Absolute determination of a large mirror surface from spatial gradients using a coordinate measuring machine

Sebastian J. Fischer Calderón; Rostyslav Mastylo; Christian Schober; Christof Pruss; Ingo Ortlepp; Guido Straube; Eberhard Manske

doi:10.1117/12.2675734

4 October 2023 Absolute determination of a large mirror surface from spatial gradients using a coordinate measuring machine

Sebastian J. Fischer Calderón, Rostyslav Mastylo, Christian Schober, Christof Pruss, Ingo Ortlepp, Guido Straube, Eberhard Manske

Author Affiliations +

Proceedings Volume 12672, Applied Optical Metrology V; 1267205 (2023) https://doi.org/10.1117/12.2675734
Event: SPIE Optical Engineering + Applications, 2023, San Diego, California, United States

Abstract

This investigation proposes a method for absolute surface determination in a coordinate measuring machine (CMM) with a planar extension of 200 x 200 mm² which is based on the measurement of two spatial gradient fields. The gradient field data was obtained by measuring a test mirror in two equidistant shifted positions along two orthogonal axes while the reference mirror stayed in a steady position. The comparison of experimental data measured in an area of 192 × 192 mm² showed a small root-mean-square deviation of 5.3 nm between the reconstruction result and a regular measurement result. For an a priori estimation of the influence of experimental error sources on the reconstruction deviation, simulations of the measurement process were carried out. Alongside determining the optimal measurement strategy, the focus was investigating positional and orientational deviations of the test surface caused by the shifting motions. While the translational deviations have a subordinate effect, the simulated results show that small orientation deviations around the motion axes cause high reconstruction deviations. To eliminate the motion-induced share of the gradient fields orientation a separation from the topography intrinsic share, which has to remain part of the data, is necessary. This is achieved by the combination of the high-precision design of the mechanical shifting stage and the implementation of an additional boundary condition in the data processing using a least square algorithm.

Conference Presentation

(2023) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Sebastian J. Fischer Calderón, Rostyslav Mastylo, Christian Schober, Christof Pruss, Ingo Ortlepp, Guido Straube, and Eberhard Manske "Absolute determination of a large mirror surface from spatial gradients using a coordinate measuring machine", Proc. SPIE 12672, Applied Optical Metrology V, 1267205 (4 October 2023); https://doi.org/10.1117/12.2675734

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