Method for CCD Edge Signal Processing

2013 ◽  
Vol 441 ◽  
pp. 695-698
Author(s):  
Guo Sheng Xu
Keyword(s):  
Least Square ◽  
Digital Data ◽  
Edge Point ◽  
Precise Position ◽  
Order Curve ◽  
Least Square Fit ◽  
Edge Location ◽  
Edge Detection Method ◽  
The One ◽  
Fitting Part

In order to improve the measuring precision of the one-dimension line-matrix CCD, a new sub-pixel edge detection method is proposed. Firstly the date collected by the line-matrix CCD is converted to digital data by virtual oscillograph. Base on threshold comparison, the fitting part of the edge signal is picked up for further processing; secondly, the pixels are expanded following the edge direction of the edge point, and the edge signal is fitted through the two order multinomial; finally, comparing the two order curve with the threshold voltage through the least square fit method, the precise position of the edge point can achieve the sub-pixel edge location precision.

scholarly journals Semi-Analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian Expansion of Distance Operators W= RC1-nRD1-M, RC1-Nr12-M, R12-Nr13-M

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Gaussian Function ◽  
Approximate Solutions ◽  
Equation System ◽  
Least Square ◽  
Position Vector ◽  
Least Square Fit ◽  
Analytic Expressions ◽  
The One ◽  
Analytical Expressions ◽  
Coulomb Integrals

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)…rho(rk) W(r1,…,rk) dr1…drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer, positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|^-u, of which only the u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation calculations. Solving the related linear equation system (LES), the expansion |r|^-u about equal SUM(k=0toL)SUM(i=1toM) Cik r^2k exp(-Aik r^2) is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|^-u) are useful for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian.

scholarly journals Shell model calculations in the A=80-100 mass region and study of double β transitions

2020 ◽  
Vol 1 ◽  
pp. 156
Author(s):  
J. Sinatkas ◽  
L. D. Skouras ◽  
D. Strottman ◽  
J. D. Vergados
Keyword(s):  
Shell Model ◽  
Satisfactory Agreement ◽  
Effective Interaction ◽  
Model Space ◽  
Mass Region ◽  
Least Square ◽  
Matrix Elements ◽  
Model Calculations ◽  
Least Square Fit ◽  
The One

The structure of the Ζ,Ν < 50 nuclei is examined in a model space consisting of the 0g9/2, 1p1/2, 1p3/2 and the 0f5/2 hole orbitals outside the doubly closed 100Sn core. The effective interaction for this model space is derived by introducing second order corrections to the Sussex matrix elements, while the one-hole energies are deduced by a least square fit to the observed levels. The results of the calculation are found to be in very satisfactory agreement with experiment for all nuclei with 38<Ζ<46 but for Ζ<38 this agreement begins to deteriorate. Such a feature possibly indicates the appearance of deformation and the breaking of the Ν=50 core. The wavefunctions of the calculation are used to determine double β matrix elements in the Ge, Se, Sr and Kr isotopes.

Target Plane Confidence Boundaries: Mathematics of The 1997 XF11 Scare

1999 ◽  
Vol 172 ◽  
pp. 369-370
Author(s):  
Andrea Milani ◽  
Giovanni B. Valsecchi
Keyword(s):  
Linear Approximation ◽  
Close Approach ◽  
Confidence Regions ◽  
Least Square ◽  
Computational Load ◽  
Approach Distance ◽  
The Monte Carlo Method ◽  
Hazardous Object ◽  
Least Square Fit ◽  
The One

The uncertainty of the close approach distance of a Potentially Hazardous Object (PHO), either an asteroid or a comet, can be represented on the Modified Target Plane (MTP), a modification of the one used by Öpik. The MTP is orthogonal to the geocentric velocity at the closest approach along the nominal orbit, solution of the least square fit to the observations. The confidence regions of this solution in the 6-D space of orbital elements (for an epoch close to the observations) are well approximated by a family of concentric ellipsoids, if the observed arc is not too short. In the linear approximation these ellipsoids are mapped on the MTP into concentric ellipses, which can be computed by solving for the state transition matrix.For a PHO observed at only one opposition, with a close approach expected after many revolutions, the ellipses on the MTP become extremely elongated and the linear approximation may fail. In this case the confidence boundaries on the MTP, i.e. the nonlinear images of the confidence ellipsoids, may not be well approximated by the ellipses. The Monte Carlo method (Muinonen and Bowell, 1993) can be used to find nonlinear confidence regions, but the computational load is very heavy: to estimate a low probability event the number of test cases must be larger than the inverse of the probability. We propose a new method to compute semilinear confidence boundaries on the MTP (Milani and Valsecchi, 1998), based on the theory developed to compute confidence boundaries for predicted observations (Milani, 1999). This method is a good compromise between reliability and computational load, and can be used for real time risk assessment.

