scholarly journals Polarized radiative transfer equation in some nontrivial coordinate systems

2011 ◽  
Vol 7 (S283) ◽  
pp. 360-361
Author(s):  
Juris Freimanis
Keyword(s):  
Refractive Index ◽  
Differential Operator ◽  
Radiative Transfer ◽  
Euclidean Space ◽  
Coordinate System ◽  
Transfer Equation ◽  
Effective Refractive Index ◽  
Radiative Transfer Equation ◽  
Coordinate Systems ◽  
Prolate Spheroidal

AbstractExplicit expressions for the differential operator of stationary quasi-monochromatic polarized radiative transfer equation in Euclidean space with piecewise homogeneous real part of the effective refractive index are obtained in circular cylindrical, prolate spheroidal, elliptic conical, classic toroidal and simple toroidal coordinate system.

scholarly journals Polarized Radiative Transfer Equation in Some Geometries of Elliptic Type

2011 ◽  
Vol 7 (S282) ◽  
pp. 253-254
Author(s):  
Juris Freimanis
Keyword(s):  
Refractive Index ◽  
Differential Operator ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Elliptic Type ◽  
Coordinate Systems ◽  
Prolate Spheroidal ◽  
Oblate Spheroidal ◽  
General Method

AbstractA general method, which allows us to derive explicit expressions for the differential operator of stationary quasi-monochromatic polarized radiative transfer equation in Euclidean space, with piecewise homogeneous real part of the effective refractive index, is applied to ellipsoidal, oblate spheroidal, prolate spheroidal and elliptic conical coordinate systems.

Transfer Equation in General Curvilinear Coordinates

2011 ◽  
Vol 20 (2) ◽  
Author(s):  
J. Freimanis
Keyword(s):  
Differential Operator ◽  
Radiative Transfer ◽  
Coordinate System ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Dimensional Space ◽  
Polarization Plane ◽  
Curvilinear Coordinates ◽  
Reference Plane ◽  
Metric Tensor

AbstractThe differential operator of the monochromatic polarized radiative transfer equation is studied in case of statistically homogeneous turbid medium in Euclidean three-dimensional space, with arbitrary curvilinear coordinate system defined in it. An apparent rotation of the polarization plane along the light ray with respect to the chosen polarization reference plane generally takes place, due to purely geometric reasons. Using methods of tensor analysis, analytic expressions for the differential operator of the transfer equation depending on the components of the metric tensor and their derivatives are found. Considerable simplifications take place if the coordinate system is orthogonal. As an example, the differential operator of the vector radiative transfer equation in both elliptical conical coordinate system and oblate spheroidal coordinate system is written down. Nonstandard parameterization of standard elliptical conical coordinate system is proposed.

A Reconstruction Scheme Based on the Radiative Transfer Equation for Graded Index Semi-Transparent Media

2010 ◽  
Author(s):  
Joan Boulanger ◽  
Olivier Balima ◽  
Andre´ Charette
Keyword(s):  
Refractive Index ◽  
Radiative Transfer ◽  
Least Squares ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Flow Visualisation ◽  
Refractive Index Gradient ◽  
Radiative Transport ◽  
Inversion Algorithm ◽  
Gradient Based

Graded refractive index media appear in numerous industrial applications such as non-isothermal flows, optics material processing, biological imaging. Refractive index gradient has been an early help for combusting flow visualisation. The numerical treatment of radiative transport is difficult in such media due to the curvature of rays, especially when the media are not optically thick. Computer-aided remote probing (inversion) is done today with the help of the diffusion approximation adapted to varying refractive index media but is unsuitable for thin media. Therefore, it is important to develop an approach allowing the use of the radiative transport equation which is the most complete formalism for radiative transfer to date and to couple it to reconstruction schemes. The aim of this study is to demonstrate the reconstruction of an arbitrary refractive index distribution from a least-squares gradient-based iterative inversion algorithm taking advantage of the full transient Radiative Transfer Equation (tRTE). The finite-difference discrete-ordinates method for the tRTE and its adjoint has been implemented, accounting for spatial changes in the distribution of the refractive index in a semi-transparent medium. A least-squares gradient-based iterative algorithm has been designed and elementary tests have been carried to demonstrate reconstruction possibilities.

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