Global High-Accuracy Intercomparison of Slope Measuring Instruments

Siewert, Frank; Assoufid, Lahsen; Cocco, Daniele; Hignette, O.; Irick, Steven C.; Lammert, Heiner; McKinney, Wayne R.; Ohashi, Haruhiko; Polack, F.; Qian, Shen‐En; Rah, Seungyu; Rommeveaux, Amparo; Schönherr, Veit; Sostero, Giovani; Takacs, Peter Z.; Thomasset, Muriel; Yamauchi, Kazuto; Yashchuk, Valeriy V.; Zeschke, Thomas

doi:10.1063/1.2436160

Cited by 12 publications

(15 citation statements)

References 2 publications

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“…1) with the S3 reference mirror, [23][24][25] and provide a comparison with the corresponding results obtained with the world's best slope measuring instrument, the BESSY NOM. 16 The DLTP experiment with the S3 reference mirror consisted of a total of six overnight measurement series, each composed of multiple scans.…”

Section: Dltp Measurements With Reversing Scanning Directionmentioning

confidence: 99%

Optimal measurement strategies for effective suppression of drift errors

Yashchuk

2009

Review of Scientific Instruments

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Drifting of experimental set-ups with change of temperature or other environmental conditions is the limiting factor of many, if not all, precision measurements. The measurement error due to a drift is, in some sense, in-between random noise and systematic error. In the general case, the error contribution of a drift cannot be averaged out using a number of measurements identically carried out over a reasonable time. In contrast to systematic errors, drifts are usually not stable enough for a precise calibration. Here a rather general method for effective suppression of the spurious effects caused by slow drifts in a large variety of instruments and experimental set-ups isdescribed. An analytical derivation of an identity, describing the optimal measurement strategies suitable for suppressing the contribution of a slow drift described with a certain order polynomial function, is presented. A recursion rule as well as a general mathematical proof of the identity is given. The effectiveness of the discussed method is illustrated with an application of the derived optimal scanning strategies to precise surface slope measurements with a surface profiler.

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Section: Dltp Measurements With Reversing Scanning Directionmentioning

confidence: 99%

Optimal measurement strategies for effective suppression of drift errors

Yashchuk

2009

Review of Scientific Instruments

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“…38,39 Recent publications 38,39,55,56 describe a successful application of ARMA modeling to the experimental surface slope data for a 1280 m spherical reference mirror. 57,58 In the next section, we apply ARMA modeling to the results of slope metrology with the mirror, shown in Fig. 2. …”

Section: Brief Review Of Arma Modelingmentioning

confidence: 99%

Specification of x-ray mirrors in terms of system performance: a new twist to an old plot

2014

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Abstract. In the early 1990s, Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution. We show that these limitations are fatal, especially in the case of highly collimated coherent x-ray beams, like beams from x-ray free electron lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested by Yashchuk and Yashchuk in 2012, based on an autoregressive moving average modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example specific to the x-ray optical systems under design at the European XFEL. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…23,24 The data were obtained with the Advanced Light Source (ALS) developmental long trace profiler (DLTP) 25 and verified in cross-comparison with measurements performed with the HZB/BESSY-II nanometer optical component measuring machine, [26][27][28][29] one of the world's best slope measuring instruments.…”

Section: Autoregressive Moving Average Modelingmentioning

confidence: 99%

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

Yashchuk

Tyurin²,

Tyurina³

2016

Opt. Eng

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of surface metrology of state-of-theart x-ray mirrors as a result of stochastic polishing process," Opt. Eng. 55 (7) Abstract. The design and evaluation of the expected performance of optical systems requires sophisticated and reliable information about the surface topography of 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 <0.1 μrad. The unprecedented high angular resolution and throughput of future x-ray space observatories require high-quality optics of 100 m 2 in total area. The uniqueness of the optics and limited number of proficient vendors make the fabrication extremely time-consuming and expensive, mostly due to the limitations in accuracy and measurement rate of metrology used in fabrication. We continue investigating the possibility of improving metrology efficiency via comprehensive statistical treatment of a compact volume of metrology of surface topography, which is considered the result of a stochastic polishing process. We suggest, verify, and discuss an analytical algorithm for identification of an optimal symmetric time-invariant linear filter model with a minimum number of parameters and smallest residual error. If successful, the modeling could provide 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 of metrology data for optics made by the same vendor and technology. The forecast data are 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.

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Global High-Accuracy Intercomparison of Slope Measuring Instruments

Cited by 12 publications

References 2 publications

Optimal measurement strategies for effective suppression of drift errors

Optimal measurement strategies for effective suppression of drift errors

Specification of x-ray mirrors in terms of system performance: a new twist to an old plot

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

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