scholarly journals Semi-Analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian Expansion of Distance Operators W= RC1-nRD1-M, RC1-Nr12-M, R12-Nr13-M

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Gaussian Function ◽  
Approximate Solutions ◽  
Equation System ◽  
Least Square ◽  
Position Vector ◽  
Least Square Fit ◽  
Analytic Expressions ◽  
The One ◽  
Analytical Expressions ◽  
Coulomb Integrals

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)…rho(rk) W(r1,…,rk) dr1…drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer, positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|^-u, of which only the u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation calculations. Solving the related linear equation system (LES), the expansion |r|^-u about equal SUM(k=0toL)SUM(i=1toM) Cik r^2k exp(-Aik r^2) is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|^-u) are useful for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian.

Least-square refinement of structure parameters from CBED integrated intensities: application to determination of temperature factors in Y BA2CU3O7

1992 ◽  
Vol 50 (2) ◽  
pp. 1456-1457
Author(s):  
Kjersti Gjønnes ◽  
Jon Gjønnes
Keyword(s):  
Least Square ◽  
Measured Intensity ◽  
Structure Information ◽  
Accurate Temperature ◽  
Least Square Fit ◽  
Case Application ◽  
Integrated Intensities ◽  
Temperature Factors ◽  
Narrow Bands

Electron diffraction intensities can be obtained at large scattering angles (sinθ/λ ≥ 2.0), and thus structure information can be collected in regions of reciprocal space that are not accessable with other diffraction methods. LACBED intensities in this range can be utilized for determination of accurate temperature factors or for refinement of coordinates. Such high index reflections can usually be treated kinematically or as a pertubed two-beam case. Application to Y Ba2Cu3O7 shows that a least square refinememt based on integrated intensities can determine temperature factors or coordinates.LACBED patterns taken in the (00l) systematic row show an easily recognisable pattern of narrow bands from reflections in the range 15 < l < 40 (figure 1). Integrated intensities obtained from measured intensity profiles after subtraction of inelastic background (figure 2) were used in the least square fit for determination of temperature factors and refinement of z-coordinates for the Ba- and Cu-atoms.

Array design

1968 ◽  
Vol 58 (3) ◽  
pp. 977-991
Author(s):  
Richard A. Haubrich
Keyword(s):  
High Resolution ◽  
Data Processing ◽  
Least Square ◽  
Wave Number ◽  
Array Design ◽  
Least Square Fit ◽  
The Difference ◽  
Set Of Points ◽  
Array Output

abstract Arrays of detectors placed at discrete points are often used in problems requiring high resolution in wave number for a limited number of detectors. The resolution performance of an array depends on the positions of detectors as well as the data processing of the array output. The performance can be expressed in terms of the “spectrum window”. Spectrum windows may be designed by a general least-square fit procedure. An alternate approach is to design the array to obtain the largest uniformly spaced coarray, the set of points which includes all the difference spacings of the array. Some designs obtained from the two methods are given and compared.

Digital Fractional Order Savitzky-Golay Differentiator and Its Application

2011 ◽  
Author(s):  
Dali Chen ◽  
Dingyu Xue ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Least Square ◽  
One Dimension ◽  
Order Derivative ◽  
Noisy Signal ◽  
Fractional Order Derivative ◽  
Least Square Fitting ◽  
Image Enhancing ◽  
The One ◽  
Derivatives Of

Firstly the one-dimension digital fractional order Savitzky-Golay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure robust and accuracy. Experiments demonstrate that 1-D DFOSGD can estimate the fractional order derivatives of both ideal signal and noisy signal accurately. Secondly, the two-dimension DFOSGD is obtained from 1-D DFOSGD by defining a group of direction operators, and a new image enhancing method based on 2-D DFOSGD is presented. Experiments demonstrate that 2-D DFOSGD has very good performance on image enhancement.

