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Title: Binary pseudo-random array standards for calibration of 3D optical surface profilers used for metrology with aspheric x-ray optics

Conference ·
DOI:https://doi.org/10.1117/12.2633163· OSTI ID:1994326

High-accuracy surface metrology is vitally important in manufacturing ultra-high-quality free-form mirrors designed to manipulate x-ray light with nanometer-scale wavelengths. The current and potential capabilities of x˗ray mirror manufacturing are limited by inherent imperfections of the integrated metrology tools. Metrology tools are currently calibrated with super-polished flat test-standard/reference mirrors. This is acceptable for fabrication of slightly curved x-ray optics. However, for even moderately curved aspherical x-ray mirrors the flat-reference calibration is not sufficiently accurate. For micro-stitching interferometry developed for surface measurements with curved x-ray mirrors, the tool aberration errors are known to be transferred into the optical surface topography of x-ray mirrors. Our approach to improving metrology is to thoroughly calibrate the measuring tool and apply the results of the calibration to deconvolution of the measured data. Here we explore the application of a recently developed technique for calibrating the instrument transfer function (ITF) of 3D optical surface profilers to metrology with significantly curved x-ray optics. The technique, based on test standards patterned with two-dimensional (2D) binary pseudo-random arrays (BPRAs), employs the unique properties of the BPRA patterns in the spatial frequency domain. The inherent 2D power spectral density of the pattern has a deterministic white-noise-like character that allows direct determination of the ITF with uniform sensitivity over the entire spatial frequency range and field of view of an instrument. The high efficacy of the technique has been previously demonstrated in application to metrology with flat and slightly curved optics. Here, we concentrate on development of an efficient fabrication process for production of highly randomized (HR) BPRA test standards on flat and 500-mm spherical optical substrates. We also compare and discuss the results of the ITF calibration of an interferometric microscope when using the HR BPRA standards on flat and curved substrates.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Materials Sciences & Engineering Division (SC-22.2)
DOE Contract Number:
AC02-05CH11231
OSTI ID:
1994326
Resource Relation:
Conference: SPIE Optical Engineering + Applications, San Diego, CA (United States), 2022
Country of Publication:
United States
Language:
English

References (70)

