6,565 research outputs found
Phase Unwrapping and One-Dimensional Sign Problems
Sign problems in path integrals arise when different field configurations
contribute with different signs or phases. Phase unwrapping describes a family
of signal processing techniques in which phase differences between elements of
a time series are integrated to construct non-compact unwrapped phase
differences. By combining phase unwrapping with a cumulant expansion, path
integrals with sign problems arising from phase fluctuations can be
systematically approximated as linear combinations of path integrals without
sign problems. This work explores phase unwrapping in zero-plus-one-dimensional
complex scalar field theory. Results with improved signal-to-noise ratios for
the spectrum of scalar field theory can be obtained from unwrapped phases, but
the size of cumulant expansion truncation errors is found to be undesirably
sensitive to the parameters of the phase unwrapping algorithm employed. It is
argued that this numerical sensitivity arises from discretization artifacts
that become large when phases fluctuate close to singularities of a complex
logarithm in the definition of the unwrapped phase.Comment: 42 pages, 16 figures. Journal versio
One shot profilometry using iterative two-step temporal phase-unwrapping
This paper reviews two techniques that have been recently published for 3D
profilometry and proposes one shot profilometry using iterative two-step
temporal phase-unwrapping by combining the composite fringe projection and the
iterative two-step temporal phase unwrapping algorithm. In temporal phase
unwrapping, many images with different frequency fringe pattern are needed to
project which would take much time. In order to solve this problem, Ochoa
proposed a phase unwrapping algorithm based on phase partitions using a
composite fringe, which only needs projecting one composite fringe pattern with
four kinds of frequency information to complete the process of 3D profilometry.
However, we found that the fringe order determined through the construction of
phase partitions tended to be imprecise. Recently, we proposed an iterative
two-step temporal phase unwrapping algorithm, which can achieve high
sensitivity and high precision shape measurement. But it needs multiple frames
of fringe images which would take much time. In order to take into account both
the speed and accuracy of 3D shape measurement, we get a new, and more accurate
unwrapping method based on composite fringe pattern by combining these two
techniques. This method not only retains the speed advantage of Ochoa's
algorithm, but also greatly improves its measurement accuracy. Finally, the
experimental evaluation is conducted to prove the validity of the proposed
method, and the experimental results show that this method is feasible.Comment: 14 pages, 15 figure
Unwrapping phase fluctuations in one dimension
Correlation functions in one-dimensional complex scalar field theory provide
a toy model for phase fluctuations, sign problems, and signal-to-noise problems
in lattice field theory. Phase unwrapping techniques from signal processing are
applied to lattice field theory in order to map compact random phases to
noncompact random variables that can be numerically sampled without sign or
signal-to-noise problems. A cumulant expansion can be used to reconstruct
average correlation functions from moments of unwrapped phases, but points
where the field magnitude fluctuates close to zero lead to ambiguities in the
definition of the unwrapped phase and significant noise at higher orders in the
cumulant expansion. Phase unwrapping algorithms that average fluctuations over
physical length scales improve, but do not completely resolve, these issues in
one dimension. Similar issues are seen in other applications of phase
unwrapping, where they are found to be more tractable in higher dimensions.Comment: 14 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1806.0183
Temporal phase unwrapping using deep learning
The multi-frequency temporal phase unwrapping (MF-TPU) method, as a classical
phase unwrapping algorithm for fringe projection profilometry (FPP), is capable
of eliminating the phase ambiguities even in the presence of surface
discontinuities or spatially isolated objects. For the simplest and most
efficient case, two sets of 3-step phase-shifting fringe patterns are used: the
high-frequency one is for 3D measurement and the unit-frequency one is for
unwrapping the phase obtained from the high-frequency pattern set. The final
measurement precision or sensitivity is determined by the number of fringes
used within the high-frequency pattern, under the precondition that the phase
can be successfully unwrapped without triggering the fringe order error.
Consequently, in order to guarantee a reasonable unwrapping success rate, the
fringe number (or period number) of the high-frequency fringe patterns is
generally restricted to about 16, resulting in limited measurement accuracy. On
the other hand, using additional intermediate sets of fringe patterns can
unwrap the phase with higher frequency, but at the expense of a prolonged
pattern sequence. Inspired by recent successes of deep learning techniques for
computer vision and computational imaging, in this work, we report that the
deep neural networks can learn to perform TPU after appropriate training, as
called deep-learning based temporal phase unwrapping (DL-TPU), which can
substantially improve the unwrapping reliability compared with MF-TPU even in
the presence of different types of error sources, e.g., intensity noise, low
fringe modulation, and projector nonlinearity. We further experimentally
demonstrate for the first time, to our knowledge, that the high-frequency phase
obtained from 64-period 3-step phase-shifting fringe patterns can be directly
and reliably unwrapped from one unit-frequency phase using DL-TPU
Robust Phase Unwrapping by Convex Optimization
The 2-D phase unwrapping problem aims at retrieving a "phase" image from its
modulo observations. Many applications, such as interferometry or
synthetic aperture radar imaging, are concerned by this problem since they
proceed by recording complex or modulated data from which a "wrapped" phase is
extracted. Although 1-D phase unwrapping is trivial, a challenge remains in
higher dimensions to overcome two common problems: noise and discontinuities in
the true phase image. In contrast to state-of-the-art techniques, this work
aims at simultaneously unwrap and denoise the phase image. We propose a robust
convex optimization approach that enforces data fidelity constraints expressed
in the corrupted phase derivative domain while promoting a sparse phase prior.
The resulting optimization problem is solved by the Chambolle-Pock primal-dual
scheme. We show that under different observation noise levels, our approach
compares favorably to those that perform the unwrapping and denoising in two
separate steps.Comment: 6 pages, 4 figures, submitted in ICIP1
A fringe projection profilometry scheme based on embedded speckle patterns and robust principal component analysis
2019 SPIE. Phase unwrapping is one of the key steps for fringe projection profilometry (FPP)-based 3D shape measurements. Conventional spatial phase unwrapping schemes are sensitive to noise and discontinuities, which may suffer from low accuracies. Temporal phase unwrapping is able to improve the reliability but often requires the acquisition of additional patterns, increasing the measurement time or hardware costs. This paper introduces a novel phase unwrapping scheme that utilizes composite patterns consisting of the superposition of standard sinusoidal patterns and randomly generated speckles. The low-rankness of the deformed sinusoidal patterns is studied. This is exploited together with the sparse nature of the speckle patterns and a robust principal component analysis (RPCA) framework is then deployed to separate the deformed fringe and speckle patterns. The cleaned fringe patterns are used for generating the wrapped phase maps using the standard procedures of phase shift profilometry (PSP) or Fourier Transform profilometry (FTP). Phase unwrapping is then achieved by matching the deformed speckle patterns that encode the phase order information. In order to correct the impulsive fringe order errors, a recently proposed postprocessing step is integrated into the proposed scheme to refine the phase unwrapping results. The analysis and simulation results demonstrate that the proposed scheme can improve the accuracy of FPP-based 3D shape measurements by effectively separating the fringe and speckle patterns
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