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Fresnel zone

About: Fresnel zone is a research topic. Over the lifetime, 2337 publications have been published within this topic receiving 37650 citations.


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TL;DR: In this article, a new method is described that makes it feasible to include scattered and converted surface waves into waveform inversions for the three-dimensional (3-D) structure of the Earth.
Abstract: A new method is described that makes it feasible to include scattered and converted surface waves into waveform inversions for the three-dimensional (3-D) structure of the Earth. The single scattering (Born) approximation forms the basis of the method. In order to minimize the amplitude of the scattered wave field, the background model is first adapted to correct for nonconverted, forward-scattered wave energy. We then perform Born inversion of the difference between the measured and synthetic waveforms, including a suite of Love and Rayleigh modes. The Born approximation yields linear equations of the form Aδγ = δu Bor n, which allow the determination of the three-dimensional perturbations γ to the background model from the scattered wave field δu Born . This procedure is followed separately for each source-receiver pair to allow for optimized background models for each signal, as well as to minimize the computational burden. We winnow the data vector for each path by performing singular value decomposition using a diagonalization of AA T . In a realistic example we found that each vertical component seismogram yields 30-40 linear constraints on the 3-D Earth, significantly more than with conventional pure-path (WKBJ) inversions. In a synthetic test, one seismogram is shown to be able to image a simple model of a point scatterer off the great circle. As a spin-off of the formulation of the multimode inverse scattering problem, we not only obtain a series of eigenvectors that rank the sensitivity of a seismogram to Earth structure in a series of geometrical patterns, we also can compute the surface wave equivalent of a Fresnel zone.

61 citations

Journal ArticleDOI
TL;DR: In this paper, the indirect boundary element method (BEM) is used to model the seismic waveforms scattered from an arbitrary number of fractures that are either empty, or contain elastic or fluid material.
Abstract: SUMMARY We use a numerical method that can model the seismic waveforms scattered from an arbitrary number of fractures that are either empty, or contain elastic or fluid material. The indirect boundary element method (BEM) is capable of generating the full elastic wavefield and is programmed in 2-D. The governing equations and discrete implementation of the technique are described. We explain in detail a new approach for evaluating the improper boundary integrals. The method is shown to be highly accurate from a comparison with mode summation. Subsequently, the BEM is applied to modelling hydrofractures. Synthetic examples, calculated for cross-well and single well geometries, demonstrate the effects of crack length, opening and infill on recorded displacements. It is shown that diffractions from the tips can, in principle, be used to locate and determine the hydrofracture size. These arrivals depart from ray theoretical travel-times due to defocusing over a Fresnel zone. S-wave diffractions generally have a larger amplitude than the diffracted P-waves, and so may provide a better indication of fracture size. Energy which is converted to interface waves and subsequently diffracted from the crack tips is also observed. The presence of water allows energy to pass through the fracture; this is clearly evident on the cross-well seismograms. Closure of the fracture causes a further increase in transmission amplitude as less energy is attenuated through internal multiples.

61 citations

Journal ArticleDOI
TL;DR: In this paper, the design and fabrication of the static and dynamic, on-and off-axis Fresnel zone lenses as well as their optical and switching properties are presented, and the switching behavior of the dynamic lenses is studied.
Abstract: Static and dynamic Fresnel zone lenses were fabricated in quartz glass by means of microstructuring techniques. Two types of on-axis and offaxis lenses with different focal lengths and of different apertures were designed to operate at wavelengths of 1·52 μm and 633 nm. The blazed profile of the onaxis and off-axis lenses was approximated by up to 16 and up to four discrete levels respectively. Dynamic, that is electrically switchable, lenses have been realized by filling the structured surface with liquid crystal. The optical properties of the lenses, such as the focal spot sizes and the diffraction efficiencies, were investigated. Further the switching behaviour of the dynamic lenses was studied. The design and fabrication of the static and dynamic, on-and off-axis Fresnel zone lenses as well as their optical and switching properties will be presented.

60 citations

Journal ArticleDOI
TL;DR: This work presents a comprehensive analysis, based on the leading term and the linear superposition principle, of the focusing performances of various Fresnel zone plates and most of the obtained results are also applicable to multilevel diffractive lenses.
Abstract: A series-form expression for the individual diffracted field of a general annular ring is derived from the Rayleigh-Sommerfeld diffraction integral. It can be used for the accurate and fast simulation of any diffractive focusing element composed of concentric transparent rings. We present a comprehensive analysis, based on the leading term and the linear superposition principle, of the focusing performances of various Fresnel zone plates. Many problems, such as the equivalent aperture function, the diffraction efficiency, the focal spot pattern, the suppression of higher orders and the appearance of "fractional orders," and the explanation for the appearance of Fraunhofer diffraction patterns, are analytically investigated in detail. Because of the great similarity between Fresnel zone plates and multilevel diffractive lenses, most of the obtained results are also applicable to multilevel diffractive lenses.

60 citations

Journal ArticleDOI
TL;DR: In this paper, the growth and characterization of a depth-graded multilayer suitable for use as a zone plate for hard x-ray focusing was presented, which has a total of 470 alternating layers of WSi2 and Si with thicknesses increasing monotonically from 15 to 60 nm.
Abstract: Fresnel zone plates for x-ray focusing optics are typically made using lithographic techniques. To achieve optimum efficiency for hard x rays, a depth of several microns is required, which limits the minimum zone width and hence minimum focal spot size achievable using lithography. We are exploring the fabrication of zone plates by an alternative technique that surmounts these limitations: the growth of a multilayer film to be used in transmission (Laue) diffraction geometry, in which the thickness of consecutive layers gradually increases according to the Fresnel zone formula; the film is sectioned after growth to the required depth. For a planar multilayer, this produces a linear zone plate that can focus x rays in one dimension. Here we report the growth and characterization of a depth-graded multilayer suitable for use as a zone plate for hard x-ray focusing. The multilayer has a total of 470 alternating layers of WSi2 and Si with thicknesses increasing monotonically from 15 to 60 nm, for a total thic...

59 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202326
202249
202137
202052
201965
201878