China
Africa
Explore chapters and articles related to this topic
Polarized Electromagnetic Waves
Published in José J. Gil, Razvigor Ossikovski, Polarized Light and the Mueller Matrix Approach, 2022
José J. Gil, Razvigor Ossikovski
Random processes involving two or more normally (Gaussian) distributed random variables are quite frequent in the description of physical situations. A stationary Gaussian process is necessarily ergodic. All statistical properties of a Gaussian process are determined by the mean and the second-order correlation function. Thus, weak stationarity of a Gaussian process implies strong stationarity. Moreover, a linear transformation of a Gaussian leads to a Gaussian process. Furthermore, the Fourier transform of a Gaussian function is again a Gaussian function. All the above concepts are straightforwardly extended to stochastic processes involving n variables, as for instance 2D polarization states (n=2), 3D polarization states (n=3) and Mueller states (n=4, see Chapter 5).
Diffraction in Optical Systems
Published in Daniel Malacara-Hernández, Zacarías Malacara-Hernández, Handbook of OPTICAL DESIGN, 2017
Daniel Malacara-Hernández, Zacarías Malacara-Hernández
where ρ is the distance from the point being considered to the optical axis and w is the value of ρ when the irradiance is 1/e2 of its axial value. These beams appear in the light beams emitted by gas lasers and have very interesting and important properties that have been studied by Kogelnik (1959, 1979). A spherical convergent Gaussian wavefront becomes flat and Gaussian at the focus. This is easy to understand if we remember that the Fourier transform of a Gaussian function is also a Gaussian function. After going through this focus, the wavefront diverges again with a spherical shape and a Gaussian distribution of amplitudes. As shown in Figure 9.20, the beam is perfectly symmetrical, with the center of symmetry at the focus. This focus or minimum diameter of the beam is called a waist. The semidiameter w0 of the waist is related to the angle of convergence θ by () θ=λπw0.
From Microphysics to Mesophysics: Obtaining Effective Properties from Microscopic Behaviors
Published in Didier Felbacq, Guy Bouchitté, Metamaterials Modeling and Design, 2017
It is simplest to consider the homogenization of a onedimensional system. A reasonable first try for f~(k) $ \tilde{f}({\mathbf{k}}) $ is the Gaussian function, whose Fourier transform is also a Gaussian. This choice works fine if the wavelength is very large, so that kB $ {\mathbf{k}}_{\text{B}} $ ≈0 $ \approx {\mathbf{0}} $ (see Fig. 3.3, with K = 2 [au]). When the wavelength is very large, the kB $ {\mathbf{k}}_{\text{B}} $ term in Eq. (3.41) can be virtually ignored and the Bloch harmonics coincide with the reciprocal lattice vectors of the periodic medium. The homogenization process can then be seen to consist of filtering out all but the lowest harmonic corresponding to n = 0.
Numerical modeling of ship wave generation using Green’s functions based on linear dispersive wave theory
Published in Coastal Engineering Journal, 2020
Jumpei Morioka, Yoshimitsu Tajima, Yusuke Yamanaka, Magnus Larson, Yoshiaki Kuriyama, Takenori Shimozono, Shinji Sato
Determination of σ, the standard deviation of the Gaussian pulse used for computing the Green’s functions may be one of the most important factors in the present model, since the magnitude of σ determines the frequency range of the dominant spectrum of generated waves. Besides σ = 0.15 s, used in all the aforementioned analysis, this section also applied σ = 0.3 s and 0.075 s. Fourier transform of the Gaussian function, determined by
Evaluating Visual Consistency of Icon Usage in Across-Devices
Published in International Journal of Human–Computer Interaction, 2023
Xiaojiao Chen, Xiaoteng Tang, Ying Zhao, Tengyu Huang, Ran Qian, Jiayi Zhang, Wei Chen, Xiaosong Wang
We assumed that there is a bias between the perceived and physical values of the icon coding features. Based on Weber’s law (Sanders & McCormick, 1998), the bias of the participants on the icon coding features can be calculated by finding the difference between the SEV and OEV. The probability of participants selecting the test icon over the reference icon when the size of the test icon is smaller than the reference icon “test is less than reference” was studied, and an analysis of the data was done through curve fitting, as shown in Figure 7. Particularly, the OEV is obtained when the actual features of the reference and test icons are the same in physical space. When the participants subjectively assessed that the features of the reference and test icons are equal in value, the probability of selecting the test icon over the reference icon is 0.5. Moreover, if the participants perceive the values to be the same, they might make a random selection. Therefore, if there is an interval of equal value of the reference and test icons, we regarded this interval as cognitive bias, namely, a cognitive bias is a difference between the SEV and OEV. Figure 7 is an example of how cognitive bias in E2 is measured. The x-axis represents the size value of the test icons in pixels, and the y-axis represents the probability that the size of the test icon is smaller than the reference icon. In particular, the SEV is 67.43 pixels, OEV is 68 pixels, and at a 1.5× scale, the bias of the positive polarity × plane in terms of perceived size (67.43 − 68 = −0.57) is −0.57 pixels. Using MATLAB, a data analysis software, the best-fitting curve was generated by using a cumulative Gaussian function. Then the ordinate was set to 0.5 to obtain the abscissa values on the fitted curve. The abscissa values are defined as the SEVs here. The equivalent for the physical values is the OEV.
Pipeline leak diagnosis based on leak-augmented scalograms and deep learning
Published in Engineering Applications of Computational Fluid Mechanics, 2023
Muhammad Farooq Siddique, Zahoor Ahmad, Jong-Myon Kim
A Gaussian filter is a linear filter that uses a Gaussian function to smooth out an image. The Gaussian function is a curve that looks like a bell, and the mean and standard deviation tell us what it looks like. The amount of smoothing that is done to an image is based on the standard deviation of the Gaussian function. Gaussian filters are commonly used to eliminate noise from an image because they can smooth out small, random fluctuations in pixel intensity while preserving the overall structure of the image (Gupta, 2022).