Passive Athermalization Color Correction in a Housing

There exists another nomograph for selecting optical material pairs for achromatic color correction and passive athermalization in a housing with a non zero coefficient of thermal expansion. Adding the housing CTE complicates  this nomograph. If you are having difficulty understanding this please refer to the method, by Gibbons, that does not include the housing.

Background
To predict the thermal defocus of a lens floating in air:

But a lens does not float in air. It images upon film or a detector. A structure, or housing, holds the lens relative to the detector. This housing will also expand with temperature and should be accounted for in your lens design. Therefore


The concept is to design a lens whose thermal defocus matches the growth due to the housing structure. Factoring in color requirements one can still construct a nomograph to select material pairs for color correction and thermal defocus to match a housing CTE.

This method was pioneered in the 70s by the reference sited below (authors from Carl Zeiss). They do not use thermal V number, but the therm optic coefficient (although they use γ instead of β) 

How does this nomograph work? R. Kremer helped me decipher the nomograph.The slope between two optical pairs will be color corrected and passively athermal for a housing whose coefficient of thermal expansion matches the slope between the two material points. Example. Let us assume we have four optical materials: Rhino, Giraffe, Cheetah and Zebra. We plot them. Slope between pairs tell us housing CTE:
Here is a quick diagram of the optical system:
The animated nomograph has a material named "Giraffe" which simulates a diffractive, whose Color V number is strictly a function of your waveband and center wavelength. In fact Giraffe could be a diffractive made of material "Zebra" or any other material already on the nomograph. The slope between would represent a housing solution for a hybrid, which is a single piece of material that focuses by both refraction and diffraction.

If the "Material 2" element is a diffractive then it will be on one of the surfaces of the "Material 1" element. In fact, the diffractive will actually have positive power, not negative as a refractive flint. The positive diffractive is due to the negative sign on the color V number.

Sources:
"Design of athermal lens systems" H. Kohler and F. Strahle in Space Optics, B.J. Thompson and R.R. Shannon Editors, National academy of Sciences 1974... 
and it has been reprinted in Selected Papers on Optomechanical Design SPIE Volume 770, Edited by O'She and Thompson

"Use of Hybrids in the 3-5µm infrared band" P.J. Rogers in Current Developments in Optical Design and Engineering V,SPIE proceedings Vol 2540
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Scott Sparrold,
Oct 9, 2011, 12:44 PM
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Scott Sparrold,
Oct 9, 2011, 12:58 PM
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Scott Sparrold,
Oct 9, 2011, 11:21 AM
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Scott Sparrold,
Oct 10, 2011, 11:08 AM