Defining Apochromatism
by Thomas Back
Updated 6-29-03
With the proliferation of apochromatic refractors that are available to the
amateur
astronomer, it is time to define the parameters of a true apochromatic
objective lens.
The modern definition of "apochromat" is the following: An objective in which
the wave aberrations do not exceed 1/4 wave optical path difference (OPD) in
the spectral range
from C (6563A - red) to F (4861A - blue), while the g wavelength (4358A -
violet) is 1/2
wave OPD or better, has three widely spaced zero color crossings and is
corrected for
coma.
Here is a more detailed analysis for those that are interested. The term
"Apochromat" is
loosely used by many manufacturers and amateurs astronomers. Let's look at
the history
of the definition, and maybe a more modern one. Ernst Abbe, in 1875, met and
worked for
Carl Zeiss, a small microscope, magnifier and optical accessory company. They
realized
that they needed to find improved glass types, if they were going to make
progress with
the optical microscope. In 1879, Abbe met Otto Schott. Together they
introduce the first abnormal dispersion glasses under the name of Schott and Sons.
Abbe discovered that
by using optically clear, polished natural fluorite, in a microscope
objective, that
apochromatism could be achieved. These first true apochromatic microscope
objectives
were so superior to the competition, that Zeiss gained nearly the entire high
end market.
So secret was the use of fluorite, that Abbe marked an "X" on the data sheet
for the fluorite element, so as to keep it secret from the other optical
companies.
Abbe's definition of apochromatism was the following. Apochromat: an
objective corrected parfocally for three widely spaced wavelengths and corrected for
spherical aberration and
coma for two widely separated wavelengths. This definition is not as simple
as it sounds.
I have designed thousands of lenses: simple achromats, complex achromats,
semi-apos, apochromats, super-achromats, hyper-achromats, and Baker
super-apochromats. Abbe's definition, to put it in clearer terms (I hope) is that a true
apochromat is an objective that has three color crossings that are spaced far
apart in the visual spectrum (~4000A, deep violet to ~7000A, deep red). However,
just because a lens has three color crossings, doesn't mean
that it is well corrected. Let's say that a 4" lens has three color crossings
at the F, e and C wavelengths (4861A, 5461A and 6563A). Fine, this objective
is now considered an
apochromat by most amateurs and even optical designers because it has three
color
crossings in the blue, green and red -- the common definition of an
apochromat. But what
about the levels of spherical aberration at each of these wavelengths? If the
lens is 2 waves overcorrected at 4861A, and 1.5 waves undercorrected at
6563A, is it still an apochromat?
No. It is no better than an achromat, as the OPD wavefront error is worse
than a 4" f/15 achromat.
Abbe, in his definition of apochromat, states that spherical aberration must
be corrected
for two widely spaced wavelengths. Now I will tell you what happens when you
correct
spherical for two widely spaced wavelengths: you correct for all the
wavelengths between
them too. This is called correcting for spherochromatism (the variation of
spherical
aberration with a change in wavelength). Only with extremely long focal
lengths, advanced Petzval designs, aspherics, large air spaces, or a combination of
these designs/factors, can
you correct for this aberration. It is the designer that must come up with a
good compromise
of color correction, lack of spherical aberration (3rd order and zonal) and
controlling spherochromatism, so as not to degrade the image contrast.