scholarly journals Mueller Quaternion with Matrix Coefficients for Depolarizing and Nondepolarizing Media

2019 ◽  
Author(s):  
Mehmet Ali Kuntman ◽  
Ahmet Kuntman
Keyword(s):  
Optical Media ◽  
Matrix Coefficients ◽  
Mueller Matrices

It is shown that a Mueller quaternion can be formulated as a quaternion with matrix coefficients, and this Mueller quaternion  transforms the Stokes quaternion for depolarizing  process as well as for nondepolarizing process. Mueller quaternion keeps track of the phase acquired by the Stokes quaternion and, in general,  quaternion states of optical media comprises all properties of Jones, Mueller-Jones and Mueller matrices.

Vector and matrix states for Mueller matrices of nondepolarizing optical media

2016 ◽  
Vol 34 (1) ◽  
pp. 80 ◽  
Author(s):  
Ertan Kuntman ◽  
M. Ali Kuntman ◽  
Oriol Arteaga
Keyword(s):  
Optical Media ◽  
Mueller Matrices

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Modelling Light Transmission in a Fiber-Optical Reflection System

2004 ◽  
Vol 9 (1) ◽  
pp. 55-63
Author(s):  
V. Kleiza
Keyword(s):  
Optical Sensors ◽  
Light Transmission ◽  
External Cavity ◽  
Linear Displacement ◽  
Fiber System ◽  
Light Emitting ◽  
Optical Media ◽  
Reflected Light ◽  
Fiber Optical ◽  
Fiber Optical Sensors

Light transmission in the reflection fiber system, located in external optical media, has been investigated for application as sensors. The system was simulated by different models, including external cavity parameters such as the distance between light emitting and receiving fibers and mirror positioning distance. The sensitivity to a linear displacement of the sensors was studied as a function of the distance between the tips of the light emitting fiber and the center of the pair reflected light collecting fibers, by positioning a mirror. Physical fundamentals and operating principles of the advanced fiber optical sensors were revealed.

Cataract. Diagnostic errors at referring patients to surgery

2020 ◽  
Author(s):  
V.V. Egorov ◽  
◽  
E.L. Sorokin ◽  
G.P. Smoliakova ◽  
O. V. Kolenko ◽  
...  
Keyword(s):  
Clinical Diagnosis ◽  
Diagnostic Errors ◽  
Ophthalmological Examination ◽  
Slit Lamp ◽  
Critical View ◽  
Optical Media

The textbook examines the most common diagnostic errors of ophthalmologists when making a clinical diagnosis of "cataract". Clinical examples point to a more critical view of the cataract diagnosis. Due to the fact that most of the errors are based on a superficial examination of the eye, clear recommendations are given for conducting a clinical ophthalmological examination of cataracts. At the same time, special attention is paid to the types of examination of the lens with the help of a slit lamp, to the peculiarities of performing various types of ophthalmoscopy with moderate opacity of optical media.

scholarly journals Anisotropic dielectric susceptibility matrix of anisotropic medium

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wanrong Gao
Keyword(s):  
Light Scattering ◽  
Anisotropic Medium ◽  
Polarized Light ◽  
Scattering Matrix ◽  
Dielectric Susceptibility ◽  
Anisotropic Dielectric ◽  
New Methods ◽  
Mueller Matrices ◽  
Anisotropic Structures ◽  
The Fourier Transform

AbstractIn this work, we introduce the concept of anisotropic dielectric susceptibility matrix of anisotropic medium for both nondepolarizing and depolarizing medium. The concept provides a new way of analyzing light scattering properties of anisotropic media illuminated by polarized light. The explicit expressions for the elements of the scattering matrix are given in terms of the elements of the Fourier transform of the anisotropic dielectric susceptibility matrix of the medium. Finally, expressions for the elements of the Jones matrix of a thin layer of a deterministic anisotropic medium and the elements of the Mueller matrix of a depolarizing medium are given. The results obtained in this work is helpful for deriving information about the correlated anisotropic structures in depolarizing media from measured Mueller matrices. The findings in this work may also well prove stimulating to researchers working on new methods for analyzing light scattering properties.

scholarly journals Universal Synthesizer of Mueller Matrices Based on the Symmetry Properties of the Enpolarizing Ellipsoid

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 983
Author(s):  
José J. Gil ◽  
Ignacio San José
Keyword(s):  
Mathematical Structure ◽  
Mueller Matrix ◽  
Morphological Properties ◽  
Nondestructive Analysis ◽  
Structural Decomposition ◽  
Symmetry Properties ◽  
Mueller Matrices ◽  
Scattering Measurement ◽  
The Way

Polarimetry is today a widely used and powerful tool for nondestructive analysis of the structural and morphological properties of a great variety of material samples, including aerosols and hydrosols, among many others. For each given scattering measurement configuration, absolute Mueller polarimeters provide the most complete polarimetric information, intricately encoded in the 16 parameters of the corresponding Mueller matrix. Thus, the determination of the mathematical structure of the polarimetric information contained in a Mueller matrix constitutes a topic of great interest. In this work, besides a structural decomposition that makes explicit the role played by the diattenuation-polarizance of a general depolarizing medium, a universal synthesizer of Muller matrices is developed. This is based on the concept of an enpolarizing ellipsoid, whose symmetry features are directly linked to the way in which the polarimetric information is organized.

scholarly journals Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam
Keyword(s):  
Least Squares ◽  
Iterative Algorithm ◽  
Gradient Descent ◽  
Main Idea ◽  
Full Column Rank ◽  
Minimum Error ◽  
Matrix Coefficients ◽  
Special Cases ◽  
Efficiency And Effectiveness ◽  
Associated Matrix

AbstractThis paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.

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