Wavefront Model Research Articles

Statistical Model of Ocular Wavefronts With Accommodation.

The purpose of this study was to determine the minimum number of orthonormal basis functions, applying Principal Component Analysis (PCA), to represent the most wavefront aberrations at different accommodation stages. The study also aims to generate synthetic wavefront data using these functions. Monocular wavefront data from 191 subjects (26.15 ± 5.56years old) were measured with a Hartmann-Shack aberrometer, simulating accommodation from 0 diopters (D) to 5 D in 1 D steps. The wavefronts for each accommodative demand were rescaled for different pupil sizes: 4.66, 4.76, 4.40, 4.09, 4.07, and 3.68mm. PCA was applied to 150 wavefront parameters (25 Zernike coefficients × 6 accommodation levels) to obtain eigenvectors for dimensional reduction. A total of 49 eigenvectors were modeled as a sum of 2 multivariate Gaussians, from which 1000 synthetic data sets were generated. The first 49 eigenvectors preserved 99.97% of the original data variability. No significant differences were observed between the mean values and standard deviation of the generated and original 49 eigenvectors (two one-sided test [TOST], P > 0.05/49) and (F-test, P > 0.05/49), both with Bonferroni correction. The mean values of the generated parameters (1000) were statistically equal to those of the original data (TOST, P > 0.05/150). The variability of the generated data was similar to the original data for the most important Zernike coefficients (F-test, P > 0.05/150). PCA significantly reduces the dimensionality of wavefront aberration data across 6 accommodative demands, reducing the variable space by over 66%. The synthetic data generated by the proposed wavefront model for accommodation closely resemble the original clinical data.

Construction of a wavefront model for internal solitary waves and its application in the Northern South China Sea

Internal solitary waves (ISWs) play a crucial role in the development of various physical and biological processes, and numerous high-precision two-dimensional or three-dimensional numerical models have been developed to simulate the generation and propagation processes of ISWs. However, these numerical models, especially when simulating the interaction between ISWs and ocean circulation, require substantial computational resources. This burden can make it challenging to apply them in real-time or short-term forecasting scenarios. In this study, we propose a new numerical model for ISWs by combining traditional one-dimensional ISW theory with wave refraction theory. The proposed model resolves the issues of ray crossing and divergence, which are commonly encountered in traditional refraction models, by employing equally spaced grids along the wave crest line. As a result, this model is capable of simulating the far-field propagation of ISWs. This model enables rapid prediction of the vertical structure and wave crest morphology of ISWs in specific current fields and at given time frames, and it is utilized to investigate the characteristics and propagation of ISWs generated by the nonlinear steepening of internal tide (IT) in the South China Sea. Comparative analysis with satellite imagery demonstrates the model's accurate representation of ISW processes and phenomena, such as wave crest line discontinuities, diffraction, and wave‒wave interactions when passing through Dongsha Island. Furthermore, propagation time estimates based on this model have errors of ±0.98 h (1σ) over which the ISWs are observed by a mooring system, and the average time difference is 0.81 h

Parabolic Wavefront Model for Line-of-Sight MIMO Channels

Motivated by the widespread adoption of the parabolic wavefront model for line-of-sight (LOS) multiple-input multiple-output (MIMO) communication, this paper presents a comprehensive analysis of this model’s validity and simple conditions that ensure its applicability. Then, with the model’s scope clearly delineated, the paper expounds a number of properties of the channel that results from applying it. Connections are drawn among these properties under the umbrella of a Fourier interpretation, and their significance to LOS MIMO communication is substantiated.

