Test and theoretical comparisons for bending and springing of the Keck segmented 10 m telescope

Abstract

The 1 0 m diameter Keck telescope consists of 36 1 .8 m off-axis hyperbolic hexagonal mirror segments (glass ceramic substrates). To produce the aspheric segments in a timely fashion, shears and moments are introduced at the segment periphery, in its circular shape, to bend the mirror into the reverse of the desired shape. A true sphere is polished into the segment, after which the loads are removed and the desired optical prescription obtained. The segment is cut to the hexagonal shape and a central hole is core-drilled partially through its back. The process involves theoretical prediction of the loads required to bend the surface using a detailed finite element model. Very good agreement is found between test and theory such that the deformed surface can be achieved after as little as one iteration, accurate to the 0.1 p.m level. After the segments are cut, their shapes will warp slightly due to residual stress levels measured in the blanks. Using the same model, a first-order analysis of the springing effect is presented, and further correlation to test data is made. Results allow anticipation of the presumed spring prior to polish of the segment, minimizing the range of adjustment and force application for the corrective devices used to warp the segments to their final shape.