Super-resolution surface slope metrology of x-ray mirrors

Abstract

We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of onedimensional (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 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 ACbased 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.

Reliability investigation of the instrument transfer function calibration technique based on binary pseudo-random array standards

“…This can be thought of as an illustration of how the application of metrology data deconvolution based on the experimentally measured ITF, can advance the confidence of surface topography metrology with state-of-the-art x-ray optics. Note that this point has been experimentally justified in application to surface slope metrology with super high quality x-ray optics [37,38].…”

Investigation on lateral resolution of surface slope profilers

“…The accuracy of the ALS OSMS achieved in measurements with a significantly curved elliptical mirror with residual slope error of ~50 nrad (RMS) is on the level of 30 nrad (RMS) [66].…”

“…The spatial resolution of the AC-based slope profilers is limited by the size of the light beam aperture [66]. Similar to the XROL OSMS arrangement in this paper, a circular aperture with a diameter of about 2.5 mm is typically used.…”

“…The resolution properties of the OSMS with 2.5-mm aperture are well described with a circular aperture ITF, analytically derived in [68] and corrected in Ref. [66] with an additional term, empirically determined to better match the OSMS resolution measurements with the high-spatial-frequency pattern of the chirped slope test sample [22,23], used also here:…”

Atmospheric Plasma Jet processing for figure error correction of an optical element made from S-BSL7

“…Plasma Jet Machining (PJM) is a well-established technique for figuring and correcting various optical lens designs, such as spherical, aspherical and freeform lenses. The material variety, mainly based on silicon, for instance Si, Fused Silica or SiC, is progressively extended to adapt to the market requirements [3][4][5].…”