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Remotely measuring mirror curvature

The primary of the James Webb Space Telescope (JWST) is a sixmeter segmented mirror with each of the 18 hexagonal 1.5m lightweight mirror segments an off-axis parabola (OAP). All segments must have the same parent radius to within a fairly tight tolerance in order to ensure coincident images of the same size. In the 2007–2008 timeframe, the segments will be tested at Marshall Space Flight Center’s X-Ray Calibration Facility, which contains a large cryovac chamber originally built to test the Chandra X-Ray Observatory (modified now so that optical metrology work can be conducted in the visible regime). Among the monitoring measurements needed for each JWST mirror segment is a way to remotely determine any changes in parent radius as the segment is dropped from ambient to deep space temperatures (≈30K). Presented here is a synopsis of one proofof-concept empirical method for making this remote radius measurement. From calculus, local radii at a point on a three-dimensional surface can be determined in different directions from the osculating circle. In a parabolic surface, the tangential and sagittal radii are of interest and are given by: