Measuring the roughness of high-precision quartz substrates and laser mirrors by angle-resolved scattering

This paper presents the results of measuring the roughness of high-precision quartz substrates and of the mirrors of laser gyroscopes by angle-resolved scattering (ARS). The calculated one-dimensional and two-dimensional spectral-power-area (SPA) functions and the effective rms roughness sigma(eff) are compared with the results of measurements using atomic-force microscopy (AFM) and white-light interferometry (WLI). It is found that the roughness statistics are close to one-dimensional exponential statistics for the polished substrates and to two-dimensional exponential statistics for the laser mirrors. It is found that the best agreement of the experimental results using ARS and AFM is observed for the mirrors, which is most likely because the roughness of the sputtered coating is more homogeneous than that of the polished substrate. The sigma(eff) value strongly depends on the range of spatial frequencies of the roughness measured by the different methods. The good agreement of the results of the measurements using ARS, AFM, and WLI shows that it is suitable to use the ARS method for high-precision optical surfaces and coatings. (C) 2002 Optical Society of America.