A Probabilistic Approach for Spatio-Temporal Phase Unwrapping in Multi-Frequency Phase-Shift Coding

Multi-frequency techniques with temporally encoded pattern sequences are used in phase-measuring methods of 3D optical metrology to suppress phase noise but lead to ambiguities that can only be resolved by phase unwrapping. However, classical phase unwrapping methods do not use all the information t...

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Bibliographic Details
Published in:IEEE access 2022, Vol.10, p.52377-52397
Main Authors: Uhlig, David, Heizmann, Michael
Format: Article
Language:English
Subjects:
Cameras
circular statistics
Decoding
deflectometry
Encoding
Lighting
Measurement methods
Modelling
Optimization
Phase measurement
Phase noise
Phase-shifting
Pixels
Probabilistic logic
Probability theory
profilometry
Statistical analysis
structured illumination
Surface reconstruction
Temporal phase unwrapping
Uncertainty
von Mises distribution
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Summary:Multi-frequency techniques with temporally encoded pattern sequences are used in phase-measuring methods of 3D optical metrology to suppress phase noise but lead to ambiguities that can only be resolved by phase unwrapping. However, classical phase unwrapping methods do not use all the information to unwrap all measurements simultaneously and do not consider the periodicity of the phase, which can lead to errors. We present an approach that optimally reconstructs the phase on a pixel-by-pixel basis using a probabilistic modeling approach. The individual phase measurements are modeled using circular probability densities. Maximizing the compound density of all measurements yields the optimal decoding. Since the entire information of all phase measurements is simultaneously used and the wrapping of the phases is implicitly compensated, the reliability can be greatly increased. In addition, a spatio-temporal phase unwrapping is introduced by a probabilistic modeling of the local pixel neighborhoods. This leads to even higher robustness against noise than the conventional methods and thus to better measurement results.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2022.3174121