WHAT ASPECT OF THE PROBLEM WAS MOST DIFFICULT?
1) There were a lot of challenges:
a) My final design was an apochromatic design using 47
surfaces, 3 wavelengths and 4 field points. Tracing 4
rays on axis and 9 rays off-axis led to a ~300 term
aberration function with an additional ~50 edge
thickness terms, with ~80 variables. I found that
eventually I had to adjust each thickness manually
to avoid introducing any hard constraints into the
merit function, a very tedious task.
b)The optical challenge was to find a systematic process
to expand a preliminary Petzval lens with a field
flattening group into a apochromatic design.
c)Pushing the limits of simultaneous weight and
illumination requirements meant developing an
iterative technique, with scaling laws to predict
focal length for each solution.
WHAT INSIGHTS (IF ANY) DID YOU GAIN FROM WORKING ON THE PROBLEM?
a)It was critical to reduce the dimensionality of the
problem during intermediate design work. Early on,
before making the lens apochromatic, I used 3 field
points and the D-d chromatic terms to reduce the merit
function terms by half.
b) An effective way to achieve an apochromatic solution
is to make use of a triplet with 2 "buried surfaces",
as described by Kingslake. The triplet is composed of
special glasses which form a triangle on the P vs V diagram,
the partial dispersion vs the normal dispersion. The glasses
PSK53A, KSFS1 and TIF6 form just such a triplet, each with
an index of refraction of ~1.62 +/-.01 for all wavelengths.
I started out with 1 triplet near the aperture stop, added a
triplet closer to the image and finally ended up with 4
such triplets. The triplet inner surfaces can have very
short radii of curvature without upsetting the monochromatic
aberrations significantly.
ADDITIONAL COMMENTS:
My design strategy was:
1)I initially used three glasses:
high index crown - LASFN30 1.803 46.4
high index flint - SF59 1.953 20.4
"AIR" glass - FK54 1.437 90.7
2)I designed the Petzval front objective using the D-d method,
using a greatly reduced image size.
3)I added a second objective and field flattening elements,
expanding the image diameter to 50 mm.
4)I successively added the apochromatic triplet correctors.
5)Finally, I adjusted the focal length to achieve the
weight/illumination requirements.