Thermal Boundary Layer Credit Sky & Telescope

Thermals created at the mirror surface can dramatically reduce astronomical seeing when the mirror substrate is not at thermal equilibrium with the surrounding ambient air. The thicker the substrate, the more thermal mass, the more time to reach temperature equilibrium. The image at right shows the dramatic effect of a mirror that is warmer than the surrounding air and the resulting thermal turbulence over the mirror’s surface. All mirror materials suffer from this problem and having a zero expansion glass does nothing to remove it.  Light weight mirrors offer a significant advantage compared to solid substrates by being able to track local transient temperatures. We can for a mirror, quantify the time it takes to reach thermal equilibrium given a temperature change by the following approximation:

τ = [ρCp/k]t

where ρ is the density (kg/m3), Cp is the specific heat (J/kgK), κ is the thermal conductivity (W/mK) and t is the thickness (m) of the material. This expression allows for an order-of-magnitude calculation of the thermal time constant of a material per thickness. For most glass materials, ρ, cp and κ are all about equal. When considering our sandwich design the driving value for the thermal time constant is the cross-sectional thickness of the face plates. The following table shows this using a meter sized mirror as the baseline:Hextek Gas-Fusion™ blanks track changes in temperature quickly due to their lightweight construction consisting of thin cross-sectional areas.


Astronomical Seeing Diagram

The chart above illustrates that to the first order, a thin optical substrate has a superior thermal time constant to one that is thicker.  A crude experiment was done using an 18″ diameter Hextek substrate of standard plate and rib size to help substantiate the above theoretical calculations.  A small asymmetric heat load on one location on the back plate was applied to the mirror for 60 minutes and then shut off.  The mirror figure recovered after 20 minutes.  Although the time is almost seven times more than the calculation above, it must be remembered that the experiment represents the worse case heat load condition.  It is not unreasonable to conclude that both the meniscus and solid would have significantly longer time constants than the Hextek mirror due to the thicker face sheets.
Observatories with very large mirror substrates manage thermal issues with primary mirrors using active cooling. The University of Arizona’s Steward Mirror Lab utilizes active cooling within the cellular structure of the 8.4 meter mirrors to maintain thermal stability. This method too has been employed with great success in Hextek substrates for little cost.   Such a system can be as simple as a low flow ambient air exchange via a tube inserted into a back plate hole of each cell.  Where passive thermal management is the only option, Hextek substrates provide the best performance.