Abstract
We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope profiles over the spatial frequency range where the raw data are significantly perturbed due to the limited resolution of the measurement instrument. We characterize the spatial resolution properties of a profiler with the instrument's transfer function (ITF). To precisely measure the ITF, we apply a recently developed method utilizing test surfaces with 1D linear chirped height profiles of constant slope amplitude. Based on the results of the ITF calibration, we determine parameters of an analytical model for the ITF that is used in the original reconstruction software. Here, we treat surface slope metrology data obtained with the Optical Surface Measuring System (OSMS), using as a sensor an electronic autocollimator (AC) ELCOMAT-3000. The spatial resolution of the OSMS is limited by the size of the AC light-beam-collimating aperture. For the purposes of this investigation, the OSMS is equipped with a circular aperture with a diameter of 2.5 mm. This is a typical arrangement of most AC-based slope profilers developed for surface slope metrology of state-of-the-art x-ray mirrors. Using the example of surface slope metrology of two state-of-the-art elliptically shaped x-ray focusing mirrors, we demonstrate that the developed data reconstruction procedure allows us to significantly improve the accuracy of surface slope metrology with the OSMS over the spatial wavelength range from ∼1.6 mm to 7 mm. Thus, the amplitude of the quasi-periodic error characteristic of the deterministic polishing process used appears to be higher by a factor of ∼2 than is apparent from the rough metrology data. Underestimation of the surface slope errors in this spatial wavelength range can lead to serious errors in the expected performance of x-ray mirrors in synchrotron beamlines, especially at modern light sources utilizing coherent x rays, where the perturbations can lead to increased speckle-like intensity variation.
Highlights
We present experimental, analytical, and numerical methods, constituting a multistep procedure, developed for reconstruction of one-dimensional (1D) surface slope distribution functions of the surface topography, inherent to the surface of an x-ray mirror under test
II, we indicated that the analytical expressions (3) and (4) for the 1D point spread function (PSF) and instrument’s transfer function (ITF) derived in Ref. 1 based on the scitation.org/journal/rsi simplified model of a slope profiler with a uniformly illuminated circular aperture are not directly applicable to the Optical Surface Measuring System (OSMS) with an AC ELCOMAT-3000 equipped with a 2.5-mm diameter aperture
We have discussed experimental, analytical, and numerical methods constituting a multistep procedure developed for super-resolution surface slope metrology of x-ray mirrors
Summary
Analytical, and numerical methods, constituting a multistep procedure, developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope distribution functions (profiles) of the surface topography ( referred to as “1D” surface slope topography), inherent to the surface of an x-ray mirror under test. Due to the limited spatial resolution of the OSMS, the ratio of the measured slope variation amplitude to that of the inherent surface profile dramatically decreases with an increase in the slope variation frequency.. Where the spatial period of slope variation is about 6 mm, the profiler’s error in the variation amplitude is only about 10%, while at a 2-mm period, it reaches a factor of almost 3 This range of spatial wavelengths is of special importance for state-of-the-art aspherical x-ray optics fabricated with deterministic polishing techniques. We show that in spite of the fact that after the reconstruction, the residual slope error (after subtraction of the best-fit elliptical shape) is just slightly larger, the power spectral density (PSD) peaks of the quasi-periodic surface slope variation, characteristic for the deterministic polishing process used for the mirror fabrication, appear to be higher by a factor of up to ∼4.5. V) by summarizing the main concepts discussed in this paper and outlining a plan for future work
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
