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DFG project: Form measurement of precision components with a dynamically tracked interferometric line sensor

Optical and mechanical precision components require sub-micrometer precision when it comes to form tolerances. Optical procedures are often used to measure the form of the surface. Within the scope of a joint DFG project, a new optical measurement technique was developed, set up and tested in cooperation with the University of Kassel (Germany) in order to measure rotationally symmetric surfaces.

The aim of this project was to enhance the possibilities of asphere metrology and to develop a measuring instrument whose calibration can be traced to the material measure of length. It also aims to calibrate rotationally symmetric surfaces under test (SUTs) such as spherical or aspherical lenses. Important techniques were developed and findings gained over the course of the project. These techniques and findings are applicable beyond the scope of this particular project and have enhanced the state of the art of science in the field of optical asphere metrology.

During the measurement, the SUT is spun around its rotational axis and simultaneously scanned by means of an interferometric line sensor. The line sensor is oriented radially and records an annular strip of the surface. It is used both as a depth-scanning white-light interferometer (SWLI) and as a phase-shifting interferometer (PSI) with periodical optical path length modulation [1 7]. The white-light depth scan allows the line sensor to be tracked at a constant distance from the SUT’s surface, and the phase evaluation of the path-length-modulated interference pattern allows the annular subapertures to be reconstructed with high measurement accuracy. Moreover, the measurement system is equipped with two point-measuring interferometric sensors that are used to compensate for motion errors of the rotational axis spinning the SUT [8 10]. A stitching algorithm based on a global optimization problem is used to reconstruct the global topography of the SUT from the annular subapertures [11 13]. Using both the measured annular subapertures and the position information, the relative position and tilt of the subapertures are corrected relatively to each other. Figure 1 b) shows an example of rings that have not yet been merged. By means of virtual experiments, an estimate of the expanded measurement uncertainty was determined; this value is in good agreement with experimentally determined uncertainties [13].

Fig. 1: a) Photo of a copper SUT (D = 300 mm) (1), in PTB’s measuring system with an interferometric line sensor (2); with a point sensor (3) to register a possible wobbling of the rotation stage, and a point sensor (4) to control the concentric run of the SUT during rotation. b) Simulated subaperture rings of a spherical SUT in local coordinates. Tilting of the interferometer causes the loss of the tilt information. The total tilt can be reconstructed by means of the information from the overlapping areas or by rearranging the rings in a global optimization problem.


DFG project website: https://gepris.dfg.de/gepris/projekt/209933375?language=en

Project partner: http://www.uni-kassel.de/eecs/en/faculties/messtechnik/homepage.html

Selected publications

[1] O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement”, Applied Optics 25, 3137-3140, 1986, doi.org/10.1364/AO.25.003137

[2] O. Sasaki and H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry”, Applied Optics 25, 3152-3158, 1986, doi.org/10.1364/AO.25.003152

[3] U. Minoni, E. Sardini, E. Gelmini, F. Docchio and D. Marioli, “A high-frequency sinusoidal phase-modulation interferometer using an electro-optic modulator: Development and evaluation”, Review of Scientific Instruments 62(11), 2579-2583, 1991, doi: 10.1063/1.1142233

[4] P. Lehmann, M. Schulz and J. Niehues, “Fiber optic interferometric sensor based on mechanical oscillation”, SPIE Proceedings 7389, 738915, 2009, doi.org/10.1117/12.827510

[5] H. Knell, P. Lehmann, „High speed measurement of specular surfaces on carrier fringe patterns in a line scan Michelson interferometer setup”, Proceedings of SPIE 8788, 87880R, 2013, doi.org/10.1117/12.2020121

[6] H. Knell, S. Laubach, G. Ehret, P. Lehmann, „Continuous measurement of optical surfaces using a line-scan interferometer with sinusoidal path length modulation”, Optics Express 22, 29787-29798, 2014, doi.org/10.1364/OE.22.029787

[7] H. Knell, M. Schake, M. Schulz, P. Lehmann, „Interferometric sensors based on sinusoidal optical path length modulation”, Proceedings of SPIE 9132, 91320l, 2014, doi.org/10.1117/12.2051508

[8] Sören Laubach, Gerd Ehret, Jörg Riebling, Peter Lehmann, "Combination of a fast white-light interferometer with a phase shifting interferometric line sensor for form measurements of precision components," Proc. SPIE 10329, 2017, doi.org/10.1117/12.2269520

[9] Joerg Riebeling, Gerd Ehret, Peter Lehmann, "Optical form measurement system using a line-scan interferometer and distance measuring interferometers for run-out compensation of the rotational object stage," Proc. SPIE 11056, 2019, doi.org/10.1117/12.2526033

[10] Riebeling, J., Wellem, I., Lehmann, P., & Ehret, G., “Erfassung von Formabweichungen rotierender optischer Flächen mit linien-scannendem Interferometer, Echtzeitauswertung und Achsabweichungskompensation”, tm - Technisches Messen, 86(s1), 92-96., 2019, doi.org/10.1515/teme-2019-0049

[11] Markus Schake, Gerd Ehret, "Annular subaperture stitching interferometry with planar reference wavefront for measurement of spherical and aspherical surfaces," Proc. SPIE 11523, Optical Technology and Measurement for Industrial Applications 2020, 2020, doi.org/10.1117/12.2574754

[12] Markus Schake and Gerd Ehret, “Machine learning based fitting of Zernike polynomials for ASSI,”. DGaO-Proceedings Vol. 121, 2020. www.dgao-proceedings.de/download/121/121_a31.pdf

[13] Markus Schake, Jörg Riebeling, Gerd Ehret, "Form deviations caused by lateral displacement errors in annular subaperture stitching interferometry," Opt. Eng. 59(12) 124105, 2020, doi.org/10.1117/1.OE.59.12.124105


Dr.-Ing. Markus Schake
Phone: +49 531 592-4257
E-Mail: markus.schake(at)ptb.de

Dr.-Ing. Gerd Ehret
Phone: +49 531 592-4220
E-Mail: gerd.ehret(at)ptb.de