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

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

doi:10.1117/12.2523564

21 June 2019 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, Automated Visual Inspection and Machine Vision III; 1106103 (2019) https://doi.org/10.1117/12.2523564
Event: SPIE Optical Metrology, 2019, Munich, Germany

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.

Conference Presentation

Citation Download Citation

Stephan Allgeier, Ulrich Gengenbach, Bernd Köhler, Klaus-Martin Reichert, and Veit Hagenmeyer "Robust phase unwrapping based on non-coprime fringe pattern periods for deflectometry measurements", Proc. SPIE 11061, Automated Visual Inspection and Machine Vision III, 1106103 (21 June 2019); https://doi.org/10.1117/12.2523564

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