Please allow me to complete the discussion of my engineering tool for elastomeric mounting of mirrors.
So, according to my previous missive, the elastomer reduces the shear stresses on the back face of the mirror by two to three orders of magnitude compared to a rigid adhesive. That’s all well-and-good but how do we know that it’s good enough? Of course those of you who have picked up the source reference (SPIE: 6665-03, 2007) know the answer. You also know why there are no dimensional quantities (inches, millimeters, etc.) for the mirror in my equation,
In the derivation I assumed that the gravitational sag of the mirror was a reasonable budget for the figure errors induced by the mounting method. When I equated the deflection of the mirror due to gravity to the deflection of the mirror due to the thermally induced shear stresses on the back of the mirror the mirror’s dimensions (thickness and edge length) dropped out leaving only the adhesive’s thickness, t, the environmental temperature change, DT, the difference in coefficient of thermal expansion between the mirror and the mount, Da , the modulus of rigidity (shear modulus) of the elastomer, G, and the specific weight of the mirror substrate, s. Voila!
So, that’s my engineering tool. But plugging numbers in is the easy part. Now the engineer has to go to work. You’ll find a discussion of the engineering considerations in the source reference also.
Thank you for your patience.
‘Tis mid-winter and Valentine’s day is nigh. Ah, the joy of good company! Thank you all, again.
Yes Tiny Tim, thank you too.