Three Elment Solution

There may not be enough materials on your nomograph to locate a two element solution with "nice" housing material (CTE). Then use three elements. The advice is similar when you are doing color correction. Maximize the area in the triangle. This forces large differences in V numbers minimizing element powers (increased focal length) which induce lower aberrations.
Material 4 is most likely a diffractive. Do not underestimate the power of a diffractive for passive athermalization. I have heard of reflective laser systems using diffractives for passive athermailization. This may seem crazy.... mirrors are insensitive to color and a laser is monochromatic. Why waste your time with a diffractive? Simple: passive athermalization.

Reference:
"Thermal compensation of infrared achromatic objectives with optical materials." by J.L. Rayces and Lan Lebich in SPIE vol 1354 International Lens Design Conference 1990
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Scott Sparrold,
Oct 9, 2011, 2:26 PM