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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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Journal ArticleDOI
TL;DR: In this article, it was shown that the autocorrelation of the transmission response at two receivers along the x-axis gives the Green's function of the direct wave between these receivers.
Abstract: Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transientas in exploration seismology or a noise signalas in passive seismology, then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is the retrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surfacewave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

344 citations

Journal ArticleDOI
TL;DR: In this article, a heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed under the assumption that small-scale irradiance fluctuation fluctuations are modulated by large-scale fluctuations of the wave.
Abstract: A heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the wave. The upper bound for small turbulent cells is defined by the smallest cell size between the Fresnel zone and the transverse spatial coherence radius of the optical wave. A lower bound for large turbulent cells is defined by the largest cell size between the Fresnel zone and the scattering disk. In moderate-to-strong irradiance fluctuations, cell sizes between those defined by the spatial coherence radius and the scattering disk are eliminated through spatial-frequency filtering as a consequence of the propagation process. The resulting scintillation index from this theory has the form σI2=σx2+σy2+σx2σy2, where σx2 denotes large-scale scintillation and σy2 denotes small-scale scintillation. By means of a modification of the Rytov method that incorporates an amplitude spatial-frequency filter function under strong-fluctuation conditions, tractable expressions are developed for the scintillation index of a plane wave and a spherical wave that are valid under moderate-to-strong irradiance fluctuations. In many cases the models also compare well with conventional results in weak-fluctuation regimes. Inner-scale effects are taken into account by use of a modified atmospheric spectrum that exhibits a bump at large spatial frequencies. Quantitative values predicted by these models agree well with experimental and simulation data previously published. In addition to the scintillation index, expressions are also developed for the irradiance covariance function of a plane wave and a spherical wave, both of which have the form BI(ρ)=Bx(ρ)+By(ρ)+Bx(ρ)By(ρ), where Bx(ρ) is the covariance function associated with large-scale fluctuations and By(ρ) is the covariance function associated with small-scale fluctuations. In strong turbulence the derived covariance shows the characteristic two-scale behavior, in which the correlation length is determined by the spatial coherence radius of the field and the width of the long residual correlation tail is determined by the scattering disk.

331 citations

Journal ArticleDOI
TL;DR: In this article, a comprehensive measurement program was conducted by Telesis Technologies Laboratory (TTL) in the San Francisco Bay area using three base station antenna heights of 3.2 m, 8.7 m, and 13.4 m and two frequencies at 900 MHz and 1900 MHz.
Abstract: To acquire a knowledge of radio propagation characteristics in the microcellular environments for personal communications services (PCS), a comprehensive measurement program was conducted by Telesis Technologies Laboratory (TTL) in the San Francisco Bay area using three base station antenna heights of 3.2 m, 8.7 m, and 13.4 m and two frequencies at 900 MHz and 1900 MHz. Five test settings were chosen in urban, suburban, and rural areas in order to study propagation in a variety of environments. This paper reports the LOS measurements in different environments, all of which show variations of signal strength with distance that have distinct near and far regions separated by a break point. It was also found that the location of the break point for different frequencies and antenna heights can be calculated based on first Fresnel zone clearance. The regression analysis reveals a slope that is less than two before the break point, while it is greater than two after the break point. This break distance can be used to define the size of microcell and to design for fast hand-off. Beyond the first Fresnel zone break distance the base station antenna height gain was observed to approximately follow the square power law of antenna height. >

303 citations

Journal ArticleDOI
28 Oct 1999-Nature
TL;DR: In this article, the authors report the fabrication of high-efficiency, high-contrast gold and nickel multistep (quaternary) Fresnel zone plates using electron beam lithography.
Abstract: The development of high brilliance X-ray sources coupled with advances in manufacturing technologies has led to significant improvements in submicrometre probes for spectroscopy, diffraction and imaging applications. The generation of a small beam spot size is commonly based on three principles1: total reflection (as used in optical elements involving mirrors or capillaries), refraction (such as in refractive lenses2) and diffraction. The latter effect is employed in Bragg–Fresnel or Soret lenses, commonly known as Fresnel zone plate lenses. These lenses currently give the best spatial resolution, but are traditionally limited to rather soft X-rays—at high energies, their use is still limited by their efficiency. Here we report the fabrication of high-efficiency, high-contrast gold and nickel multistep (quaternary) Fresnel zone plates using electron beam lithography. We achieve a maximum efficiency of 55% for the nickel plate at 7 keV. In addition to their high efficiency, the lenses offer the advantages of low background signal and effective reduction of unwanted diffraction orders. We anticipate that these lenses should have a significant impact on techniques such as microscopy3, micro-fluorescence4 and micro-diffraction5, which require medium resolution (500–100 nm) and high flux at fixed energies.

274 citations

Journal ArticleDOI
TL;DR: Testing of the zone plate with the full-field transmission x-ray microscope, XM-1, in Berkeley, showed that the lens clearly resolved 12 nm lines and spaces, a significant step towards 10 nm resolution and beyond.
Abstract: To extend soft x-ray microscopy to a resolution of order 10 nm or better, we developed a new nanofabrication process for Fresnel zone plate lenses. The new process, based on the double patterning technique, has enabled us to fabricate high quality gold zone plates with 12 nm outer zones. Testing of the zone plate with the full-field transmission x-ray microscope, XM-1, in Berkeley, showed that the lens clearly resolved 12 nm lines and spaces. This result represents a significant step towards 10 nm resolution and beyond.

273 citations


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