These equations show how optical prescription parameters are thermally cycled. Ray trace codes will do this conversion for you, but here are the equations for reference:
Where,
R = Radius of curvature
D = Thickness (lens or airspace)
A_{n} = Aspheric coefficient with a semi aperture coefficient of n
C_{n} = Diffractive coefficient with semi aperture phase profile of n
α = Coefficient of thermal expansion (CTE)
Subscript denotes if optical material "substrate" for a lens thickness
or housing, if it is an airspace
ΔT = Change in temperature in °C
A prime or ' is used to denote the changed parameter after thermally cycling
One might include index of refraction here, but I have saved this for a another page.
An example of thermally cycling an aspheric term is provided here.
If you are not modeling in an optical ray trace program and want to simply know how much a lens will defocus with temperature refer to these equations.
