Progress of coating stress compensation of silicon mirrors for Lynx x-ray telescope mission concept using thermal oxide patterning method

A thermal oxide patterning method has proven to be effective for correcting coating-stress-induced distortion on flat silicon wafers. We report progress on developing this method for correcting curved silicon mirrors distorted by front-side iridium coatings. Owing to the difference in geometry, a finite element model has been established to calculate the appropriate duty cycle maps in thermal oxide hexagon patterns used for compensation. In addition, a photolithographic process, along with three-dimensional printed equipment, has been developed for creating patterns precisely on the back side of curved mirrors. The developed method has been used to recover the original surface shape of two silicon mirrors which are 100-mm long, 0.5-mm thick, having 312-mm radius of curvature, and 30 deg in azimuthal span (Wolter-I geometry). These mirrors' front sides are sputter-coated by 20-nm iridium layers with ∼-70 N / m integrated stress. Measurement results show that the developed method can mitigate coating-induced distortion by a factor of ∼5 in RMS height and ∼4 in RMS slope error, corresponding to ∼0.5 arc sec RMS slope error. Residual errors after correction are dominated by mid-frequency ripples created during the annealing process, which will be resolved in the future. The presented method is precise and inexpensive and a potential candidate for resolving the coating stress issue for Lynx optics in the future.