Phase Discontinuities Research Articles

Guiding near-source elastic waves in a semi-infinite medium.

In this work, we propose elastic metamaterials with phase discontinuities to steer the propagation of near-source bulk waves in a semi-infinite elastic medium. Our design exploits an array of embedded subwavelength resonators with tailored masses to attain a complete phase shift spanning [Formula: see text]. This phase control allows for diverse wave functionalities, such as directional refraction and energy focusing. Through the use of dispersion diagrams and the generalized Snell's law, along with a multiple scattering formulation, we analytically demonstrate the effectiveness of our design in achieving the desired wavefront manipulation. The proposed design has the potential to advance the field of guiding elastic waves using metamaterials and find practical applications in areas such as isolating ground-borne vibrations in densely urbanized regions and energy harvesting. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Measurement and advanced data post-processing of proton resonance frequency shift in 7 T MRI to obtain local temperature in a tissue-mimicking phantom

Abstract The radio-frequency (RF) transmit power deposition in tissue during magnetic resonance imaging (MRI) at ultra-high fields, i.e. B 0 ≥ 7 T, is a major challenge for pulse sequences requesting large flip angles. The absorbed RF energy can pose safety risk to patients as it is rising temperature in the tissue. The temperature can be accessed using MRI itself via the proton-resonance frequency (PRF) shift technique, which at low B 0 has been shown a valid MR thermometry method. In this paper, we explore the applicability of the PRF method to the assessment of local temperature in 7 T MRI procedures. To this end, we built a phantom filled with a material presenting electrical conductivity and permittivity close to muscle tissue. Tubes filled with oil were placed nearby the phantom to observe the time dependent B 0 drift. MRI phase images were acquired by gradient-echo (GRE) sequences at time points between spin-echo sequences with large flip angle allowing for a continuous assessment of the temperature during a 114 min RF-heating experiment. All acquired phase images were post-processed with attention to the time dependent instability of B 0, and, in addition, to potential spatial and temporal phase discontinuities, known as wraps. In this paper, we present a strategy to analyze and to unfold these phase wraps for large measurement fields and long acquisition times. It is shown that the PRF shift method is beneficial for the assessment of temperature at 7 T MRI. The temperature maps for axial and coronal planes display a temperature increase of approximately 3.5 °C during the time of the RF-heating experiment. Overall it is shown that B 0-drift correction and, importantly, the spatio-temporal unwrapping are an indispensable part of post-processing.

Keck Primary Mirror Closed-loop Segment Control Using a Vector-Zernike Wavefront Sensor

We present the first on-sky segmented primary mirror closed-loop piston control using a Zernike wavefront sensor (ZWFS) installed on the Keck II telescope. Segment cophasing errors are a primary contributor to contrast limits on Keck and will be necessary to correct for the next generation of space missions and ground-based extremely large telescopes, which will all have segmented primary mirrors. The goal of the ZWFS installed on Keck is to monitor and correct primary mirror cophasing errors in parallel with science observations. The ZWFS is ideal for measuring phase discontinuities such as segment cophasing errors and is one of the most sensitive WFSs, but has limited dynamic range. The vector-ZWFS at Keck works on the adaptive-optics-corrected wavefront and consists of a metasurface focal plane mask that imposes two different phase shifts on the core of the point-spread function to two orthogonal light polarizations, producing two pupil images. This design extends the dynamic range compared with the scalar ZWFS. The primary mirror segment pistons were controlled in closed loop using the ZWFS, improving the Strehl ratio on the NIRC2 science camera by up to 10 percentage points. We analyze the performance of the closed-loop tests, the impact on NIRC2 science data, and discuss the ZWFS measurements.

Noise reduction of electron holography observations for a thin-foiled Nd-Fe-B specimen using the wavelet hidden Markov model

In this study, we investigate the effectiveness of noise reduction in electron holography, based on the wavelet hidden Markov model (WHMM), which allows the reasonable separation of weak signals from noise. Electron holography observations from a Nd2Fe14B thin foil showed that the noise reduction method suppressed artificial phase discontinuities generated by phase retrieval. From the peak signal-to-noise ratio, it was seen that the impact of denoising was significant for observations with a narrow spacing of interference fringes, which is a key parameter for the spatial resolution of electron holography. These results provide essential information for improving the precision of electron holography studies.

Efficient and robust phase unwrapping method based on SFNet

Phase unwrapping is a crucial step in obtaining the final physical information in the field of optical metrology. Although good at dealing with phase with discontinuity and noise, most deep learning-based spatial phase unwrapping methods suffer from the complex model and unsatisfactory performance, partially due to simple noise type for training datasets and limited interpretability. This paper proposes a highly efficient and robust spatial phase unwrapping method based on an improved SegFormer network, SFNet. The SFNet structure uses a hierarchical encoder without positional encoding and a decoder based on a lightweight fully connected multilayer perceptron. The proposed method utilizes the self-attention mechanism of the Transformer to better capture the global relationship of phase changes and reduce errors in the phase unwrapping process. It has a lower parameter count, speeding up the phase unwrapping. The network is trained on a simulated dataset containing various types of noise and phase discontinuity. This paper compares the proposed method with several state-of-the-art deep learning-based and traditional methods in terms of important evaluation indices, such as RMSE and PFS, highlighting its structural stability, robustness to noise, and generalization.

Mirrored transformation optics.

A mirrored transformation optics (MTO) approach is presented to overcome the material mismatch in transformation optics. It makes good use of the reflection behavior and introduces a mirrored medium to offset the phase discontinuities. Using this approach, a high-performance planar focusing lens of transmission type is designed, which has a larger concentration ratio than the other focusing lens obtained by the generalized Snell's law. The MTO will not change any functionality of the original lens and has promising potential applications in imaging and light energy harvesting.

Weakly supervised phase unwrapping for single-camera fringe projection profilometry

Phase unwrapping is essential in fringe projection profilometry (FPP). FPP's primary focus is to simultaneously realize high-speed, high-precision three-dimensional (3D) reconstruction. The dual-frequency hierarchical temporal phase unwrapping method (DF-TPU) technique is one prominent technique for accomplishing this goal. However, phase errors are inevitable and typically limit the DF-TPU approach's maximal period number, reducing reconstruction accuracy. The fully supervised approaches based on deep learning can unwrap dual-frequency phase maps of single-camera FPP systems but require accurate labels of high-frequency absolute phase. This study proposes a novel deep learning phase unwrapping scheme suited to single-camera FPP setups. Without the need for accurate labels corresponding to the high-frequency phase maps, supervisory signals are extracted from the high-frequency phase map, the one-period phase map, and the geometry constraint to guide the training of the phase unwrapping network. This training is a weakly supervised learning, which makes the time-consuming and expertise-demanding precise labeling unnecessary. Data collected in multiple real-world circumstances, such as motion blur, isolated objects, non-uniform reflectivity, and phase discontinuities, are used to validate the effectiveness of this weakly supervised method. Experimental results demonstrate that the proposed method outperforms the fully supervised and conventional DF-TPU methods in terms of depth accuracy and measurement efficiency in terms of fringe pattern number.

Phase unwrapping for phase imaging using the plug-and-play proximal algorithm.

Phase unwrapping (PU) is essential for various scientific optical applications. This process aims to estimate continuous phase values from acquired wrapped values, which are limited to the interval (-π,π]. However, the PU process can be challenging due to factors such as insufficient sampling, measurement errors, and inadequate equipment calibration, which can introduce excessive noise and unexpected phase discontinuities. This paper presents a robust iterative method based on the plug-and-play (PnP) proximal algorithm to unwrap two-dimensional phase values while simultaneously removing noise at each iteration. Using a least-squares formulation based on local phase differences and reformulating it as a partially differentiable equation, it is possible to employ the fast cosine transform to obtain a closed-form solution for one of the subproblems within the PnP framework. As a result, reliable phase reconstruction can be achieved even in scenarios with extremely high noise levels.

Waveguide holography for 3D augmented reality glasses

Near-eye displays are fundamental technology in the next generation computing platforms for augmented reality and virtual reality. However, there are remaining challenges to deliver immersive and comfortable visual experiences to users, such as compact form factor, solving vergence-accommodation conflict, and achieving a high resolution with a large eyebox. Here we show a compact holographic near-eye display concept that combines the advantages of waveguide displays and holographic displays to overcome the challenges towards true 3D holographic augmented reality glasses. By modeling the coherent light interactions and propagation via the waveguide combiner, we demonstrate controlling the output wavefront using a spatial light modulator located at the input coupler side. The proposed method enables 3D holographic displays via exit-pupil expanding waveguide combiners, providing a large software-steerable eyebox. It also offers additional advantages such as resolution enhancement capability by suppressing phase discontinuities caused by pupil replication process. We build prototypes to verify the concept with experimental results and conclude the paper with discussion.

Linear Regression for Phase Discontinuity Compensation in a Stepped-Carrier OFDM Radar

Linear Regression for Phase Discontinuity Compensation in a Stepped-Carrier OFDM Radar

Removal of phase residues in electron holography.

Electron holography provides quantitative phase information regarding the electromagnetic fields and the morphology of micro- to nano-scale samples. A phase image reconstructed numerically from an electron hologram sometimes includes phase residues, i.e. origins of unremovable phase discontinuities, which make it much more difficult to quantitatively analyze local phase values. We developed a method to remove the residues in a phase image by a combination of patching local areas of a hologram and denoising based on machine learning. The small patches for a hologram, which were generated using the spatial frequency information of the own fringe patterns, were pasted at each residue point by an algorithm based on sparse modeling. After successive phase reconstruction, the phase components with no dependency on the vicinity were filtered out by Gaussian process regression. We determined that the phase discontinuities that appeared around phase residues were removed and the phase distributions of an atomic resolution phase image of a Pt nanoparticle were sufficiently restored.

Phase Transformation Under High Pressure Radiates as a Double Couple Deep Earthquake

AbstractDeep‐focus earthquakes (DFEs) originating at the Mantle‐Transition‐Zone (MTZ) (400–700 km) have a Double Couple (DC) radiation pattern similar to crustal earthquakes; however, their mechanism is different and governed by high pressures (15–25 GPa) at nucleation depths. We present a model of nucleation and growth of regions of phase transformation, undergoing a sudden reduction in volume (5%–10%), “volume collapse.” Successive symmetry‐breaking instabilities minimize the energy spent to move the boundary of phase discontinuity and a collapsing volume expands as a flattened pancake‐like self‐similarly expanding Eshelby ellipsoidal inclusion. At the vanishing of the M integral, expressing the balance of flows of energy across the inclusion boundary, at a critical value of the pressure, an arbitrarily small inclusion nucleates and grows at constant potential energy driven by the pressure acting on the change in volume. The inclusion develops shear eigenstrains that decompose into two DC, placing one on the basal plane to radiate without energy losses. The symmetric volume collapse radiates out as an anti‐symmetric DC, and the radiated energy is obtained as the “excess energy,” of the ambient pressure acting on the “volume collapse,” reduced by the energy consumed for the growth of the pancake surfaces, with a “pressure drop” (p0 − pcr) driving the expansion emitting a DC, even under full isotropy. The solution explains some features of the DFEs, (a) the DC radiation, (b) their large energies (the Mw 8.3 Okhotsk earthquake [2013]), (c) the absence of volumetric radiation, and (d) why they can originate in the MTZ, a long‐standing open problem.

Ultrafast Time Dynamics of Plasmonic Fractional Orbital Angular Momentum.

