Dr. Bernd Köhler Profile

Dr. Bernd Köhler

at Karlsruher Institut für Technologie

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Proceedings Article | 20 June 2021 Presentation + Paper

The effects of pattern screen surface deformation on deflectometric measurements: a simulation study

Stephan Allgeier, Ulrich Gengenbach, Bernd Köhler, Klaus-Martin Reichert, Veit Hagenmeyer

Proceedings Volume 11787, 1178708 (2021) https://doi.org/10.1117/12.2591877

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Phase-measuring deflectometry (PMD) is an optical inspection technique for full-field topography measurements of reflective sample surfaces. The measurement principle relies on the analysis of specific patterns, reflected at the sample surface. Evaluation algorithms often model the respective pattern screen as a planar light source. However, the 3200 pattern screen in our inspection setup exhibits a central bulge of its surface of about 2–3mm. This paper presents a simulation framework for PMD to evaluate the effects of a deformed screen surface. The idea is to simulate image data acquired with screen surface deformations and to examine the effects on the PMD evaluation results. The simulated setup consists of a 3200 pattern screen with an adjustable central bulge height of 0–3mm and two cameras with a field of view (FOV) of approximately 225mm by 172mm on the sample surface. A first experiment examines the reconstruction errors for a planar sample surface if the reconstruction algorithm uses perfect calibration data (i.e. the same parameters used for the simulated image acquisition). The reconstructed surfaces exhibit a tilt with a maximum height difference of 174 μm across the FOV. A second experiment repeats the reconstruction process of the same sample surface, using camera parameters determined in a simulated calibration process. The resulting surfaces possess irregular, wave-like errors with amplitudes of up to 9 μm in the FOV. The presented simulation results reveal the accuracy limits if a deformation model of the pattern screen is not explicitly included in the reconstruction process.

Proceedings Article | 21 August 2020 Presentation + Paper

Reproducibility of two calibration procedures for phase-measuring deflectometry

Stephan Allgeier, Ulrich Gengenbach, Bernd Köhler, Klaus-Martin Reichert, Veit Hagenmeyer

Proceedings Volume 11490, 114900G (2020) https://doi.org/10.1117/12.2567092

KEYWORDS: Calibration, Cameras, Mirrors, Imaging systems, Deflectometry, Image processing, Printing

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Phase-measuring deflectometry is an optical inspection technique for reflective surfaces. It enables absolute, quantitative surface measurements, given a calibrated measurement setup. Two general calibration approaches can be found in literature: First, the stepwise approach uses a calibration pattern and determines internal camera parameters and external geometrical parameters in separate, consecutive steps. Second, the holistic approach optimizes all parameters collectively, based on deflectometric measurements of a calibration mirror. Whereas both approaches have been compared regarding the accuracy of subsequent surface measurements, the present contribution focuses on experimental examination of their reproducibility. In experiment E1, we assess the parameter variability by repeating both calibration procedures ten times. In an additional experiment E2, we repeat all calibration measurements related to a mirror/pattern position ten times in a row before rearranging the mirror/pattern, in order to examine the purely noise-related parameter variability. Finally, we calculate the coordinate variability of a set of world points projected onto the image planes of the calibrated cameras. The measured variability is consistently higher in E1 than in E2 (average ratio: 3.2). Unexpectedly, in both experiments, the external parameter variability also turns out to be higher for the holistic approach compared to stepwise calibration (average ratio: 2.3). This is of importance, since the holistic approach is known from literature to be more accurate than the stepwise approach, regarding their respective application to surface measurements. The image coordinate variability is comparable for both calibration approaches with an average of 0.84 and 0.21 camera pixels for E1 and E2, respectively.

Proceedings Article | 21 June 2019 Presentation + Paper

Robust phase unwrapping based on non-coprime fringe pattern periods for deflectometry measurements

Stephan Allgeier, Ulrich Gengenbach, Bernd Köhler, Klaus-Martin Reichert, Veit Hagenmeyer

Proceedings Volume 11061, 1106103 (2019) https://doi.org/10.1117/12.2523564

KEYWORDS: Fringe analysis, Phase measurement, Cameras, Deflectometry, Printing, Phase retrieval, Inspection, Additive manufacturing

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Phase-measuring deflectometry is a technique for non-contact inspection of reflective surfaces. A camera setup captures the reflection of a sine-modulated fringe pattern shifted across a screen; the location-dependent measured phase effectively encodes the screen coordinates. As the used fringe patterns are much narrower than the screen dimension, the resulting phase maps are wrapped. The number-theoretical solution uses the Chinese remainder theorem to calculate an unwrapped phase map from repeated measurements with coprime fringe widths. The technique is highly susceptible to phase noise, i.e. small deviations of the measured phase values generally lead to unwrapped phase values with large errors. We propose a modification and show how non-coprime period widths make phase unwrapping robust against phase noise. Measurements with two non-coprime fringe period widths introduce the opportunity to discriminate between “legal” measured phase value pairs, that potentially originate from noise-free measurements, and “illegal” phase value pairs, that necessarily result from noise-affected measurements. Arranged as a matrix, the legal measurements lie on distinct diagonals. This insight not only allows to determine the legality of a measurement, but also to provide a correction by looking for the closest legal matrix entry. We present an experimental comparison of the resulting phase maps with reference phase maps. The presented results include descriptive statistics on the average rate of illegal phase measurements as well as on the deviation from the reference. The measured mean absolute deviation decreases from 1.99 pixels before correction to 0.21 pixels after correction, with a remaining maximum absolute deviation of 0.91 pixels.

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