Linear chirped slope profile for spatial calibration in slope measuring deflectometry

Abstract

Slope measuring deflectometry is commonly used by the X-ray optics community to measure the long-spatial-wavelength surface figure error of optical components dedicated to guide and focus X-rays under grazing incidence condition at synchrotron and free electron laser beamlines. The best performing instruments of this kind are capable of absolute accuracy on the level of 30-50 nrad. However, the exact bandwidth of the measurements, determined at the higher spatial frequencies by the instrument’s spatial resolution, or more generally by the instrument’s modulation transfer function (MTF) is hard to determine. An MTF calibration method based on application of a test surface with a one-dimensional (1D) chirped height profile of constant amplitude was suggested in the past. In this work, we propose a new approach to designing the test surfaces with a 2D-chirped topography, specially optimized for MTF characterization of slope measuring instruments. The design of the developed MTF test samples based on the proposed linear chirped slope profiles (LCSPs) is free of the major drawback of the 1D chirped height profiles, where in the slope domain, the amplitude strongly increases with the local spatial frequency of the profile. We provide the details of fabrication of the LCSP samples. The results of first application of the developed test samples to measure the spatial resolution of the BESSY-NOM at different experimental arrangements are also presented and discussed.

Optimization of the size and shape of the scanning aperture in autocollimator-based deflectometric profilometers

“…36 The simple model used here predicts the first zerocrossings at the spatial wavelengths of 1.5 mm and 2.05 mm for the optimal tangential and the standard circular apertures, respectively. However, in publications 25 (see also the results of our measurements in Sec. VIII), it has been shown that with the optimally aligned 2.5-mm circular aperture, 27 the spatial resolution of a NOM-like profilometer is about 1.2 mm if the first zero-crossing of the OTF is assumed as a criterion for the spatial resolution achieved.…”

“…For the spatial resolution measurement with the OSMS profilometer equipped with different apertures, we use an original test sample with two chirped surface slope patterns 24,25 - Fig. 12.…”

“…In measurements with such a sample, we obtain highly confident information of the profilometer's resolution. 25 We provide (Sec. VI) a simplified analytical description of the one-dimensional (1-D) OTF of an AC equipped with circular and rectangular apertures.…”

BioMAX – the first macromolecular crystallography beamline at MAX IV Laboratory

“…The mirrors with benders were measured and characterized at the BESSY-II Optics Lab at HZB in Berlin. The performance of the bending system and the slope error was measured by means of the BESSY-NOM slope measuring profiler (Siewert et al, 2004) which allows an inspection of the optics for the spatial frequency range between 1.2 mm up to full aperture length (Siewert et al, 2016). A white-light interferometer (WLI) was used to measure the micro-roughness of the mirrors giving an expression for the higher-spatial frequency error which would cause loss of photons because of scatter.…”

Pentaprism Measurements of Large Flat Mirrors

“…Such systems can be roughly divided into two types. The first type of pentaprism system contains one scanning pentaprism that directly measures the tilt angles on the surface [6][7][8][9][10][11][12]. This system is sensitive to errors, such as the tilt of the autocollimator, the manufacturing errors of the pentaprism, and the environmental influence.…”