An aberration correction approach for single and dual aperture ultrasound imaging of the abdomen

Abdominal ultrasound image quality is hampered by phase aberration, that is mainly caused by the large speed-of-sound (SoS) differences between fat and muscle tissue in the abdominal wall. The mismatch between the assumed and actual SoS distribution introduces general blurring of the ultrasound images, and acoustic refraction can lead to geometric distortion of the imaged features. Large aperture imaging or dual-transducer imaging can improve abdominal imaging at deep locations by providing increased contrast and resolution. However, aberration effects for large aperture imaging can be even more severe, which limits its full potential. In this study, a model-based aberration correction method for arbitrary acquisition schemes is introduced for delay-and-sum (DAS) beamforming and its performance was analyzed for both single- and dual-transducer ultrasound imaging. The method employs aberration corrected wavefront arrival times, using manually assigned local SoS values. Two wavefront models were compared. The first model is based on a straight ray approximation, and the second model on the Eikonal equation, which is solved by a multi-stencils fast marching method. Their accuracy for abdominal imaging was evaluated in acoustic simulations and phantom experiments involving tissue-mimicking and porcine material with large SoS contrast (∼100 m/s). The lateral resolution was improved by up to 90% in simulations and up to 65% in experiments compared to standard DAS, in which the use of Eikonal beamforming generally outperformed straight ray beamforming. Moreover, geometric distortions were mitigated in multi-aperture imaging, leading to a reduction in position error of around 80%. A study on the sensitivity of the aberration correction to shape and SoS of aberrating layers was performed, showing that even with imperfect segmentations or SoS values, aberration correction still outperforms standard DAS.

Cramér-Rao Bounds of Near-Field Positioning Based on Electromagnetic Propagation Model

The adoption of large-scale antenna arrays at high-frequency bands is widely envisioned in the beyond 5G wireless networks. This leads to the near-field regime where the wavefront is no longer planar but spherical, bringing new opportunities and challenges for communications and positioning. In this paper, we improve the near-field positioning technology from the classical <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spherical wavefront model</i> (SWM) to the more accurate and true <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">electromagnetic propagation model</i> (EPM). A generic near-field positioning model with different observation capabilities for three electric field types ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vector</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scalar</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">overall scalar electric field</i> ) is developed based on the complete EPM. For these three observed electric field types, the Cramér-Rao bound (CRB) is adopted to evaluate the achievable estimation accuracy. The expressions of the CRBs for different electric field observations are derived by combining electromagnetic propagation concepts with estimation theory. Closed-form expressions can be further obtained as the terminal is assumed to be on the central perpendicular line (CPL) of the receiving antenna surface. Moreover, the above discussions are extended to the system with multiple receiving antennas. In this case, the CRBs using various electric field types are derived and the effect of different numbers of receiving antennas is deeply investigated. Numerical results are provided to quantify the CRBs and validate the analytical results. Also, the impact of different system parameters, including electric field type, wavelength, size of the receiving antenna, and number of antennas, is evaluated.

Tobler's law and wavefront patterns in the spatial spread of COVID-19 across Europe during the Delta and Omicron waves.

Epidemic wavefront models predict the spread of medieval pandemics such as the plague well. Our aim was to explore whether they contribute to understanding the spread of COVID-19, the first truly global pandemic of the 21st century with its fast and frequent international travel links. We analysed the spatial spread of reaching a threshold of very high incidence of new daily infections of the virus across European countries in the autumn of 2021 in which the Delta variant was dominant, as well as an even higher threshold of incidence in the subsequent spread of infections across the same set of countries during the winter of 2021/2022 when the Omicron variant of the virus became dominant. We found patterns that are consistent with wavefront models for both periods of the pandemic in Europe. Modern means of transportation strongly accelerated the spread of the virus and typically generated diffusion patterns along bidirectional constrained mobility networks in addition to stochastic diffusion processes. However, since the majority of mobility, including mobility across international borders, is over short distances, wavefront patterns in the spread of a pandemic are still to be expected.

Simulating Large-Scale Streamer and OBN Acquisition over Subsalt Targets — an Example of Successful Remote Collaboration Between Survey Design and Survey Evaluation

In this article we look at how ray-based wavefront modelling can be used to evaluate competing acquisition techniques with significantly different illumination properties and associated acquisition cost. We compare subsurface illumination of complex sub-salt reservoirs typical of those found in the Gulf of Mexico for a variety of towed-streamer and full azimuth long offset ocean bottom node surveys. Single, dual and triple azimuth towed-streamer surveys are considered. This project was accomplished using a new connector between ACTeQ’s survey design and optimization software and Norsar’s 3D modelling software. This project is an excellent example of competitors collaborating to better achieve a customer’s needs. The project was also accomplished in a fully remote environment, and none of the authors were in the same city at any time during the project. Remote collaboration is becoming an increasingly effective low-carbon approach to complex challenges.

Comparison between Different TomoSAR Imaging Models for Airborne Platform Flying at Low Altitude

The classical planar-wavefront-based TomoSAR imaging model suffers from the problem that the effective integration interval is not enough to cover the target distribution region in the low-altitude airborne case. It will lead to a deterioration of the performance of tomogram reconstruction and inaccuracy of estimated scatterers. This paper reviews the exact and approximate forms of the aforementioned inaccurate model based on planar wavefront and points out the problem with the conventional model. To solve this problem, we propose spherical wavefront models with the exact form or an approximate form of the slant range formula. The estimated variable for the scatterer’s location is converted from elevation to off-nadir angle, and the effective integration interval has been extended. In addition, we explore relationships between the exact form of the conventional model and the exact form of the proposed model, and the relationship between the approximate form of the conventional model and the approximate form of the proposed model. This provides a basis for modifying the inversion algorithm that is designed based on the conventional model to adapt to the low-altitude airborne case. Eventually, through experiments based on simulated data and measured data, the imprecise reconstructions obtained with the conventional model are demonstrated, and the correctness of spherical wavefront models and the effectiveness of transformation between models are proved.

Hogel-Free Holography

Holography is a promising avenue for high-quality displays without requiring bulky, complex optical systems. While recent work has demonstrated accurate hologram generation of 2D scenes, high-quality holographic projections of 3D scenes has been out of reach until now. Existing multiplane 3D holography approaches fail to model wavefronts in the presence of partial occlusion while holographic stereogram methods have to make a fundamental tradeoff between spatial and angular resolution. In addition, existing 3D holographic display methods rely on heuristic encoding of complex amplitude into phase-only pixels which results in holograms with severe artifacts. Fundamental limitations of the input representation, wavefront modeling, and optimization methods prohibit artifact-free 3D holographic projections in today’s displays. To lift these limitations, we introduce hogel-free holography which optimizes for true 3D holograms, supporting both depth- and view-dependent effects for the first time. Our approach overcomes the fundamental spatio-angular resolution tradeoff typical to stereogram approaches. Moreover, it avoids heuristic encoding schemes to achieve high image fidelity over a 3D volume. We validate that the proposed method achieves 10 dB PSNR improvement on simulated holographic reconstructions. We also validate our approach on an experimental prototype with accurate parallax and depth focus effects.

Evaluation of 3D seismic survey design parameters through ray-trace modeling and seismic illumination studies: a case study

This paper describes a case study of wavefront construction-based ray-trace modeling to access the 3D seismic exploration parameters that significantly impact achieving the exploration target in seismic data acquisition. The traditional methods assessment is based on the horizontal reflector concept, which does not consider the subsurface's inhomogeneities. This case study provides a methodology by considering the effect of subsurface variations on the estimation of seismic survey parameters. As the first step in this methodology, an elastic earth model is created to propagate theoretical seismic rays from a 3D seismic survey to generate seismic ray properties. Then illumination maps and synthetic seismic sections are generated from these seismic ray attributes to evaluate seismic survey performance in seismic imaging targets. The results proved that the method helps estimate seismic survey efficiencies in seismic target imaging. Therefore, the ray-trace modeling methodology can help obtain the target fold coverage in complex geological settings by designing and verifying the seismic survey parameters.

