Elliptical Gaussian Distribution Research Articles

Precise and fast spillage estimation for a central receiver tower based solar plant

An accurate and computationally cheap method to estimate the optical efficiency of a heliostat field associated with a central receiver tower (CRT) system is essential for an optimized design. In this article, an improved method is developed to estimate the intercept efficiency of a field with flat heliostats. Based on the slant distance, a judicious combination of two different schemes, i.e. Elliptical Gaussian Distribution (EGD) and Pseudo Ray Tracing (PRT), is employed to estimate flux in an image plane. The flux from the image plane is translated to the receiver to estimate spillage. The proposed method is rigorously validated against the state of the art tool, SolTRACE, under various conditions which demonstrates robustness and accuracy of the method. The deviation of intercept efficiency from SolTRACE is small (within 1.5 %). However, such a high degree of accuracy is achieved at a meagre computational cost (below 15 %) compared to SolTRACE even without parallel computing. Thus, the intercept efficiency or spillage estimation of a given heliostat field is rendered ten times faster by the method presented in the current article without a loss of accuracy. An earlier study by the same authors showed the accurate and fast estimation of shading and blocking efficiency. The present study adds to the previous effort and proceeds towards the objective of achieving a fast and precise tool for the design and analysis of heliostat fields. The proposed tool is developed in Python environment which exploits the parallel computing features based on NumPy, Pandas and multiprocessing.

Modeling of Solar Eclipse effects on the sub-ionospheric VLF/LF signals observed by multiple stations over Japan

We present the numerical modeling of field amplitude perturbations for two VLF/LF transmitters (JJI: 22.2 kHz, JJY: 40.0 kHz) signals recorded at six places (UEC-VLF network) in Japan during the Annular Solar Eclipse of 2012 (ASE-2012). We determine the characteristics of the D-region ionospheric perturbation according to the antumbra and penumbral shadow of the annular solar eclipse. A space–time dependent 2-Dimensional Elliptical Gaussian distribution Model (2DEGM) is introduced to get the effect of ASE-2012 on the Wait’s D-region parameters, such as effective VLF/LF reflection height (h′) and sharpness factor (β). The Long Wave Propagation Capability (LWPC) code is used to simulate the VLF signal amplitude profile with the help of modelled Wait’s parameters. A method of comparison of observed and LWPC simulated VLF signal amplitude across all the considered signal propagation paths is introduced to estimate final 2DEGM related parameters and hence, to model D-region electron density perturbations during ASE-2012. Using 2DEGM + LWPC, (i) we consistently simulate the observed VLF signal amplitude profiles for almost all the propagation paths of UEC-VLF network and (ii) evaluate the percentage change in D-region electron density due to ASE-2012.

Anamorphic beam shaping system designed to optimize irradiance distribution in the Cofiblas process for glass nanofibers production

Glass fibers play a key role as reinforcements in composite materials, where increasing mechanical properties at affordable costs are required in applications such aerospace, automotive and wind turbine manufacturing. The production of glass nanofibers augurs a substantial enhancement of their performance. However, although different techniques are currently used to produce glass, polymer or carbon nanofibers, none of them is practical to continuously produce solid, non-porous and separated glass nanofibers with capability to feasibly scaling up for mass production. The continuous fiberizing by laser melting (Cofiblas), makes possible to obtain ultrafine fibers with virtually infinite length.Here, we provide a deep analysis on the influence of the laser beam shaping system on the performance of the Cofiblas technique. Two different optical systems are compared: the first one consists of a beam-splitter coupled to a set of mirrors and spherical lenses. While the second one, is based on an anamorphic system comprising a simple combination of cylindrical and spherical lenses. Both configurations are evaluated and compared in several sets of experiments with the main target of obtaining continuous glass nanofibers with the smallest diameter. The anamorphic system generates an elliptical Gaussian distribution of the laser beam irradiance, which increases the energy absorbed by the preform. As a result, continuous silica nanofibers with diameters 84.5% smaller are obtained with the anamorphic system, compared with the optical system constituted by spherical lenses.

Ellipse Encoding for Arbitrary-Oriented SAR Ship Detection Based on Dynamic Key Points

In recent years, there has been growing interest in developing oriented bounding-box (OBB) based deep learning approaches to detect arbitrary-oriented ship targets in synthetic aperture radar (SAR) images. However, most existing OBB-based detection methods suffer from boundary discontinuity problems for bounding box angle prediction and key point regression challenges. In this paper, we present a novel OBB-based detection algorithm that utilizes ellipse encoding to effectively exploit the geometric and scattering properties of ship targets. Specifically, the ship contour is fitted by an OBB inscribed ellipse that is encoded as a set of distances between dynamic key points on the bow and target center. By combining the bow angle interval and the decoding process, the negative impact of the boundary discontinuity problem is avoided. In addition, we propose an elliptical Gaussian distribution heatmap and a pooling strategy termed double peaks max-pooling (DPM), to deal with the challenge of separating densely distributed ships in inshore scenes. The former can enhance the heatmap’s ship-side score gap between neighboring ship targets, while the latter can solve the problem of target center responses being suppressed after max-pooling. Simulation experiments conducted on the benchmark Rotating SAR Ship Detection Dataset (RSSDD) and Rotated Ship Detection Dataset in SAR Images (RSDD-SAR) demonstrate the superior performance of our method for ship target detection compared to several state-of-the-art OBB-based algorithms. Ablation experiments show that elliptical Gaussian distribution heatmap and DPM can further improve the inshore detection performance.

