Minimizing Uncertainty in Cryogenic Surface Figure Measurement

A new facility at the Goddard Space Flight Center is designed to measure with unusual accuracy the surface figure of mirrors at cryogenic temperatures down to 12 K. The facility is currently configured for spherical mirrors with a radius of curvature (ROC) of 600 mm, and apertures of about 150 mm or less. The goals of the current experiment were to 1) Obtain the best possible estimate of test mirror surface figure, S(x,y) at 87 K and 20 K; 2) Obtain the best estimate of the cryo-change, Delta (x,y): the change in surface figure between room temperature and the two cryo-temperatures; and 3) Determine the uncertainty of these measurements, using the definitions and guidelines of the ISO Guide to the Expression of Uncertainty in Measurement. A silicon mirror was tested, and the cry-change from room temperature to 20K was found to be 3.7 nm rms, with a standard uncertainty of 0.23 nm in the rms statistic. Both the cryo-change figure and the uncertainty are among the lowest such figures yet published. This report describes the facilities, experimental methods, and uncertainty analysis of the measurements.