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A-Thermal OTA | A-Thermal Mirror Cell
There has been some negative results when a mirror is "glued" to its mounting
supports. Since most mirrors are made of low expansion glass, and mirror cells
are frequently made of either aluminum or iron, it is likely that the poor
performance is the result of stress caused by the differential expansion
of the mirror and its support.
It is possible to construct a mirror mounting cell that has the same apparent
Coefficient of Themal Expansion [CTE] as the mirror. This is accomplished
by balancing the expansion of a low CTE material with the oppositely
directed expansion of a material with a high CTE.
Note the diagram below. The expansion of the longer arm of the "orange"
material is offset by the countering expansion of the short "green" material.
It is straight forward to calculate the proper lengths of each element of
this scheme, given the corresponding CTEs.
To provide a thermal neutral mounting, the following relation must hold for all temperatures:
[R + r] = [L + l] - [A + a] _ or _ R + r = L + l - A - a
r = R*CTE1 * T
l = L*CTE2 * T
a = A*CTE3 * T
Where T is the temperature change,
CTEN is the corresponding coefficient of thermal expansion and,
r, l & a is the corresponding change in length.
Given: L = R + A -then- r = l - a
R*CTE1= L*CTE2 - A*CTE3
Solving for A in terms of R gives:
A = R * [CTE2 - CTE1] / [CTE3 - CTE2]
For CTE1 = 1.8 ppm/F (pyrex)
CTE2 = 6.5 (Iron)
CTE3 = 12.8 (Aluminum)
A = .746R and L = 1.746R
The design of a thermal neutral support triangle will look something like this: