A guide to the limits of resolution imposed by scattering in ray tomography

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 202-207 ◽  
Author(s):  
P. R. Williamson
Keyword(s):  
Fresnel Zone ◽  
Wave Number ◽  
Diffraction Tomography ◽  
Reconstruction Algorithms ◽  
Small Perturbations ◽  
Scattering Effects ◽  
Homogeneous Background ◽  
Computational Resources ◽  
Zone Radius ◽  
Correct Image

Tomographic imaging is now in widespread use in geophysical inversion. Most early work in this field used the ray approximation to wave propagation, but more recently scattering effects have been addressed via the formalism of diffraction tomography. However, if the correct image cannot be adequately represented as a perturbation of a simple background, this may demand considerably more computational resources than ray tomography. Therefore it is of some interest to determine the scalelength of variation below which scattering cannot be neglected, so that ray tomography is no longer reliable. In the hypothetical case of monochromatic illumination of a region consisting of small perturbations to a homogeneous background, the way in which the two reconstruction algorithms map the data into the Fourier components of the object may be directly compared to reveal the effect of neglecting scattering. These mappings begin to differ significantly at a wave‐number corresponding to the first Fresnel zone radius; it seems reasonable to expect that a similar result should apply to cases with more general background velocities, and so to iterative (nonlinear) inversions. Therefore some kind of inverse scattering approach must be employed to ensure accurate imaging beyond this wavenumber to the limit of twice that of the illuminating radiation.

Research on the Influence of Obstacles in the Airport Terminal Area on ILS Ground Station

2014 ◽  
Vol 556-562 ◽  
pp. 4672-4676
Author(s):  
Xian Hao Zhang ◽  
Wei Qi Feng ◽  
Shuo Ling Xiang
Keyword(s):  
Electromagnetic Waves ◽  
Fresnel Zone ◽  
Civil Aviation ◽  
Electromagnetic Environment ◽  
Ground Station ◽  
Radiation Distribution ◽  
Airport Terminal ◽  
Glide Slope ◽  
Zone Radius ◽  
Terminal Area

According to the theory that electromagnetic waves diffract when approaching obstacles, the thesis focuses on the airport terminal area obstacles affection on the performance of Instrument Landing System (ILS). It is done through calculating of the first Fresnel zone radius and clearance and the electromagnetic environment radiation distribution of the ground station via Single-Wedge Model on the basis of combining the Instrument Landing Systemin the civil aviation airport terminal area and abstracted general theoretical model. This research can provide theoretical basis for the arrangement of navigation station and evaluation of the ILS glide slope in a practical airport environment. Therefore, the study is of magnificent importance for the safe operation of the civil aviation airport.

scholarly journals Scalable multiple whole-genome alignment and locally collinear block construction with SibeliaZ

2019 ◽  
Author(s):  
Ilia Minkin ◽  
Paul Medvedev
Keyword(s):  
Single Machine ◽  
De Bruijn Graph ◽  
Genome Alignment ◽  
Whole Genome ◽  
Reconstruction Algorithms ◽  
De Bruijn Graphs ◽  
Significant Step ◽  
De Bruijn ◽  
Whole Genome Alignment ◽  
Computational Resources

AbstractMultiple whole-genome alignment is a challenging problem in bioinformatics. Despite many successes, current methods are not able to keep up with the growing number, length, and complexity of assembled genomes, especially when computational resources are limited. Approaches based on compacted de Bruijn graphs to identify and extend anchors into locally collinear blocks have potential for scalability, but current methods do not scale to mammalian genomes. We present an algorithm, SibeliaZ-LCB, for identifying collinear blocks in closely related genomes based on analysis of the de Bruijn graph. We further incorporate this into a multiple whole-genome alignment pipeline called SibeliaZ. SibeliaZ shows run-time improvements over other methods while maintaining accuracy. On sixteen recently-assembled strains of mice, SibeliaZ runs in under 16 hours on a single machine, while other tools did not run to completion for eight mice within a week. SibeliaZ makes a significant step towards improving scalability of multiple whole-genome alignment and collinear block reconstruction algorithms on a single machine.

scholarly journals Image reconstruction algorithms for the microwave holographic vision system with reliable gap detection at theoretical limits

