Multi-frequency Phase Unwrap from Noisy Data: Adaptive Least Squares Approach

Details Multi-frequency Phase Unwrap from Noisy Data: Adaptive Least Squares Approach Multi-frequency Phase Unwrap from Noisy Data: Adaptive Least Squares Approach

Apr 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1236..472k&link_type=abstract

INTERNATIONAL CONFERENCE ON ADVANCED PHASE MEASUREMENT METHODS IN OPTICS AND IMAGING. AIP Conference Proceedings, Volume 1236,

Physics

Optics

Particle Interferometry, Phase Measurement, Vibration Measurement, Frequency Measurement, Fourier Transform Optics, Holographic Interferometry, Other Holographic Techniques, Phase Retrieval, Vibrations And Mechanical Waves, Frequency Conversion, Harmonic Generation, Including Higher-Order Harmonic Generation, Fourier Optics

Scientific paper

Multiple frequency interferometry is, basically, a phase acquisition strategy aimed at reducing or eliminating the ambiguity of the wrapped phase observations or, equivalently, reducing or eliminating the fringe ambiguity order. In multiple frequency interferometry, the phase measurements are acquired at different frequencies (or wavelengths) and recorded using the corresponding sensors (measurement channels). Assuming that the absolute phase to be reconstructed is piece-wise smooth, we use a nonparametric regression technique for the phase reconstruction. The nonparametric estimates are derived from a local least squares criterion, which, when applied to the multifrequency data, yields denoised (filtered) phase estimates with extended ambiguity (periodized), compared with the phase ambiguities inherent to each measurement frequency. The filtering algorithm is based on local polynomial (LPA) approximation for design of nonlinear filters (estimators) and adaptation of these filters to unknown smoothness of the spatially varying absolute phase [9]. For phase unwrapping, from filtered periodized data, we apply the recently introduced robust (in the sense of discontinuity preserving) PUMA unwrapping algorithm [1]. Simulations give evidence that the proposed algorithm yields state-of-the-art performance for continuous as well as for discontinues phase surfaces, enabling phase unwrapping in extraordinary difficult situations when all other algorithms fail.

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