Manufacture of a 10-km-scale radius-of-curvature surface by use of a thin-film coating technique

We tried a method of making a 10-km-class large-radius-of-curvature surface that would satisfy both low microroughness (0.1 nm rms) and low waviness (lambda/100) by forming a spherically curved film with a low-loss coating technique on a flat surface produced by mechanical (chemical) polishing. We obtained a SiO2 surface with a 10255 +/- 250-m radius of spherical curvature that had less than lambda/30 waviness and 0.4-nm micro-roughness over a 9-cm-diameter area.