A new technology of thermoplastic glass bending for the manufacture of cylindrical surfaces of hard X-ray range mirrors

The paper presents a new technique for thermoplastic bending of glass. The technique makes it possible to produce cylindrical surfaces with a guide in the form of a parabola, ellipse, etc. for mirrors in the hard X-ray wavelength range ($\lambda\sim$ 0.1 nm). Three samples of the surface of an elliptical cylinder were prepared using this technique. The production time for each sample was two days. The deviation of the guide and its local angle from the calculated values for all samples does not exceed $\Delta y$ = 0.5 $\mu$m and $\Delta\alpha$ = 7 $\cdot$ 10$^{-5}$ rad, respectively. It is shown that when such surfaces are etched for two hours, their accuracy can be improved by more than two orders of magnitude ($\Delta y$ = 2 nm, $\Delta\alpha$ = 5 $\cdot$ 10$^{-7}$ rad).