Thermal Defocus in a Housing

As stated in a prior entry one can compute the thermal defocus of a lens knowing the
  • Focal Length, F
  • Therm Optic Coefficient, β
The relation ship is:

ΔF=F∙β∙ΔT
Here is a nomograph to design a doublet for achromatic and passively athermal correction by itself.

In reality, on has to include the housing that holds the lens relative to the focus plane. So in reality the equation is actually:

ΔF=F∙(β-αhousing)∙ΔT
Here is a nomograph to design a doublet for achromatic and passively athermal correction in a housing.
where
ΔF=focus change over temperature
F = Focal length
β = lens therm optic coefficient or 1/VT
αhousing= Housing coefficient of thermal expansion
ΔT = Change in temperature