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Better “Seeing” with Light Weight Substrates

Mirror Thermal Time Constant

Boundary layer thermals on a "warm" mirror. Photo courtesy: 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 and inertia it must overcome 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 not alleviate it.

Light weight mirrors offer a significant advantage compared to solid substrates  in tracking local transient temperature.   Hextek Gas-Fusion™ blanks track changes in temperature quickly due to their lightweight construction and thin face sheets.  The key driver is the thickness of the face sheet.  Because Hextek light weight substrates track temperature quickly the observer can maximize viewing time and worry less about ambient temperature changes impacting mirror performance and image quality.

The key to this issue is the thermal time constant of the mirror substrate.  This constant is determined by the simplified equation below:

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 glass materials,  ρ, cp and κ are close enough not to worry about.  Therefore, the driving value for the thermal time constant is the cross-sectional thickness of that material.  The table below demonstrates this using a meter sized mirror as the baseline:

*Face sheet thickness only.

In practice, the time lag associated with a mirror thermally stabilizing is much longer than shown in the chart above.  Our company tested a finished Gas-Fusion™ mirror by placing a heat source on the back plate of the mirror and observed the optical surface figure change directly with an interferometer.  The time required after the heat source was turned off to re-stabilize the mirror optically was about 20 minutes.  Or roughly seven times longer than the chart suggests.  Extrapolating this to a solid clearly pushed the time constant into hours and the meniscus to over an hour.

Observatories with very large mirror substrates manage them using active cooling of the telescope housing and mirrors.  The University of Arizona’s Steward Mirror Lab utilizes active cooling within the cellular structure of the mirror to maintain thermal stability.  This method too has been employed in Hextek substrates and can be as simple as a low flow ambient air exchange via a tube inserted into a back plate hole of each cell.  Such a system is a very solution for large demanding imaging optics.  Where passive thermal management is the only option, Hextek substrates provide excellent performance.