February 26, 1996
Two non-uniform coating conditions can
occur during the coating process: radial and
azimuthal uniformity. This document
address the azimuthal uniformity in terms
of the planned coating for the Edgar Smith
telescope mirrors. The coating design
consists of an aluminum reflector with a
thin silicon oxide overcoat. Uniformity
errors will create wave front errors similar
to figure errors on the mirror.
The figure to the right depict a uniformity error in the silicon oxide overcoat. The equations below describe the optical path difference which this non-uniformity would generate.
Since the reference plan could be placed anywhere placing it at the silicon oxide layer will simplify the calculations.
Thus 
and 
then:
if we assume the uniformity is 10% of the coating thickness then 
and
If 
Thus a 10% uniformity error will create less than 0.005 waves of wave front error.
The second error is the error in the reflective metal film. The same basic equations are used to model this error as was used in the overcoat uniformity error.
Again picking our reference plane to make
and 
and 
Where D is the metal film thickness and 
is the variation in thickness. Then:
Assuming the film thickness is 650 and the error is 10% again, for 
the figure error is:
Both errors are likely to be additive since most of the error is due to coating geometry and will exists for both coatings. Thus an error of approximately .025 waves (1/40) could be expected with a 10% coating uniformity error. My recommendation would be to use 5% as a tolerance for uniformity thus reducing the error to 0.0125 waves. This tolerance would be consistent with the current contract with Hughes who are planning a 2% tolerance for their coatings for both the primary and the secondary.