Lens Testing, Round 1
Part 6. The Sonnar Mystery
Why was the resolution of the Sonnar better wide open? As we have said, the possibilities are either camera movement of some sort (either from the shutter, the tripod, or the external conditions), or focus shift.
Camera movement is rarely uniform in all directions, and it will usually show some directional blur, as we saw on the previous page. So, let's compare the center target wide open and stopped down:
Sonnar, f/2.8 at 1/125, Center Target
Sonnar, f/8 at 1/15, Center Target
As we can see from comparing these two images, the contrast improved markedly when the lens is stopped down. This will usually make the lens seem sharper in practice, though the resolving power might not be as good. Though you can't see it on your screen, resolution is only very slightly better than wide open.
Now, let's look at the edges.
Sonnar, f/2.8 at 1/125, Edge Target
Sonnar, f/8 at 1/15, Edge Target
In the edge target, we see an interesting effect. Wide open, the lens clearly resolves the lines in Group 3. Stopped down, what is this color fringing? With blue edges on the left of each line and red edges on the right, we are seeing significant chromatic aberration. More chromatic aberration at f/8 and at f/2.8? Huh? This surely cannot be either camera movement or focus shift.
Tom Magchielse, resident optics expert on the Kiev Report, responded to earlier reports of these results, before I re-evaluated the results with a microscope:
Perhaps the Sonnar does not present such a mystery after all. Let's consider the formation of an image by the various rays through the lens. The rays coming through the center, the central rays, come together at a common focus not far from the paraxial focus point.The rays coming through a zone at around 70% of the radius of the lens, the zonal rays, have a common focus point closer to the lens. The marginal rays, passing through the edge of the lens, have a focus point that may be either closer to the lens than the paraxial focus (the lens is undercorrected for sperical aberration), may be at the paraxial focus point (the lens is corrected) or may be further away than the paraxial focus (the lens is overcorrected).
The distance between these focus points and the true paraxial focus is the longitudinal spherical aberration. If the lens openings are so large that diffraction plays no role for the image quality, the lenses are often designed to have undercorrected spherical. The best focus point wide open is then closer to the lens than the paraxial focus. The zonal rays produce a blurred image that mainly causes a loss of contrast because they focus much closer to the lens, the central and marginal rays together produce a sharp image. The edges are less sharp, because the field is curved inward. By stopping down you cut off the marginal and most of the zonal rays. Cutting off the zonal rays will restore the contrast, and produce a focus shift outward, towards the paraxial focus point. This leads to a lower resolution (the lens is now out of focus) and a higher contrast in the centre of the field. The outward focus shift causes the edges that were curved inwards, to slip into focus. The edges become sharp, including the usual chromatic errors, that are now clearly depicted. That more or less explains the behaviour of the Sonnar and at the same time illustrates the behaviour of a well balanced lens design.By the way, the "bokeh" of a lens with undercorrected spherical is not supposed to be very nice.
As regards the Sonnar, the results you reported are quite good. Stopping down the center seems sharper because of the better contrast, while the edges seem sharper because in fact they are sharper. The only thing to complain about is chromatism in the edge. We must remember that the Sonnar was designed in 1936 for the Berlin olympics, and is in fact not a telephoto lens but a classical Sonnar like the Jupiter 8. In this design the back principal surface can be shifted so far forward that it behaves like a telephoto. The lens formula is that of the Jupiter 8, exept that the last element is not a cemented doublet with a Merte surface to correct chromatism, but a single positive element.
In pondering these concepts, I decided to extend the test for this lens to other apertures. The results are shown below:
|Aperture||Center Resolution (lines/mm)||Edge Resolution|
Tom suggests that if center contrast improves but resolution degrades, it is the results of the aperture cutting off undercorrected zonal rays. He suggests that the smaller aperture cause a slight shift in focus at the edges, that bring the chromatic aberration into sharp focus. The notion is that wide open, the chromatic aberration is masked by other effects, such as spherical aberration. Even though his diagnosis may need revision based on these new data, the notion that chromatic aberration is revealed at smaller apertures probably still holds.
But the more important of his conclusions is the concept of balance. He suggests that by creating effects that cover each other, one can design a lens that performs consistently throughout the range. If this were a musical instrument, it would be said to have good scale. The Sonnar performs remarkably consistently throughout the range of apertures, and this makes reasonable sense from a design perspective. Why design a fast telephoto to be outstanding at f/8 or f/11 if it is unusable wide open? The whole point of such a lens is to provide good performance at f/2.8. Otherwise, why create a lens of such bulk?
In the final page, we will wrap it up with a discussion of vignetting and some concluding remarks.