scholarly journals Error Analysis and Calibration Improvement of the Imaging Section in a Mueller Matrix Microscope

2020 ◽  
Vol 10 (13) ◽  
pp. 4422
Author(s):  
Jiewei Yu ◽  
Xuemin Cheng ◽  
Maolin Li
Keyword(s):  
Maximum Error ◽  
Coefficient Matrix ◽  
Mueller Matrix ◽  
Quarter Wave Plate ◽  
Source Analysis ◽  
Matrix Elements ◽  
Standard Samples ◽  
Comparison Results ◽  
Calibration Methods ◽  
The Matrix

Currently, there are various calibration methods available to reduce the errors caused by the polarizing section of a dual-rotating-retarder polarimeter. Although these methods have high measurement accuracy, their robustness must be improved and the influence of the imaging section needs be discussed when they are applied in Mueller matrix microscopes. In this paper, a method of error source analysis and element calibration for the Mueller matrix microscope is proposed by using error transform coefficient matrices to account for the polarizing effect of the imaging section. Using Taylor expansion, an approximate linear relationship is established between the sources of errors and the Mueller matrix elements of the measured sample. From this relationship, error magnification coefficient matrices are calculated to determine the specific parameter errors in both the polarizing and imaging sections. Furthermore, elements in the fourth row or column of the error magnification coefficient matrix are especially important for the imaging section. The measurement and simulation results for an air sample and a quarter-wave plate sample as the standard samples, as well as a Daphnia organism sample with complex internal structure, are investigated and discussed. Furthermore, the comparison results reveal the effect of the imaging section on the birefringence characteristics of the Mueller matrix. With the proposed method, the maximum error can be reduced to be less than 0.01 for all the matrix elements and for the amplitude parameter of birefringence, even when the two system parameters a 2 and a 3 of the rotating mechanical part deviate from the default.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

ANALYSIS OF SOLDERS ON TIN AND LEAD BASES BY X-RAY FLOORESCENT SPECTROSCOPY

2021 ◽  
pp. 124-131
Author(s):  
A.V. Alekseev ◽  
◽  
G.V. Orlov ◽  
P.S. Petrov ◽  
A.V. Slavin ◽  
...  
Keyword(s):  
Emission Spectroscopy ◽  
High Resolution Mass Spectrometry ◽  
Analytical Signal ◽  
Atomic Emission ◽  
Standard Samples ◽  
X Ray ◽  
Fundamental Parameters ◽  
The Matrix ◽  
Resolution Mass

The determination of the elements Cu, Ni, Sb, Bi, Pb, Zn and Fe in the tin-based solder VPr35, as well as the elements Sn, Ni, Sb, Bi and In in the lead-based VPr40 solder by the method of х-ray fluorescence spectroscopy has been carried out. The calibration dependences are corrected taking into account the superposition of signals from interfering elements on the analytical signal and changes in intensity caused by inter-element influences in the matrix. The analysis was carried out by the method of fundamental parameters without using standard samples. The correctness of the results obtained was confirmed by their comparative analysis by atomic emission spectroscopy and high-resolution mass spectrometry with a glow discharge.

Notizen: The Dipole Moment Function of HF Molecule Using Morse Potential

1977 ◽  
Vol 32 (8) ◽  
pp. 897-898 ◽  
Author(s):  
Y. K. Chan ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for HF molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r - re)n. These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M 1 and M 2.

Leach Behavior of SRL TDS-131 Defense Waste Glass in Water at High&Low Flow Rates

1983 ◽  
Vol 26 ◽  
Author(s):  
Aaron Barkatt ◽  
William Sousanpour ◽  
Alisa Barkatt ◽  
Morad A. Boroomand ◽  
Pedro B. Macedo
Keyword(s):  
Contact Time ◽  
Protective Layer ◽  
High Flow ◽  
Low Flow ◽  
Matrix Elements ◽  
Flow Rates ◽  
Low Concentrations ◽  
Controlling Mechanism ◽  
The Matrix ◽  
Leach Behavior

ABSTRACTLeach tests carried out on SRL TDS-131 Defense Waste Class indicate that at high flow rates the controlling mechanism is simple corrosion. The matrix elements (Si, Al) are leached out at rates similar to those of the leaching of the alkalis and of boron, and the leaching process is nearly linear with time. At slow flow rates (below 1 m/yr) leaching becomes controlled by the build-up of a protective layer. Al and most of the Si remain in the leached surface layer. The leach rates decrease in the course of the test before leveling off at constant values which are almost inversely proportional to the contact time, indicating that leachate concentrations have become solubility-limited. The low concentrations observed at this stage indicate the formation of alteration products.

scholarly journals CONSTRUCTION OF MINIMAX CONTROL FOR ALMOST CONSERVATIVE CONTROLLED DYNAMIC SYSTEMS WITH THE LIMITED PERTURBATIONS

2017 ◽  
Vol 2 ◽  
pp. 9-15
Author(s):  
Iryna Svyatovets
Keyword(s):  
Riccati Equation ◽  
Infinite System ◽  
Conservative System ◽  
Coefficient Matrix ◽  
Necessary Condition ◽  
Existence Of A Solution ◽  
Minimax Control ◽  
System Of Matrix Equations ◽  
System A ◽  
The Matrix

The problem is considered for constructing a minimax control for a linear stationary controlled dynamical almost conservative system (a conservative system with a weakly perturbed coefficient matrix) on which an unknown perturbation with bounded energy acts. To find the solution of the Riccati equation, an approach is proposed according to which the matrix-solution is represented as a series expansion in a small parameter and the unknown components of this matrix are determined from an infinite system of matrix equations. A necessary condition for the existence of a solution of the Riccati equation is formulated, as well as theorems on additive operations on definite parametric matrices. A condition is derived for estimating the parameter appearing in the Riccati equation. An example of a solution of the minimax control problem for a gyroscopic system is given. The system of differential equations, which describes the motion of a rotor rotating at a constant angular velocity, is chosen as the basis.

scholarly journals Worldline master formulas for the dressed electron propagator. Part 2. On-shell amplitudes

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
N. Ahmadiniaz ◽  
V. M. Banda Guzmán ◽  
F. Bastianelli ◽  
O. Corradini ◽  
J. P. Edwards ◽  
...  
Keyword(s):  
Cross Sections ◽  
Drop Out ◽  
Matrix Elements ◽  
Fermion Propagator ◽  
Particle Path ◽  
Path Integral Representation ◽  
Fermion Line ◽  
Electron Propagator ◽  
The Matrix ◽  
Standard Linear

Abstract In the first part of this series, we employed the second-order formalism and the “symbol” map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N-photon kernel,” where this kernel appears also in “subleading” terms involving only N − 1 of the N photons.In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications.We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for “all +” photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

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