Make Any Lens Using Only The Cheapest Crown and Flint Glasses!
John Savard
professional optical designers.
I am not talking about the idea used by Paul Rudolph in designing the
Planar lens (patent 583,336), where he used a crown glass and a flint
glass having the same index of refraction. It is true that today, from
places that sell optical glass, an optical grade of the most popular
barium crown is actually cheaper than plain window glass made to optical
glass tolerances, and thus making a lens from BaK 4 and LF 5 would come
close to using the cheapest glasses available.
No, what I speak of is applicable even to cases such as where one is
trying to make an all-plastic lens, and hence one only has acrylic for
crown and polycarbonate for flint; thus, the case in glass is the one
where one can only make an 'old-achromat' lens, using, say, K5 (or BK7)
and F2.
How can one make 'any' lens using those two glasses?
Everyone knows that, to make a Cooke triplet (patent 568,052) you have
to start with a high-index crown, whether like BaK 4 or, better yet, a
crown using lanthanum, and then choose just the right flint on the old
glass line (the old glass line is the traditional curve of plain crowns
and flints, as compared to the glass line, which is a straight line on
the curve of partial dispersion against dispersion) so that the relative
sizes of the positive and negative elements are required to correct the
monochromatic Seidel aberrations!
Ah, yes. But let us look at H. Dennis Taylor's _earlier_ patent on a
more primitive form of the Cooke triplet, U.S. patent 540,122.
If one allows oneself to have six elements in three cemented groups,
rather than just three elements, then one can have an old-achromat
positive lens, followed by an old-achromat negative lens, and then an
old-achromat positive lens - and the ratios of the powers of the three
groups, positive, negative, and positive can be anything you like.
Of course, this makes the elements thicker, and the surface between the
crown and the flint adds aberrations.
This applies to my notion of a plastic apochromat in this way: let us
say I wish to take a lens, consisting of two positive old-achromat glass
lenses with an achromatic acrylic and polycarbonate lens between them,
with powers chosen so as to eliminate secondary color - and then, I want
to modify the power of the negative element relative to the positive
elements so as to make an aplanatic triplet out of the thing.
I can do that by accompanying the central plastic element with either a
flint glass element, filching negative power from the two glass
elements, or a crown glass element, filching positive power from the two
glass elements.
(And, it might be noted, if mounting the lenses on contrivances of iron
and brass rods to make the spacings compensate for changes in focal
length with temperature, giving only a linear correction, does not work
over a broad enough temperature range, I can mount the three groups as
though I were making a mechanically compensated zoom lens - and turn the
thing with a bimetallic spiral, just like in a dial thermometer! Of
course, when laying out the curve, I must not forget that the sleeve
itself expands and contracts with heat and cold...)
Thus, while the result will be thicker, and the f/ratio probably not as
great, if one wished to make all of the elements achromatic, one *could*
actually make a fancy Double-Gauss lens entirely from acrylic and
polycarbonate, or entirely from K5 and F2. For example.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
John Savard
(John Savard) wrote, in part:
>This applies to my notion of a plastic apochromat in this way: let us
>say I wish to take a lens, consisting of two positive old-achromat glass
>lenses with an achromatic acrylic and polycarbonate lens between them,
>with powers chosen so as to eliminate secondary color - and then, I want
>to modify the power of the negative element relative to the positive
>elements so as to make an aplanatic triplet out of the thing.
>
>I can do that by accompanying the central plastic element with either a
>flint glass element, filching negative power from the two glass
>elements, or a crown glass element, filching positive power from the two
>glass elements.
And _this_ technique, not making all the elements 'achromatic', but just
adding one cemented element, was noted in the second, "real", triplet
patent as well; absent suitable crown and flint glasses, instead of
making all three elements achromats, simply add a crown element to the
middle flint one.
Since secondary color is the goal here, though, I start with achromats
in all three positions to make things simple.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html