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Mathematical Modelling and Data Analysis

Department 8.4

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Title: Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments
Author(s): A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz and C. Elster
Journal: Precision Engineering
Year: 2011
Volume: 35
Issue: 2
Pages: 183--190
DOI: 10.1016/j.precisioneng.2010.08.007
ISSN: 01416359
Web URL: http://www.sciencedirect.com/science/article/pii/S014163591000125X
Keywords: Interferometry,Simulation,Stitching,Virtual experiment,virtual experiment
Tags: 8.42,Form,SimOpt
Abstract: We present a virtual experiment for the accuracy assessment of the sub-aperture interferometric measurement of a synchrotron mirror involving several thousand sub-aperture topographies. The virtual experiment simulates the measurement process and accounts for the influence of positioning device errors, interferometer errors, non-perfect calibration of machine geometry as well as errors in the interferometer reference. Two principles are considered for reconstructing the form of a test specimen from the conducted sub-aperture topographies, a stitching procedure and a direct measurement method. The virtual experiments are applied to the task of absolute form measurement (including its radius of curvature) of a synchrotron mirror with a length of 30cm, a width of 4cm, a maximum curvature of about 44mm−1 and a peak-to-valley of 5mm. As a result, reconstruction accuracies can be expected to be in the range of 100nm when the stitching method is applied, which outperforms the direct measurement method by a factor of about 3.

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