Opto-Mechanical Systems Design, Volume 1, 4th Edition

A temperature gradient deforms the optical surface of a mirror. An axial temperature gradient along the optical axis of the mirror or from front to back changes the optical radius of curvature. The change in radius of curvature ΔR for a mirror of optical radius R₀ is given by

$\Delta R=\frac{\alpha }{k}Q{R}_0^2$

(3.17)

where

α is the thermal coefficient of expansion of the mirror material

k is the thermal conductivity of the mirror material

Q is the heat flux per unit area producing the temperature gradient

The ratio α/k is the thermal distortion index of the mirror material and the figure of merit for performance when subject to a temperature gradient. To minimize distortion from temperature gradients, α/k should be small, implying a large thermal conductivity and ...