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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: Comparisons of several analytic ray-based approximations with numerical parabolic-equation simulations to determine their accuracies are reviewed.
Abstract: Simulations of laser-beam propagation through atmospheric turbulence and acoustic pulse propagation though ocean internal waves in the presence of a transverse waveguide are described. Both these problems are amenable to the parabolic wave equation for propagation in the forward direction. In the optical case, the question treated is the irradiance variance and spatial spectrum. In the ocean case, pulse propagation over long ranges is investigated. Determining the travel time of a pulse requires expanding the numerical simulation in a broadband, multifrequency calculation that takes even more time. Much effort has been expended in approximating the propagation by rays, so that the trajectory of the energy propagating from a given source to a given receiver can be tracked, and coherence calculations can be ray-based, using semi-classical formulas. This paper reviews the comparisons of several analytic ray-based approximations with numerical parabolic-equation simulations to determine their accuracies.

9 citations

Journal ArticleDOI
01 Jan 2004-Optik
TL;DR: In this article, the authors proposed a criterion based on the angle subtended by the first minimum of the diffraction pattern from the centre of a diffracting aperture, which can be expressed in terms of the number of Fresnel zones delimited by the aperture.

9 citations

Journal ArticleDOI
TL;DR: The self-imaging phenomenon of a square wave binary amplitude grating is studied in this paper, where the intensity distributions in the Fresnel diffraction image planes lying at distances z = (M -1/4)d 2/u from the grating illuminated by a plane wave are calculated.
Abstract: The self-imaging phenomenon of a square wave binary amplitude grating is studied. The intensity distributions in the Fresnel diffraction image planes lying at distances z = (M -1/4)d 2/u from the grating illuminated by a plane wave are calculated. It is found that these images are very similar to the object structure. As a consequence, some potential applications are proposed.

9 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of variations of the crust on smaller length scales are considered when interpreting deep reflection profiles, which can be used to constrain the degree to which the crustal elasticity varies on small length scales.
Abstract: SUMMARY a geological feature to be resolved in a seismic reflection profile its size must be comparable with the dimensions of the Fresnel zone for its depth and the frequency-content of the seismic wavefield. Since the diameter of the Fresnel zone is over 5 km for lower-crustal reflections, the effects of variations of the crust on smaller length scales must be considered when interpreting deep reflection profiles. Modelling the seismic wavefield using first-order scattering theory shows how the reflections observed in a small-offset profile are affected by the statistical distribution of elastic vanations within the crust. Crustal heterogeneities on length-scales smaller than the seismic wavelength cause frequency-dependent attenuation which can be comparable with the losses due to anelastic absorption. Larger scale elastic variations cause rapid loss of coherence in the seismic field. The observation of deep seismic reflections can thus be used to constrain the degree to which the crustal elasticity varies on small length scales. Coherent seismic reflections from the lower crust limit the fractional variation of elasticity averaged over the entire crust to a few percent on a wide range of length-scales.

9 citations

Book ChapterDOI
01 Jan 1968
TL;DR: In this article, it is shown that the sharply defined image is surrounded by a halo having a diameter of a few minutes of arc for the above-mentioned micro-zone plates, and that the brightness distribution of the halo agrees with the one obtained by a pinhole camera, provided the diameter of the hole and that of the zone plate are equal.
Abstract: It is well known that Fresnel zone plates act as a lens with a focal length inversely proportional to the wavelength. At Professor Moellenstedt’s Institute of Applied Physics in Tubingen, a technique has been developed to manufacture micro-zone plates electronoptically from Buckbee-Mears zone plates. These micro-zone plates have a diameter of 0·5 mm approximately, 38 zones and a focal length of 30 cm for X-rays of nearly 50 A. Their resolving power is of the order of a few seconds of arc (Einighammer et al, 1966). One finds, however, experimentally as well as theoretically that the sharply defined image is surrounded by a halo having a diameter of a few minutes of arc for the above-mentioned zone plates. Whereas for a point source the intensity of a halo is poor and therefore unimportant, for extended sources it becomes large as a result of the superposition of the contributions from the individual points of the source. This has been demonstrated by the photometer curves of the images of circular sources by Einighammer (1966) (Figure 1). The halo is not noticeable in case of very narrow sources (curves a and b). With increasing diameter of the source the intensity of the halo rapidly increases (curves c and d). For the same source the brightness distribution of the halo agrees practically with the one obtained by a pinhole camera, provided the diameter of the hole and that of the zone plate are equal; these brightness distributions are represented by the dashed lines c′d′ in Figure 1.

9 citations


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