Three-dimensional wavefront modeling of secondary sonic booms

There is an abundance of previous work in the literature regarding the Mach cone of a supersonic vehicle and its associated ground intercepts identifying where and when the primary sonic boom reaches the ground. Likewise, there is excellent past research that models where the secondary sonic boom reaches the ground due to the reflection and refraction of the sonic boom emanating from above and below a supersonic vehicle. This work will provide a bridge between the two aforementioned aspects of past research. The Mach cone for both above the aircraft and below the aircraft after it reaches the ground will be extended to model the three-dimensional wavefront evolution of the secondary sonic boom as it propagates to the ground. The secondary sonic boom wavefronts modeled in this work will only consist of rays that refract in the vicinity of the stratosphere. The present work will show several cases of the secondary sonic boom wavefront propagation in three dimensions for a variety of aircraft headings and geographic locations around the world with representative upper air temperature and wind conditions.

Wave-optics simulation software for synchrotron radiation from 4th generation storage rings based on a coherent modes model.

The evolution from 3rd to 4th generation of storage rings significantly enhanced the coherence of synchrotron radiation sources, making coherent scattering techniques such as coherent X-ray diffraction imaging (CXDI) and X-ray photon correlation spectroscopy more accessible. In conformance with the design requirements of coherent beamlines at the High Energy Photon Source (HEPS), we have developed wave optics simulation software, the Coherence Analysis Toolbox, based on coherent modes decomposition and a wavefront propagation model. Simulations of beamline performance and a CXDI experiment on the hard X-ray coherent scattering beamline at HEPS were carried out. This software is open source and now available on GitHub.

Distribution and Source Sites of Nonlinear Internal Waves Northeast of Hainan Island

The distribution and source sites of nonlinear internal waves (NLIWs) northeast of Hainan Island were investigated using satellite observations and a wavefront propagation model. Satellite observations show two types of NLIWs (here referred to as type-S and type-D waves). The type-S waves are spaced at a semidiurnal tidal period and the type-D waves are spaced at a diurnal tidal period. The spatial distribution of the two types of NLIWs displays a sandwich structure in which the middle region is influenced by both types of NLIWs, and the northern and southern regions are governed by the type-S and type-D waves, respectively. Solving the wavefront model yields good agreement between simulated and observed wavefronts from the Luzon Strait to Hainan Island. We conclude that the NLIWs originate from the Luzon Strait.

Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock.

The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a differentiation wavefront, which provides the positional information indicating where each pair of somites is formed. Shortly after the clock and wavefront paradigm was introduced, Meinhardt presented a conceptually different mathematical model for morphogenesis in general, and somitogenesis in particular. Recently, Cotterell et al. [A local, self-organizing reaction-diffusion model can explain somite patterning in embryos, Cell Syst. 1, 257-269 (2015)] rediscovered an equivalent model by systematically enumerating and studying small networks performing segmentation. Cotterell et al. called it a progressive oscillatory reaction-diffusion (PORD) model. In the Meinhardt-PORD model, somitogenesis is driven by short-range interactions and the posterior movement of the front is a local, emergent phenomenon, which is not controlled by global positional information. With this model, it is possible to explain some experimental observations that are incompatible with the clock and wavefront model. However, the Meinhardt-PORD model has some important disadvantages of its own. Namely, it is quite sensitive to fluctuations and depends on very specific initial conditions (which are not biologically realistic). In this work, we propose an equivalent Meinhardt-PORD model and then amend it to couple it with a wavefront consisting of a receding morphogen gradient. By doing so, we get a hybrid model between the Meinhardt-PORD and the clock-and-wavefront ones, which overcomes most of the deficiencies of the two originating models.