The creation and manipulation of optical vortices, both in free space and in two-dimensional systems such as surface plasmon polaritons (SPPs), has attracted widespread attention in nano-optics due to their robust topological structure. Coupled with strong spatial confinement in the case of SPPs, these plasmonic vortices and their underlying orbital angular momentum (OAM) have promise in novel light-matter interactions on the nanoscale with applications ranging from on-chip particle manipulation to tailored control of plasmonic quasiparticles. Until now, predominantly integer OAM values have been investigated. Here, we measure and analyze the time evolution of fractional OAM SPPs using time-resolved two-photon photoemission electron microscopy and near-field optical microscopy. We experimentally show the field's complex rotational dynamics and observe the beating of integer OAM eigenmodes at fractional OAM excitations. With our ability to access the ultrafast time dynamics of the electric field, we can follow the buildup of the plasmonic fractional OAM during the interference of the converging surface plasmons. By adiabatically increasing the phase discontinuity at the excitation boundary, we track the total OAM, leading to plateaus around integer OAM values that arise from the interplay between intrinsic and extrinsic OAM.

A U-Net Approach for InSAR Phase Unwrapping and Denoising

The interferometric synthetic aperture radar (InSAR) imaging technique computes relative distances or surface maps by measuring the absolute phase differences of returned radar signals. The measured phase difference is wrapped in a 2π cycle due to the wave nature of light. Hence, the proper multiple of 2π must be added back during restoration and this process is known as phase unwrapping. The noise and discontinuity present in the wrapped signals pose challenges for error-free unwrapping procedures. Separate denoising and unwrapping algorithms lead to the introduction of additional errors from excessive filtering and changes in the statistical nature of the signal. This can be avoided by joint unwrapping and denoising procedures. In recent years, research efforts have been made using deep-learning-based frameworks, which can learn the complex relationship between the wrapped phase, coherence, and amplitude images to perform better unwrapping than traditional signal processing methods. This research falls predominantly into segmentation- and regression-based unwrapping procedures. The regression-based methods have poor performance while segmentation-based frameworks, like the conventional U-Net, rely on a wrap count estimation strategy with very poor noise immunity. In this paper, we present a two-stage phase unwrapping deep neural network framework based on U-Net, which can jointly unwrap and denoise InSAR phase images. The experimental results demonstrate that our approach outperforms related work in the presence of phase noise and discontinuities with a root mean square error (RMSE) of an order of magnitude lower than the others. Our framework exhibits better noise immunity, with a low average RMSE of 0.11.

Accurate multi-target vital signs detection method for FMCW radar

The frequency modulated continuous wave (FMCW) radar has gained increasing attention in the field of noncontact vital signs detection. However, the detection of the target chest’s range bin is easily influenced by various clutters and interferences, posing numerous challenges to vital signs detection, particularly in scenarios involving multiple targets This paper proposes an anti-clutter and interference method that combinates moving target indication (MTI), constant false alarm rate (CFAR) detection, K-means clustering, and local search with moving average filtering to accurately detect multi-target vital signs. Moreover, it employs the extended differentiate and cross multiply algorithm for phase demodulation to overcome phase discontinuity. The proposed method is evaluated using a 77 GHz FMCW radar in an office environment. Experimental results demonstrate that the proposed method can effectively detect multiple targets amidst various clutters and small random body movement, yielding mean accuracies of 94.2 % and 95.1 % for breathing rate and heartbeat rate, respectively.

GPS PPP-AR frequency transfer and its application for comparing atomic fountain primary frequency standards between NRC and PTB

We report on the first characterization of the frequency transfer performance of the GPS precise point positioning with carrier-phase integer ambiguity resolution (PPP-AR) implemented by the Natural Resources Canada (NRCan) online service CSRS-PPP. We show that continuous PPP-AR links of multiple days can be formed by carefully fixing the day boundary phase discontinuity. The stability of the links can reach and (Allan deviation) at 1 d and 7 d averaging times, respectively, and mid to low 10−17 at 20 d–30 d. We compared the atomic fountain primary frequency standards (PFS) between NRC in Ottawa, Canada and PTB in Braunschweig, Germany for 135 d via GPS PPP-AR and precise point positioning links. The NRC and PTB PFS agree within a few parts in 1016, which is well below the combined systematic uncertainty. It is expected that with uncertainty at 10−17, the PPP-AR links will become a powerful tool for remote comparisons of atomic optical clocks, essential for the future redefinition of the SI second.

