Shape measurement of precision components by use of a dynamically tracking interferometric line sensor
Final Report Abstract
The aim of the project was to extend the possibilities of aspherical metrology and to develop a device that can be calibrated traceably with respect to the material measure of length and that can precisely measure rotationally symmetric samples such as spherical or aspherical lenses. In the course of this project some techniques were developed and insights were gained, which are applicable beyond the actual project and have extended the state of the art in the field of optical asphere metrology. Real-time topography determination: The acquisition of the measurement data and the data processing were synchronized by a real-time microcontroller unit. Thus, upon completion of a white light scan (SWLI) or a subaperture measurement employing the optical pathlength modulated refer- ence mirror, the phase map of the sample surface is retrieved and ready for further processing. The data processing and measurement sequence are controlled by an efficient C++ software. Therefore, millions of data points can be obtained in less than one second. This is of interest for the implemen- tation in an industrial environment, e.g. a production line, where the process is real-time controlled based on the measurement results and no additional time is available for an evaluation of the mea- surement data in a separate software or a separate evaluation process. Correction of rotational axis errors: A fundamental problem of measuring rotating objects are errors of the rotational axis, which cannot be distinguished from surface form deviations by the interferometric system. By combination of the line sensor with two interferometric point sensors ori- ented parallel and perpendicular to the rotational axis the surface of a well-known reference object is measured during the axis rotation. The movement errors of the axis appear as deviations from the reference surface and can be detected. Thus, the measured topography of the test object can be corrected accordingly. Stitching algorithm development: The challenge of subaperture stitching algorithms is the align- ment of the subapertures recorded in their local coordinate systems to form a topography in the global coordinate system. Within the scope of this project a cumulative and a global stitching algorithm were developed, which reconstruct the missing piston, tip and tilt information between the subapertures, if the lateral position of the measured values is correctly assigned. The employed global optimization problem uses a combination of cartesian and polar coordinates and combines a Zernike polynomial- based and a cartesian polynomial-based stitching, which enables extended applications. Simulation of the expanded measurement uncertainty: The expanded measurement uncertainty is of great importance for the comparability of the measured values. However, an experimental determination of the expanded measurement uncertainty is problematic due to the large number of samples required. Instead, a virtual experiment is performed simulating the dominant statistical error caused by lateral positioning errors and an estimation of the expanded measurement uncertainty of the topography measurement values is determined. This estimation shows a good agreement with the standard uncertainty from a series of experimental measurements. The use of a Zernike polynomial coefficient representation of the measurement uncertainty allows the documentation of the position dependent measurement uncertainty in a compact, scalable format.
Publications
- “Continuous measurement of optical surfaces using a line-scan interferometer with sinusoidal path length modulation”. Opt. Express (2014). Vol. 22(24), 29,787–29,798
Holger Knell et al.
(See online at https://doi.org/10.1364/OE.22.029787) - “Interferometric sensors based on sinusoidal optical path length modulation”. SPIE Proceedings 9132 (2014). pp. 118 – 127
Holger Knell et al.
(See online at https://doi.org/10.1117/12.2051508) - “Calibration Strategies for a New Fast Line-based Form Measuring System,”. DGaO Proceedings (2015). Vol. 116
Sören Laubach et al.
- Robust interferometric sensors based on sinusoidal phase modulation”. European Optical Society Annual Meeting (EOSAM) (2016)
Peter Lehmann et al.
- “A new form measurement system based on subaperture stitching with a line-scanning interferometer”. Advanced Optical Technologies (2016). Vol. 5(5-6), 415 – 422
Sören Laubach et al.
(See online at https://doi.org/10.1515/aot-2016-0039) - “Interferometrischer Liniensensor zur Formmessung von optischen Oberflächen”. XXX. Messtechnisches Symposium des AHMT (2016). pp. 125–132
Sören Laubach, Gerd Ehret, and Peter Lehmann
(See online at https://doi.org/10.1515/9783110494297-017) - “Interferometrischer Liniensensor zur Formmessung von rotationssymmetrischen optisch glatten Oberflächen”. tm - Technisches Messen (2017). Vol. 84(3), 166 – 173
Sören Laubach et al.
(See online at https://doi.org/10.1515/teme-2016-0067)