Determinates of Islamic banks liquidity

2020 ◽  
Vol 11 (8) ◽  
pp. 1619-1632
Author(s):  
Ahmad Al-Harbi
Keyword(s):  
Monetary Policy ◽  
Deposit Insurance ◽  
Fixed Effect Model ◽  
Least Square ◽  
Data Set ◽  
Content Type ◽  
Effect Model ◽  
Ratio Size ◽  
Cross Country ◽  
The One

Purpose The purpose of this paper is to investigate the determinants of Islam banks (IBs) liquidity. Design/methodology/approach In this paper, the author uses a generalized least square fixed effect model on an unbalanced panel data set of all IBs operating in the Organization of Islamic Cooperation countries over the period 1989-2008. Findings The estimation results show that all the determinants have statistically significant relationships with IBs’ liquidity but with different signs. On the one hand, foreign ownership, credit risk, profitability, inflation rate, monetary policy and deposit insurance negatively affected IBs liquidity. On the other hand, capital ratio, size gross domestic product growth and concentration have a positive nexus with IBs’ liquidity. Originality/value According to the best of the author’s knowledge, this is the first empirical study to investigate the determinants of IBs liquidity using cross-country data with a large sample of IBs (110 banks) and over a long period (19 years). Also, the paper included variables that had not been discussed on the previous studies, which used cross-country data, such as efficiency, deposit insurance, monetary policy, concentration and market capitalization.

scholarly journals Atmospheric CO<sub>2</sub>, CH<sub>4</sub>, and CO with the CRDS technique at the Izaña Global GAW station: instrumental tests, developments, and first measurement results

2019 ◽  
Vol 12 (4) ◽  
pp. 2043-2066 ◽  
Author(s):  
Angel J. Gomez-Pelaez ◽  
Ramon Ramos ◽  
Emilio Cuevas ◽  
Vanessa Gomez-Trueba ◽  
Enrique Reyes
Keyword(s):  
Flow Rate ◽  
Random Noise ◽  
Least Square ◽  
Spatial Inhomogeneity ◽  
Inlet Pressure ◽  
Processing Scheme ◽  
Linear Relationships ◽  
Least Square Fit

Abstract. At the end of 2015, a CO2/CH4/CO cavity ring-down spectrometer (CRDS) was installed at the Izaña Global Atmosphere Watch (GAW) station (Tenerife, Spain) to improve the Izaña Greenhouse Gases GAW Measurement Programme, and to guarantee the renewal of the instrumentation and the long-term maintenance of this program. We present the results of the CRDS acceptance tests, the raw data processing scheme applied, and the response functions used. Also, the calibration results, the implemented water vapor correction, the target gas injection statistics, the ambient measurements performed from December 2015 to July 2017, and their comparison with other continuous in situ measurements are described. The agreement with other in situ continuous measurements is good most of the time for CO2 and CH4, but for CO it is just outside the GAW 2 ppb objective. It seems the disagreement is not produced by significant drifts in the CRDS CO World Meteorological Organization (WMO) tertiary standards. The more relevant contributions of the present article are (1) determination of linear relationships between flow rate, CRDS inlet pressure, and CRDS outlet valve aperture; (2) determination of a slight CO2 correction that takes into account changes in the inlet pressure/flow rate (as well as its stability over the years), and attributing it to the existence of a small spatial inhomogeneity in the pressure field inside the CRDS cavity due to the gas dynamics; (3) drift rate determination for the pressure and temperature sensors located inside the CRDS cavity from the CO2 and CH4 response function drift trends; (4) the determination of the H2O correction for CO has been performed using raw spectral peak data instead of the raw CO provided by the CRDS and using a running mean to smooth random noise in a long water-droplet test (12 h) before performing the least square fit; and (5) the existence of a small H2O dependence in the CRDS flow and of a small spatial inhomogeneity in the temperature field inside the CRDS cavity are pointed out and their origin discussed.

Microwave Spectrum and Dipole Moment of Methylenecyclobutenone

1974 ◽  
Vol 29 (10) ◽  
pp. 1498-1500 ◽  
Author(s):  
W. Czieslik ◽  
L. Carpentier ◽  
D. H. Sutter
Keyword(s):  
Dipole Moment ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
Ground State ◽  
Stark Effect ◽  
Microwave Spectrum ◽  
Least Square ◽  
Rotational Constants ◽  
Vibrational Ground State ◽  
Least Square Fit

Abstract The microwave spectrum of Methylenecyclobutenone has been investigated in the vibrational ground state in the range of 8 to 26.5 GHz. From a least square fit of 12 lines with J ≦ 4 the rotational constants have been calculated as A =5.775664±0.000009 GHz, B = 4.312314 ± 0.000007 GHz, C = 2.467814±0.000008 GHz. The inertia defect Δ = - 0.09 amuÅ2 indicates that the molecule is planar. From Stark-effect measurements the components of the molecular electric dipole moment were obtaied as |μa| = 2.04 ± 0.02 D, |μb| = 2.70±0.03 D, |μtotal| = 3.39 ± 0.05 D.

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