A coupled finite element formulation for the modeling of freezing processes within the Theory of Porous Media using a discontinuous approximation for the volume fraction ice

AbstractThis work presents a multi‐phase approach to model freezing processes within a coupled finite element formulation using the Theory of Porous Media (TPM), see also [1]. The focus of the study is to enhance the numerical stability for the volume fraction ice as is it highly sensitive to phase discontinuities. To address this issue, a discontinuous approximation is employed for the volume fraction ice while the remaining degrees of freedom are still continuously approximated. As a result, the corresponding degrees of freedom are independently solved for each element, as the element nodes are not interconnected with other elements. Academic examples are provided within a standard Galerkin procedure to highlight the optimization effect, comparing the results obtained with a continuous and discontinuous approximation for the volume fraction ice. Additionally, the implementation of the discontinuous approximation allows for the application of static condensation, resulting in reduced computation time.

Off‐Resonance Spin‐Locked Metasurfaces Empowered by Quasi‐Bound States in the Continuum for Optical Analog Computing

AbstractMetasurfaces with engineered phase discontinuity offer extra degrees of freedom to control the angular spectrum characteristics of light and can be used to construct planar metalenses with a variety of anomalous functionalities. Here, off‐resonance spin‐locked metasurfaces empowered by quasi‐bound states in the continuum are reported, in order to achieve a concept of hybridized analog computing over both frequency and angular spectrum domains. By introducing two types of asymmetric degrees, high‐quality resonance empowered by the symmetry‐protected bound states in the continuum emerges in an image‐coupled resonance system. Such high‐quality resonance can be excited in a broadband spin‐locked scattering spectrum, promising required functions for scalar multiplication and convolution operations. Off‐resonance meta‐splitter and meta‐deflector are experimentally implemented to verify the concept of hybridized analog computing in two domains, as well as providing an advantage of high robustness against scattering interference from environment. Optical spatial‐frequency processing by engineering the off‐resonance metasurfaces is also discussed. The findings provide an alternative approach toward optical analog computing over multi‐domains.

Broadband absorption and asymmetric reflection of flexural wave by deep-subwavelength lossy elastic metasurface

The elastic metasurface with phase discontinuities has received much attention for realizing diverse wave steering applications. To date, the elastic metasurfaces capable of realizing the multi-reflection-enhanced absorption of flexural waves at a deep subwavelength scale have rarely been reported. Here, we propose a novel concept of deep-subwavelength lossy elastic metasurface (DLEM) composed of gradient lossy force-moment resonators with a small amount of loss. Based on the diffraction theorem, we provide an accurate approach for predicting diffracted flexural wave behaviors considering the coupling of flexural and longitudinal diffraction modes in a plate and DLEM. The underlying mechanism of high-efficiency broadband absorption and asymmetric reflection of flexural wave is theoretically revealed, which stems from multi-reflection-enhanced absorption of the n=0 and n=-1 order diffractions. For the composite subunit of the DLEM implemented by a lead block atop damping silicone rubber block, a simplified two degree-of-freedom (2DOF) mass-spring-damping model and the corresponding accurate model are both theoretically derived to reveal the deep-subwavelength mechanism of controlling the reflected wave phase. The experiments of the broadband wave absorption and asymmetric reflection are further carried out to validate the performance of the designed DLEMs. The proposed methodology opens a new perspective for broadband vibration suppression and wave manipulation of lossy elastic metasurface with a deep-subwavelength thickness.

АЛГОРИТМ ОБНАРУЖЕНИЯ ФМ-СИГНАЛОВ НА ОСНОВЕ ВИНЕРОВСКОЙ ФИЛЬТРАЦИИ С ПРЕДВАРИТЕЛЬНОЙ НЕЛИНЕЙНОЙ ОБРАБОТКОЙ

In this paper, an algorithm for preprocessing of PSK - signals based on wiener filtration is proposed. The aim of preprocessing is to extract the phase discontinuities when filtering harmonic filling of a signal. This method allows us to avoid compensation of unknown frequency shift in the problems of determining the time delay of signals during multichannel propagation. The study checks the conditions of algorithm applicability and its stability to a noise level in the observed channels.