An improved planar wavefront model to estimate rocking seismic motion spectra using translational spectra at a single station

It is convenient to synthesize the Fourier spectra of the rocking ground motions at a station from the recorded translational motions at the same station. The conventional models in this approach assume (1) the seismic source to be a point source, (2) the medium to be a horizontally stratified elastic half-space, and (3) the translational motions to be caused primarily by the planar wavefronts of the body waves. An improved ‘planar wavefront’ model is proposed under this approach such that (1) the model applies also to near the epicenter, with the hypocentral distance of the station assumed to be much larger than the wavelengths of the incident waves, (2) the information on the underlying focal mechanism is accounted for, and (3) both in-plane and out-of-plane rocking spectra can be estimated. The proposed model assumes the material properties of the stratified medium to vary smoothly with depth. Further, it considers the spatial variations of both the amplitudes and the incidence angles of the incoming waves. The spatial variation of the amplitudes is formulated by considering the physics of (1) the radiation of body waves emitted by a kinematic shear dislocation point source and (2) the propagation of those waves through the stratified medium. A numerical study shows that the proposed model leads to more accurate rocking spectra over a large range of fault parameters and frequencies. Further, a few example near-epicenter records of translational ground motions illustrate the disparities between the time-domain estimates of the proposed model with those of the conventional models as well as between the responses of simple structures subjected to the two sets of motions.

Conditional and Unconditional Cramér-Rao Bounds for Near-Field Localization in Bistatic MIMO Radar Systems

The location estimation problem has been attracting a lot of research interest in recent years due to its significance for different areas of signal processing. This paper deals with a bistatic MIMO radar system where the targets are located in the near-field region. In this work, we derive the Cramér-Rao bound (CRB) for bistatic MIMO radar systems using the exact spherical wavefront model to evaluate the performance of target parameter estimation algorithms. The conditional and unconditional CRBs are derived for a system with one and multiple targets. For the one target system, we provide an analytical inversion of the Fisher Information Matrix (FIM) and obtain closed-form analytical non-matrix expressions of the CRB corresponding to the Cartesian and spherical coordinates of the targets. We compare the derived conditional and unconditional CRB with the performance of state-of-the-art localization algorithms and analyse the dependence of the CRB on various system parameters.

A synthetic Roman Space Telescope High-Latitude Imaging Survey: simulation suite and the impact of wavefront errors on weak gravitational lensing

ABSTRACT The Nancy Grace Roman Space Telescope (Roman) mission is expected to launch in the mid-2020s. Its weak lensing program is designed to enable unprecedented systematics control in photometric measurements, including shear recovery, point spread function (PSF) correction, and photometric calibration. This will enable exquisite weak lensing science and allow us to adjust to and reliably contribute to the cosmological landscape after the initial years of observations from other concurrent Stage IV dark energy experiments. This potential requires equally careful planning and requirements validation as the mission prepares to enter its construction phase. We present a suite of image simulations based on galsim that are used to construct a complex, synthetic Roman weak lensing survey that incorporates realistic input galaxies and stars, relevant detector non-idealities, and the current reference 5-yr Roman survey strategy. We present a first study to empirically validate the existing Roman weak lensing requirements flowdown using a suite of 12 matched image simulations, each representing a different perturbation to the wavefront or image motion model. These are chosen to induce a range of potential static and low- and high-frequency time-dependent PSF model errors. We analyse the measured shapes of galaxies from each of these simulations and compare them to a reference, fiducial simulation to infer the response of the shape measurement to each of these modes in the wavefront model. We then compare this to existing analytic flowdown requirements, and find general agreement between the empirically derived response and that predicted by the analytic model.

Ventricular transmural decremental conduction explains short t-peak-t-end interval in “in silico” ECG reconstruction model

