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.