Surface figure correction using differential deposition of WSi$_2$

The surface figure of an x-ray mirror was improved by differential deposition of WSi$_2$ layers. DC magnetron sputtering through beam-defining apertures was applied on moving substrates to generate thin films with arbitrary longitudinal thickness variations. The required velocity profiles were calculated using a deconvolution algorithm. Height errors were evaluated after each correction iteration using offline visible light surface metrology. WSi$_2$ was selected as a promising material since it conserves the initial substrate surface roughness and limits the film stress to acceptable levels. On a 300 mm long flat Si mirror the shape error was reduced to less than 0.2 nm RMS.