Abstract Introduction In chronic hepatic cirrhosis (CHC), T-wave peak to T-wave end interval (TPTE) has shown prognostic value for survival and liver transplantation. Altered cellular ionic regulatory systems may produce decremental conduction in ventricular endocardial to epicardial activation wavefront propagation and ECG waveforms, particularly the T-wave. It was investigated whether ventricular transmural activation wavefront conduction may affect T-wave shape and impact TPTE duration, using “in silico” ECG reconstruction. Methods Mammalian-derived ventricular endocardial to epicardial AP waveforms (APW) were simulated and deployed in 10 discrete layers in homogeneous impedance ventricular wedge-like model. A uniform conduction model was employed to mimic normal heart, in which the speed of propagation of the activation wavefront was nonzero and constant in all layers. In CHC heart, a decremental conduction model was employed, in which the speed of propagation of the activation wavefront was maximal at the endocardial layer and exponentially decayed to greater than zero speed at the epicardial layer. ECG was computed as the sum of dipoles weighted by the inverse of the squared distance to an observation electrode arbitrarily located outside the wedge. One dipole was one layer thick, and its charge was assumed as the time-integral of the current generated by the difference of potential between adjacent APW, from endocardial to epicardial layers. ECG was reconstructed in one axis. Results Two-dimensional transmural APW distribution and respective reconstructed ECGs are presented in Figures 1 and 2. In uniform endocardial to epicardial transmural conduction model, QRS complex was taller and shorter as well as TPTE was larger (Fig. 1) than respective counterparts in decremental conduction model (Fig. 2). Additionally, peak-amplitude of the T-wave as well as the maximal slope of the TPTE were lower in decremental as compared to uniform conduction model. Conclusion Using “in silico” ECG reconstruction, decrementally conducted model of epicardial to endocardial ventricular transmural activation wavefront propagation yields wider and lower amplitude QRS complex as well as shorter TPTE, as compared to respective counterparts in uniformly conducted activation wavefront model. Ventricular transmural decremental conduction model offers an insight into electrophysiological background of ECG findings in CHC. (NCT01433848) Transmural APW distribution vs ECG Funding Acknowledgement Type of funding source: Public Institution(s). Main funding source(s): Universidade do Estado do Rio de Janeiro; Rio de Janeiro, RJ - Brazil

Validation of PSF models for HST and other space-based observations

ABSTRACT Forthcoming space-based observations will require high-quality point spread function (PSF) models for weak gravitational lensing measurements. One approach to generating these models is using a wavefront model based on the known telescope optics. We present an empirical framework for validating such models to confirm that they match the actual PSF to within requirements by comparing the models to the observed light distributions of isolated stars. We apply this framework to Tiny Tim, the standard tool for generating model PSFs for the Hubble Space Telescope (HST), testing its models against images taken by HST’s Advanced Camera for Surveys in the Wide Field Channel. We show that Tiny Tim’s models, in the default configuration, differ significantly from the observed PSFs, most notably in their sizes. We find that the quality of Tiny Tim PSFs can be improved through fitting the full set of Zernike polynomial coefficients that characterize the optics, to the point where the practical significance of the difference between model and observed PSFs is negligible for most use cases, resulting in additive and multiplicative biases both of order ∼4 × 10−4. We also show that most of this improvement can be retained through using an updated set of Zernike coefficients, which we provide.

Somite boundary determination in normal and clock-less vertebrate embryos.

Vertebrate segments called somites are generated by periodic segmentation of the presomitic mesoderm (PSM). In the most accepted theoretical model for somite segmentation, the clock and wavefront (CW) model, a clock that ticks to determine particular timings and a wavefront that moves posteriorly are presented in the PSM, and somite positions are determined when the clock meets the posteriorly moving wavefront somewhere in the PSM. Over the last two decades, it has been revealed that the molecular mechanism of the clock and wavefront in vertebrates is based on clock genes including Hes family transcription factors and Notch effectors that oscillate within the PSM to determine particular timings and fibroblast growth factor (FGF) gradients, acting as the posteriorly moving wavefront to determine the position of somite segmentation. A clock-less condition in the CW model was predicted to form no somites; however, irregularly sized somites were still formed in mice and zebrafish, suggesting that this was one of the limitations of the CW model. Recently, we performed interdisciplinary research of experimental and theoretical biological studies and revealed the mechanisms of somite boundary determination in normal and clock-less conditions by characterization of the FGF/extracellular signal-regulated kinase (ERK) activity dynamics. Since features of the molecular clock have already been described in-depth in several reviews, we summarized recent findings regarding the role of FGF/ERK signaling in somite boundary formation and described our current understanding of how FGF/ERK signaling contributes to somitogenesis in normal and clock-less conditions in this review.