Derivation of closed-form ellipsoidal X-ray mirror shapes from Fermat's principle journal June 2022
Inspection of a Spherical Triple VLS-Grating for Self-Seeding of FLASH at DESY
  • Siewert, Frank; Lammert, Heiner; Reichardt, Gerd
  • SYNCHROTRON RADIATION INSTRUMENTATION: Ninth International Conference on Synchrotron Radiation Instrumentation, AIP Conference Proceedings https://doi.org/10.1063/1.2436150
conference January 2007
Standard reference specimens in quality control of engineering surfaces journal May 1991
Development of figure correction system for inner surface of ellipsoidal mirrors journal July 2018
APS deposition facility upgrades and future plans conference September 2014
Characterization of electron microscopes with binary pseudo-random multilayer test samples
  • Yashchuk, Valeriy V.; Conley, Raymond; Anderson, Erik H.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 649, Issue 1 https://doi.org/10.1016/j.nima.2010.11.124
journal September 2011
Long Trace Profile Measurements On Cylindrical Aspheres conference January 1989
Recent Developments in UV Optics for Ultra-Short, Ultra-Intense Coherent Light Sources journal January 2015
Coded aperture imaging with uniformly redundant arrays journal January 1978
Calibration of the modulation transfer function of surface profilometers with binary pseudorandom test standards: expanding the application range to Fizeau interferometers and electron microscopes journal September 2011
Requirements on hard x-ray grazing incidence optics for European XFEL: analysis and simulation of wavefront transformations conference May 2009
Coded aperture imaging in X- and gamma-ray astronomy journal September 1987
X-ray mirror figure correction by differential deposition and off-line metrology journal October 2019
Determination of the Optical Transfer Function Directly from the Edge Spread Function* journal January 1965
Advanced environmental control as a key component in the development of ultrahigh accuracy ex situ metrology for x-ray optics journal October 2015
The instrument transfer function for optical measurements of surface topography journal February 2021
Figuring and smoothing capabilities of elastic emission machining for low-thermal-expansion glass optics
  • Kanaoka, M.; Liu, C.; Nomura, K.
  • Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, Vol. 25, Issue 6 https://doi.org/10.1116/1.2789440
journal November 2007
Method for Obtaining the Transfer Function from the Edge Response Function journal January 1965
Analytic descriptions of parabolic X-ray mirrors journal May 2022
Super-resolution surface slope metrology of x-ray mirrors journal July 2020
Differential deposition technique for figure corrections in grazing-incidence x-ray optics journal October 2011
Binary pseudo-random gratings and arrays for calibration of modulation transfer functions of surface profilometers
  • Barber, Samuel K.; Anderson, Erik D.; Cambie, Rossana
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 616, Issue 2-3 https://doi.org/10.1016/j.nima.2009.11.046
journal May 2010
Measurement of diffraction gratings with a long trace profiler with application for synchrotron beamline gratings conference January 1997
Relative angle determinable stitching interferometry for hard x-ray reflective optics journal April 2005
Correlation methods in optical metrology with state-of-the-art x-ray mirrors
  • Yashchuk, Valeriy V.; Centers, Gary; Gevorkyan, Gevork S.
  • Correlation Optics 2017, Thirteenth International Conference on Correlation Optics https://doi.org/10.1117/12.2305441
conference January 2018
Modulation Transfer Function Measurement Using Three- and Four-bar Targets journal January 1995
Discrepancies between roughness measurements obtained with phase-shifting and white-light interferometry journal January 2005
Design Of A Long Trace Surface Profiler conference April 1987
Grating metrology for X-ray and V-UV synchrotron beamlines at SOLEIL journal February 2019
Two-dimensional differential deposition: figure correction of thin-shell mirror substrates for x-ray astronomy conference September 2015
Diaboloid mirror for a bending magnet beamline conference September 2021
Characterization of surface texture-measuring optical microscopes using a binary pseudo-random array standard conference October 2022
Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror conference September 2007
Calibration of numerical aperture effects in interferometric microscope objectives journal January 1989
Determination of the transfer function for optical surface topography measuring instruments—a review journal March 2013
Multifunctional light beam source for surface slope measuring long trace profilers conference August 2020
Fringe modulation skewing effect in white-light vertical scanning interferometry journal January 2000
Modulation transfer function measurement technique for small-pixel detectors journal January 1992
An ultrahigh-resolution soft x-ray microscope for quantitative analysis of chemically heterogeneous nanomaterials journal December 2020
Linear chirped slope profile for spatial calibration in slope measuring deflectometry journal May 2016
Some issues in SEM-based metrology conference June 1998
A new x-ray optics laboratory (XROL) at the ALS: mission, arrangement, metrology capabilities, performance, and future plans conference September 2014
Binary pseudo-random patterned structures for modulation transfer function calibration and resolution characterization of a full-field transmission soft x-ray microscope journal December 2015
1.5nm fabrication of test patterns for characterization of metrological systems conference March 2017
Characterization and operation optimization of large aperture optical interferometers using binary pseudorandom array test standards conference August 2018
Optics for coherent X-ray applications journal August 2014
Characterization of groove density variation of VLS gratings with ALS XROL LTP-II in different operation modes conference August 2020
Measuring the spatial frequency transfer function of phase-measuring interferometers for laser optics
  • Wolfe, C. Robert; Downie, John D.; Lawson, Janice K.
  • Third International Workshop on Laser Beam and Optics Characterization, SPIE Proceedings https://doi.org/10.1117/12.259943
conference November 1996
Microstitching interferometry for x-ray reflective optics journal May 2003
Binary pseudorandom array test standard optimized for characterization of large field-of-view optical interferometers conference August 2020
Binary pseudorandom grating standard for calibration of surface profilometers journal July 2008
Binary pseudo-random array test standard optimized for characterization of interferometric microscopes conference August 2021
Modulation transfer function of a lens measured with a random target method journal January 1999
Generation of pseudorandom sequences for use in cross‐correlation modulation journal August 1992
Optimal measurement strategies for effective suppression of drift errors journal November 2009
Binary arrays with perfect odd-periodic autocorrelation journal September 1997
Step-height standard for surface-profiler calibration
  • Takacs, Peter Z.; Li, Michelle X.; Furenlid, Karen
  • SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, SPIE Proceedings https://doi.org/10.1117/12.162661
conference December 1993
Upgrade of long trace profiler for characterization of high-precision X-ray mirrors at SPring-8
  • Senba, Y.; Kishimoto, H.; Ohashi, H.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 616, Issue 2-3 https://doi.org/10.1016/j.nima.2009.12.007
journal May 2010
Binary pseudo-random grating as a standard test surface for measurement of modulation transfer function of interferometric microscopes conference September 2007
Analytical expressions of the surface shape of ‘diaboloid’ mirrors conference August 2020
Diaboloidal mirrors: algebraic solution and surface shape approximations journal June 2021
Investigation on lateral resolution of surface slope profilers conference September 2019
Spatially resolved height response of phase-shifting interferometers measured using a patterned mirror with varying spatial frequency journal September 2010
Ex situ metrology and data analysis for optimization of beamline performance of aspherical pre-shaped x-ray mirrors at the advanced light source journal February 2019
Development of nano-roughness calibration standards journal February 2012
Simulations of applications using diaboloid mirrors journal June 2021
Measuring the phase transfer function of a phase-shifting interferometer conference August 2008
Hard x-ray nanofocusing by multilayer Laue lenses journal June 2014
Technique for measuring the groove density of diffraction gratings using the long trace profiler journal July 2003
Calibration, modeling, parameterization, and verification of the instrument transfer function of an interferometric microscope conference October 2022

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