Temporal and spatial anti-aliasing for rendering reflections on water waves

The reflection of a bright light source on a dynamic surface such as water with waves can be difficult to render well in real time due to reflection aliasing and flickering. In this paper, we propose a solution to this problem by approximating the reflection direction distribution for the water surface as an elliptical Gaussian distribution. Then we analytically integrate the reflection contribution throughout the rendering interval time. Our method can render in real time an animation of the time integrated reflection of a spherical light source on highly dynamic waves with reduced aliasing and flickering.

Development of a new flux density function for a focusing heliostat

It is important to calculate solar flux distribution with a precise and simple method for the design and optimization of solar tower systems. In this paper, the Gaussian flux density function at the image plane is deduced after simulating the image function of the heliostat with Gaussian distribution function. The flux density distribution of various round or rectangular focusing heliostats at the receiver plane can be calculated through projection. The simulation results are compared with SolTrace analysis and experimental data. Comparison of the flux density distributions between this method and SolTrace show excellent agreement especially when the optical error is equivalent to or larger than the Gaussian function parameter of heliostat image which fits to most of heliostats in a solar tower system. Although it increases error to simulate the image of the heliostat with elliptical Gaussian distribution, compared with the experimental data, the average prediction error of the elliptical Gaussian function is 2.24%, which is less than that of SolTrace because SolTrace applies the circular Gaussian distribution for optical error which bring more errors. Therefore, the Gaussian flux density function proposed is validated and can be used to simulate and optimize the design of solar heliostats field.

Solar flux density calculation for a heliostat with an elliptical Gaussian distribution source

The calculation of solar flux density is a key work for the design and optimization of solar tower system. Because of the great amount of calculation, the source distribution is often regarded as a radial distribution, which is not consistent with the reality. This paper presents a new method to calculate the flux density distribution by a focusing heliostat with an elliptical Gaussian distribution source. The two-dimensional convolution integration is proposed and converted into a one-dimensional integration. We use the Gauss-Legendre integration method to reduce the amount of calculation and accelerate the speed of integration. This method can be used to calculate the solar flux at image and receiver plane by most of the heliostat. It needs only 0.1% time of the ray tracing method for calculating the efficiency of the heliostat. It can be applied for design optimization of the solar heliostat field which is superior to the present methods in both accuracy and computation requirements.

NOISE IN THE CROSS-POWER SPECTRUM OF THE VELA PULSAR

We compare the noise in interferometric measurements of the Vela pulsar from ground- and space-based antennas with theoretical predictions. The noise depends on both the flux density and the interferometric phase of the source. Because the Vela pulsar is bright and scintillating, these comparisons extend into both the low and high signal-to-noise regimes. Furthermore, our diversity of baselines explores the full range of variation in interferometric phase. We find excellent agreement between theoretical expectations and our estimates of noise among samples within the characteristic scintillation scales. Namely, the noise is drawn from an elliptical Gaussian distribution in the complex plane, centered on the signal. The major axis, aligned with the signal phase, varies quadratically with the signal, while the minor axis, at quadrature, varies with the same linear coefficients. For weak signal, the noise approaches a circular Gaussian distribution. Both the variance and covariance of the noise are also affected by artifacts of digitization and correlation. In particular, we show that gating introduces correlations between nearby spectral channels.

Two-dimensional visible synchrotron light interferometry for transverse beam-profile measurement at the SPring-8 storage ring.

A two-dimensional visible synchrotron light interferometer has been developed to measure the transverse profile of an electron beam at the SPring-8 storage ring. The new interferometer enables the simultaneous measurement of beam sizes along the major and minor axes and the beam-tilt angle of an assumed elliptical Gaussian distribution. The principle of the interferometer is explained through basic formulae. To calibrate the point-spread function of the interferometer, a simple error model was assumed for disturbances in the amplitude and phase of the light; these disturbances were presumably caused by optical elements, such as mirrors and lenses. The experimental method to determine the parameters in the error model is shown. To verify the two-dimensional profiling capabilities of the interferometer, an electron beam stored in the SPring-8 storage ring operated at various working points was observed. A beam broadening from 20 to 120 microm in the vertical direction and changes in the beam-tilt angle were clearly observed at working points close to the differential resonance. However, the vertical spatial resolution is limited by the available vertical separation of the apertures of the diffracting mask because of the narrow aperture of the upstream vacuum duct.

Integration of the general bivariate Gaussian distribution over an offset circle

1. Introduction. An efficient method is described in this paper for the numerical evaluation by a high-speed digital computer of the integral of any uncorrelated elliptical Gaussian distribution over the area of any arbitrarily centered circle in the plane. Actually, by introducing at most four linear transformations of coordinates, the present method can be used to cover the general problem of integrating any correlated or uncorrelated bivariate normal distribution over an arbitrary ellipse in the plane. The basic integral to be evaluated is expressible in the form ( 1 ) x p (r) exp [-2 2+ Y 2) dxdy, where the exponential represents an uncorrelated bivariate normal distribution centered at the origin with standard deviations o-x and o-. A point target T is assumed at some arbitrary point (h, k) in the Oxy plane. The distance r is ordinary distance [(x - h)2 + (y - k1)2]112, where (x, y) is an arbitrary burst point in the plane. The function p(r) by definition has the value one if r does not exceed a given constant R, and p(r) is zero otherwise. This has the effect of limiting the field of integration to a circle with center at (h, k) and radius R. Hence the integral can be written as