Cross-check of different techniques for two-dimensional power spectral density measurements of x-ray optics

The consistency of different instruments and methods for measuring two-dimensional (2D) power spectral density (PSD) distributions are investigated. The instruments are an interferometric microscope, an atomic force microscope (AFM) and the X-ray Reflectivity and Scattering experimental facility, all available at Lawrence Berkeley National Laboratory. The measurements were performed with a gold-coated mirror with a highly polished stainless steel substrate. It was shown that these three techniques provide essentially consistent results. For the stainless steel mirror, an envelope over all measured PSD distributions can be described with an inverse power-law PSD function. It is also shown that the measurements can be corrected for the specific spatial frequency dependent systematic errors of the instruments. The AFM and the X-ray scattering measurements were used to determine the modulation transfer function of the interferometric microscope. The corresponding correction procedure is discussed in detail. Lower frequency investigation of the 2D PSD distribution was also performed with a long trace profiler and a ZYGO GPI interferometer. These measurements are in some contradiction, suggesting that the reliability of the measurements has to be confirmed with additional investigation. Based on the crosscheck of the performance of all used methods, we discuss the ways for improving the 2D PSD characterization of X-ray optics.