18 June 2007 Stability analysis for the TMS method: Influence of high spatial frequencies
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The Traceable Multi Sensor (TMS) system is a scanning system for the measurement of the topography of large optical surfaces. The system uses a compact interferometer with an aperture of some millimetres to realize multiple distance sensors and an autocollimator for the angle measurement. In contrast to common stitching techniques, the systematic sensor errors are calculated in addition to the entire topography by the TMS algorithm. Additionally, piston and tilt at each position of the interferometer are determined by the algorithm. An essential requirement for the algorithm is the exact lateral positioning of the sensor at given locations. The goal of this paper is to investigate the influence of a class of error sources on the resulting topography estimation using computer simulations. The errors of this class result in inexact measurement positions of the distance sensors. Especially the lateral positioning errors of the scanning stage lead to increasing errors for short wavelengths. For topography wavelengths below 3mm with an amplitude of 100nm the resulting topography error increases to 3nm and more. For longer wavelengths the positioning errors are no longer the dominant error source and the root mean square error of the resulting topography is approximately 1 nm for positioning errors with a standard deviation of 5 &mgr;m. The pixel distance error and distortion of the interferometer strongly influence the topography measurement of specimens with large deviations from a plane. The simulations show that for a topography with a peak to valley of 50 &mgr;m the root mean square error of the reconstructed topography is below 10 nm. Furthermore, a possibility to compensate the lateral positioning error of the scanning stage is presented which makes the TMS method nearly independent of positioning errors of the scanning stage. As a consequence, it is possible to use systems of non equidistant distance sensors whose lateral distances are independent of the positioning interval.
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Axel Wiegmann, Axel Wiegmann, Clemens Elster, Clemens Elster, Ralf D. Geckeler, Ralf D. Geckeler, Michael Schulz, Michael Schulz, "Stability analysis for the TMS method: Influence of high spatial frequencies", Proc. SPIE 6616, Optical Measurement Systems for Industrial Inspection V, 661618 (18 June 2007); doi: 10.1117/12.726116; https://doi.org/10.1117/12.726116

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