That is Kingslake's classification, he is being very
rigorous. In his book on lens history he definitely
separates perfectly symmetrical lenses from those having
similar construction but different powers in each half. For
instance, he calles the original Planar a symmetrical lens
but the Opic a non-symmetrical one. The curious thing is
that he includes the Schneider Angulon in his discussion of
symmetrical lenses even though it has a similar shift of
power from one side to the other.
I think this overlooks the way symmetry works in a lens.
The idea is that the three lateral aberrations in each half
have similar values but opposite signs and will cancel, at
least to some degree. In a completely unsymmetrical lens,
like the Tessar, this doesn't happen because the two sides
of the stop have completely different properties. The front
(as normally made) has an overall negative power and the
back positive power. In fact, the Tessar uses the front
section to correct the aberrations of the back, the front,
of course, being a negative lens, will not form an image.
The back will form a highly aberrated image.
Lenses of the symmetrical or partially symmetrical type
have aberrations and powers distributed in both halves and
both halves will form images by themselves.
The 5 element Planar or Xenotar looks at first sight as
though it has no symmetry. In fact, it has quite a lot. The
approach to this design was to eliminate one element of a
Planar type by combining the powers of two of the elements
into one. In the Planar, and its decendants, the cemented
surfaces in the negative elements are used to correct
chromatic aberration. Where a wider choice of glass is
available its possible to correct the chromatic by means of
the positive and negative elements in the half lens. So, in
the Xenar one has a front positive element, a negative
component composed of two cemented elements, and, in back of
the stop, a negative element consisting of a single lens,
and a positive element consisting of a single lens. The
arrangement in the 5 element Planar is a little different
because it is the front component that has the cemented
surface, but the overall arrangement is the same i.e., four
components arranged as +,-, stop, -, +. Again, both halves
are positive in overall power and will form real images. The
distribution of power and aberrations is such as to obtain a
significant amount of cancellation of the lateral
aberrations. This cancellation is one reason this type
performs better at large apertures than the Tessar. In
addition, the Planar either five or six element, has much
less oblique spherical aberration that the Tessar. Since
this aberration, like coma, is dependant on image height, as
well as the aperture, having some means of correcting it
allows the use of larger apertures and and allows a larger
image field for a given aperture.
The three Wynne patents Kingslake cites for the 5 element
lens are worth reading.
USP 2,499,264 2,487,749 2.487,750
Also, see if you can find one of Kingslake's books on lens
design, he wrote a couple and goes into this more
completely. Another good book on lens design that is
reasonably understandable is _Modern Lens Design_ Warren J.
Smith. This has run to a second edition. If you are rich get
the second, otherwise the first edition is just fine. Smith
was one of the developers of the lens design program now
known as Oslo, and, like Kingslake, is a particularly lucid
writer.
---
Richard Knoppow
Los Angeles, CA, USA
dickburk@xxxxxxxxxxxxx
---
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