Binary pseudo-random grating as a standard test surface for measurement of modulation transfer function of interferometric microscopes

The task of designing high performance X-ray optical systems requires the development of sophisticated X-ray scattering calculations based on rigorous information about the optics. One of the most insightful approaches to these calculations is based on the power spectral density (PSD) distribution of the surface height. The major problem of measurement of a PSD distribution with an interferometric and/or atomic force microscope arises due to the unknown Modulation Transfer Function (MTF) of the instruments. The MTF characterizes the perturbation of the PSD distribution at higher spatial frequencies. Here, we describe a new method and dedicated test surfaces for calibration of the MTF of a microscope. The method is based on use of a specially designed Binary Pseudo-random (BPR) grating. Comparison of a theoretically calculated PSD spectrum of a BPR grating with a spectrum measured with the grating provides the desired calibration of the instrumental MTF. The theoretical background of the method, as well as results of experimental investigations are presented.