Proceedings Article | 1 August 1990
KEYWORDS: Mirrors, Polishing, Mathematical modeling, Adaptive optics, Telescopes, Birefringence, Aspheric lenses, Surface finishing, Finite element methods, Systems modeling
The ten meter diameter Reck telescope, currently the largest of the telescopes
under construction in the world today, consists of thirty-six 1.8 meter diameter
off-axis hyperbolic hexagonal mirror segments. These are comprised of near zero
coefficient of expansion glass ceramic substrates manufactured by Schott Glaswerke
of Germany under the trade name of Zerodur. The blanks are approximately 1.9
meters in diameter and 7.5 centimeters thick. To produce the aspheric segments
(consisting of six different configurations) in a timely fashion, scientists at the
University of California have developed the technique of stressed mirror polishing.
This method employs the introduction of shears and moments about the segment
periphery, in its circular shape, to bend the mirror into the reverse of the
desired shape . A true sphere is then ground and subsequently polished into the
segment, after which the loads are removed and the desired optical prescription
obtained. Next, the segment is cut to the hexagonal shape and a central hole,
0.25 meters in diameter, is core drilled partially through its hack. The segment
is then mounted to its final support structure,
Mirrors constructed in this fashion have many advantages, which include avoidance
of the large capital facilities needed to cast large monolithic blanks, and
logistical problems of transportation or risk in fabrication or repair.
Conventional polishing techniques for segments, however, which have no symmetrical
axis, are very expensive and time-consuming, unlike the stressed mirror process
which involves the fabrication of spheres using a single, large tool.
The process involves theoretical prediction of the loads required to bend the
surface, and iterative solutions based on test measurements to fine tune the
desired shape. The iteration requires the use of the theoretical math model, which
consists of a closed form solution to a flat plate, as well as a detailed finite
element model of the segment, which includes the effects of shear and curvature.
This paper discusses some of the theoretical and test correlations achieved to
produce the required configurations. Very good agreement is found, such that the
deformed surface can be achieved after as little as one iteration accurate to the
tenth of a micron level.
After the segments are cut, their shape may warp slightly due to residual stress
levels in the blank itself. Using the detailed finite element model, a first order
analysis of the springing effect, including the cutting of the central hole, is
presented, and further correlation to test data made. Stress birefringence data
has been successfully utilized in determining the magnitude and shape of the
expected change. Again, results show a reasonable correlation can be made,
allowing anticipation of the presumed spring prior to polish of the segment.
Prediction allows for adequate range of adjustment and minimized force application
for the corrective devices used to warp the segments to their final shape.