2018 ◽  
Vol 185 ◽  
pp. 01004
Author(s):  
Dmitry Leshchiner ◽  
Konstantin Zvezdin ◽  
Anatoly Popkov ◽  
Grigory Chepkov ◽  
Pietro Perlo
Keyword(s):  
Image Reconstruction ◽  
Fresnel Zone ◽  
Vision System ◽  
Reconstruction Algorithm ◽  
Gap Detection ◽  
Reconstruction Algorithms ◽  
Maximal Interval ◽  
Microwave Scattering ◽  
Zone Width ◽  
Microwave Detector

We present a reliable image reconstruction algorithm suitable for a microwave holographic vision system with several sensors coupled to the spin-diode based microwave detector and a single emission source. An objective is, by reconstructing the spatial microwave scattering density on the scene, to detect the presence and the nature of road obstacles impeding driving in the near vehicle zone. The idea of holographic visualization is to reconstruct the spatial microwave scattering density of an object by detecting an amplitude and phase of a reflected signal by lattice of sensors. We discuss versions of an algorithm, determine and analyse its resolution limits for various distances with different number of sensors for a one-dimensional test problem of detecting two walls (or posts) separated by a gap at a fixed distance. The maximal interval between sensors needed for a reliable reconstruction equals approximately Fresnel zone width. We show that maximal resolution achieved by our algorithm with an appropriate number of sensors was about 40% of Fresnel zone width for wall detection and about 30% of zone width for gap detection.

Phase Retrieval from Two Defocused Images by the Transport-Ofintensity Equation Formalism with Fast Fourier Transform

2001 ◽  
Vol 7 (S2) ◽  
pp. 430-431
Author(s):  
V.V. Volkov ◽  
Y. Zhu
Keyword(s):  
Phase Retrieval ◽  
Optical Axis ◽  
Fresnel Zone ◽  
Diffraction Tomography ◽  
X Ray ◽  
Intensity Measurements ◽  
Magnetic Inductance ◽  
Experimental Parameters ◽  
Transport Of Intensity Equation ◽  
Made In

The problem of phase retrieval from intensity measurements plays an important role in many fields of physical research, e.g. optics, electron and x-ray microscopy, crystallography, diffraction tomography and others. in practice the recorded images contain information only on the intensity distribution I(x,y) = ψ*ψ*= |A|2 of the imaging wave function ψ = A*exp(-iϕ) and the phase information (ϕ(x,y) is usually lost. in general, the phase problem can be solved either by special holographic/interferometric methods, or by noninterferometric approaches based on intensity measurements in far Fraunhofer zone or in the Fresnel zone at two adjacent planes orthogonal to the optical axis. The latter approach uses the transport-of-intensity equation (TIE) formalism, introduced originally by Teague [1] and developed later in [2]. Applications of TIE to nonmagnetic materials and magnetic inductance mapping were successfully made in [3,4]. However, this approach still needs further improvement both in mathematics and in practical solutions, since the result is very sensitive to many experimental parameters.

Resolution limits in ray tomography due to wave behavior: Numerical experiments

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 727-735 ◽  
Author(s):  
Paul R. Williamson ◽  
M. H. Worthington
Keyword(s):  
Fresnel Zone ◽  
Synthetic Data ◽  
Original Model ◽  
Data Sets ◽  
Diffraction Tomography ◽  
Feature Size ◽  
Resolution Limits ◽  
Minimum Feature Size ◽  
Experimental Geometry ◽  
Fresnel Zones

Several factors limit the resolution obtained in ray tomography. Of these the least thoroughly discussed in the geophysical literature is the effect of the ray approximation itself; scattering is ignored and the information contained in a seismic trace is reduced to one traveltime pick. Frequency domain comparisons of ray tomography with diffraction tomography have suggested that the minimum feature size resolvable by ray tomography is of the order of the width of the first Fresnel zone. We investigate resolution in the spacetime domain with a numerical experiment. Four synthetic data sets were generated with a finite‐difference program corresponding to crosshole tomographic surveys at two hole separations and two frequencies. The scale of resolution achieved in tomograms derived from these is then assessed by calculating their semblance to filtered versions of the original model and reconstructions from data sets obtained by tracing rays through the original models. The results broadly confirm the relation of resolution to Fresnel zones. It is therefore possible that such limits on resolution may be at least as significant as those due to other factors such as experimental geometry.

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