Modeling of surface metrology of state-of-the-art x-ray mirrors as a result of stochastic polishing process

The design and evaluation of the expected performance of new optical systems requires sophisticated and reliable information about the surface topography for planned optical elements before they are fabricated. The problem is especially severe in the case of x-ray optics for modern diffraction-limited-electron-ring and free-electron-laser x-ray facilities, as well as x-ray astrophysics missions, such as the X-ray Surveyor under development. Modern x-ray source facilities are reliant upon the availability of optics of unprecedented quality, with surface slope accuracy < 0.1μrad. The unprecedented high angular resolution and throughput of future x-ray space observatories require high quality optics of hundreds square meters in total area. The uniqueness of the optics and limited number of proficient vendors makes the fabrication extremely time consuming and expensive, mostly due to the limitations in accuracy and measurement rate of metrology used in fabrication. In this work we continue investigating the possibility to improve metrology efficiency via comprehensive statistical treatment of a compact volume of metrology data, considered to be a result of a stochastic polishing process. If successful, the modeling could provide a feedback to deterministic polishing processes, avoiding time-consuming, whole scale metrology measurements over the entire optical surface with the resolution required to cover the entire desired spatial frequency range. The modeling also allows forecasting metrology data for optics made by the same vendor and technology. The forecast data is vital for reliable specification for optical fabrication, evaluated from numerical simulation to be exactly adequate for the required system performance, avoiding both over- and underspecification.

[1]  Valeriy V. Yashchuk,et al.  Specification of x-ray mirrors in terms of system performance: a new twist to an old plot , 2014 .

[2]  Frank Siewert,et al.  First report on a European round robin for slope measuring profilers , 2005, SPIE Optics + Photonics.

[3]  Valeriy V. Yashchuk,et al.  Reliable before-fabrication forecasting of expected surface slope distributions for x-ray optics , 2012 .

[4]  Stephan Friedrich,et al.  Photon Beamlines and Diagnostics at LCLS , 2011 .

[5]  Frank Siewert,et al.  The Nanometer Optical Component Measuring Machine , 2008 .

[6]  Valeriy V. Yashchuk,et al.  A new x-ray optics laboratory (XROL) at the ALS: mission, arrangement, metrology capabilities, performance, and future plans , 2014, Optics & Photonics - Optical Engineering + Applications.

[7]  Valeriy V. Yashchuk,et al.  Application of the time-invariant linear filter approximation to parametrization of surface metrology with high-quality x-ray optics , 2014 .

[8]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .

[9]  Valeriy V. Yashchuk,et al.  Correlation analysis of surface slope metrology measurements of high quality x-ray optics , 2013, Optics & Photonics - Optical Engineering + Applications.

[10]  Valeriy V. Yashchuk,et al.  Specification of x-ray mirrors in terms of system performance: new twist to an old plot , 2014 .

[11]  Malcolm R. Howells,et al.  Future metrology needs for synchrotron radiation grazing-incidence optics , 2000 .

[12]  T. Zeschke,et al.  The Nanometer Optical Component Measuring Machine: a new Sub-nm Topography Measuring Device for X-ray Optics at BESSY , 2004 .

[13]  Bore-Kuen Lee,et al.  Maximum likelihood parameter estimation of F-ARIMA processes using the genetic algorithm in the frequency domain , 2002, IEEE Trans. Signal Process..

[14]  Hsiao-Chun Wu,et al.  Novel Fast Computation Algorithm of the Second-Order Statistics for Autoregressive Moving-Average Processes , 2009, IEEE Trans. Signal Process..

[15]  Hidekazu Mimura,et al.  Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations , 2009, Optics + Optoelectronics.

[16]  Valeriy V. Yashchuk,et al.  Application of time-invariant linear filter approximation to parametrization of one- and two-dimensional surface metrology with high quality x-ray optics , 2013, Optics & Photonics - Optical Engineering + Applications.

[17]  Valeriy V. Yashchuk,et al.  Advanced environmental control as a key component in the development of ultrahigh accuracy ex situ metrology for x-ray optics , 2015 .

[18]  Samuel K. Barber,et al.  Sub-microradian surface slope metrology with the ALS Developmental Long Trace Profiler , 2009 .

[19]  Hidekazu Mimura,et al.  Wave-optical analysis of submicron focus of hard x-ray beams by reflective optics , 2002, SPIE Optics + Photonics.

[20]  Valeriy V. Yashchuk,et al.  Global High‐Accuracy Intercomparison of Slope Measuring Instruments , 2007 .

[21]  Jana Buchheim,et al.  Characterization and calibration of 2nd generation slope measuring profiler , 2010 .

[22]  I. Fukumoto,et al.  Improvement of ground surface roughness in Al-Si alloys , 1990 .

[23]  S. Wu,et al.  Mathematical model of a ground surface profile with the grinding process as a feedback system , 1976 .

[24]  Antoine Llebaria,et al.  Autoregressive process for characterizing statistically rough surfaces , 1993 .

[25]  A model of mechanical polishing in the presence of a lubricant , 2005 .

[26]  Simon R. Bandler,et al.  The X-ray Surveyor Mission: a concept study , 2015, SPIE Optical Engineering + Applications.