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Proceedings Paper

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

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.

Paper Details

Date Published: 21 June 2019
PDF: 10 pages
Proc. SPIE 11061, Automated Visual Inspection and Machine Vision III, 1106103 (21 June 2019); doi: 10.1117/12.2523564
Show Author Affiliations
Stephan Allgeier, Karlsruher Institut für Technologie (Germany)
Ulrich Gengenbach, Karlsruher Institut für Technologie (Germany)
Bernd Köhler, Karlsruher Institut für Technologie (Germany)
Klaus-Martin Reichert, Karlsruher Institut für Technologie (Germany)
Veit Hagenmeyer, Karlsruher Institut für Technologie (Germany)

Published in SPIE Proceedings Vol. 11061:
Automated Visual Inspection and Machine Vision III
Jürgen Beyerer; Fernando Puente León, Editor(s)

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