fraunhofer approximation
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2020 ◽  
Vol 223 (3) ◽  
pp. 1864-1878
Author(s):  
Pawan Bharadwaj ◽  
Chunfang Meng ◽  
Aimé Fournier ◽  
Laurent Demanet ◽  
Mike Fehler

SUMMARY We present a robust factorization of the teleseismic waveforms resulting from an earthquake source into signals that originate from the source and signals that characterize the path effects. The extracted source signals represent the earthquake spectrum, and its variation with azimuth. Unlike most prior work on source extraction, our method is data-driven, and it does not depend on any path-related assumptions, for example, the empirical Green’s function. Instead, our formulation involves focused blind deconvolution (FBD), which associates the source characteristics with the similarity among a multitude of recorded signals. We also introduce a new spectral attribute, to be called redshift, which is based on the Fraunhofer approximation. Redshift describes source-spectrum variation, where a decrease in high-frequency content occurs at the receiver in the direction opposite to unilateral rupture propagation. Using the redshift, we identified unilateral ruptures during two recent strike-slip earthquakes. The FBD analysis of an earthquake, which originated in the eastern California shear zone, is consistent with observations from local seismological or geodetic instrumentation.


2013 ◽  
Vol 312 ◽  
pp. 95-100
Author(s):  
Guo Sheng Zhang ◽  
Yan Xu

In order to realize the detection of diffractive light after the image segmentation using cylinder grating, the parameters of a cylinder grating was optimized using the wave optics theory. By analyzing the relation of optical path length variation with the diffraction angle of single cylinder lens diffraction, and by Fraunhofer approximation, the analytical expressions of cylinder lens diffraction was given. By setting parameters to calculate and simulate, it was found that to increase the ratio of curvature radius and grating period could effectively reduce the spatial distribution of the diffraction light intensity. For the gratings that already exist, by reducing the ratio of refractive index of the gratings material and environment, the spatial light distribution of the grating could be reduced. If the cylinder grating period is too small, the overlap part of images segmentation light diffraction intensity will increase. But it occupies smaller proportion of the total light intensity. After the optimization design of cylinder grating, the results showed that it could be used for non-contact speed measurement in the range of some parameter.


2013 ◽  
Vol 28 (02) ◽  
pp. 1340009 ◽  
Author(s):  
CHIH-CHING CHEN ◽  
PISIN CHEN ◽  
CHIA-YU HU ◽  
K.-C. LAI

We propose a new flavor identification method to distinguish mu and tau type ultra high energy cosmic neutrinos (UHECN). Energy loss of leptons in matter is an important information for the detection of neutrinos originated from high energy astrophysical sources. 50 years ago, Askaryan proposed to detect Cherenkov radiowave signals emitted from the negative charge excess of neutrino-induced particle shower. The theory of Cherenkov radiation under Fraunhofer approximation has been widely studied in the past two decades. However, at high energies or for high density materials, electromagnetic shower should be elongated due to the Landau-Pomeranchuck-Migdal (LPM) effect. As such the standard Fraunhofer approximation ceases to be valid when the distance between the shower and the detector becomes comparable with the shower length. Monte Carlo simulations have been performed recently to investigate this regime. Here we adopt the deduced relationship between the radio signal and the cascade development profile to investigate its implication to lepton signatures. Our method provides a straightforward technique to identify the neutrino flavor through the detected Cherenkov signals.


2002 ◽  
Vol 758 ◽  
Author(s):  
Edward M. Nadgorny ◽  
Changgong Zhou ◽  
Jaroslaw Drelich ◽  
Randy Zahn

ABSTRACTTwo laser-based direct-write techniques to guide particles from a mist source to a target substrate by laser beams were recently developed at Michigan Tech. The laser-guided direct-write (LGDW) technique uses a hollow optical fiber, while the laser-guided microsensor patterning (LGMP) technique uses a micrometer-sized aperture. The techniques are suggested to be utilized for patterning microstructures made of nanoparticles that are either crystallized from liquid precursors or directly deposited from nanoparticle-in-liquid suspensions. The computational results based on the paraxial Fraunhofer approximation of a Gaussian beam diffracted by a circular aperture and experimental measurements of corresponding deposition rate under different conditions suggest several factors for setup optimization of LGMP. The results indicate that among the most important factors are the aperture size relative to the laser beam-waist size and the divergence of the beam near the aperture. Examples of gold-thiolate, protein-coated polystyrene, and carbon-polymer composites deposition are presented.


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