physical apertures at identical marked apertures, and would have the
"depth-of-field characteristics appropriate to their respective physical
"apertures.

As you correctly note: it are convenient 'rules'. Indeed the optical
formula enters into the overall equation, but that is a difficult matter. I
have to remark that the path of the light rays through the ASPH is totally
different from the ones in  the non-ASPH version. The optical correction is
also quite different.
Your explanation is quite ingenious, and almost correct.  The real diameter
of the physical aperture can change between two lenses of identical focal
length. But the amount of light passing through the lens is the same. The
differences in diameter then are not caused by more or less inefficient
transmission. It is the relative position of the aperture within the
lenssystem that causes the differences in the physical diameter.
But they behave as identical apertures. The sharpness difference you note
has a different explanation. For a point A on the filmplane to be sharper
than  a point B the size of the light patch must be smaller. To be smaller
the rays must converge more sharply. But that also means that for more
distant object points behind the ones that are sharply focused the rays
will meet in front of the image plane at a sharper angle and will then
produce a disc of light in the image plane that is wider than in the  less
sharp case. It is difficult to imagine. I will try a picture next time. But
the bigger shape of the unsharpness blur (or patch of light in the image
plane) in the case of the ASPH gives the more pronounced unsharpness idea.
It is a matter of the greater sharpness of the in focus object points of
the ASPH.
Erwin