Derivation of the radiative transfer equation for scattering media with a spatially varying refractive index

2003 ◽  
Vol 228 (1-3) ◽  
pp. 33-38 ◽  
Author(s):  
Jean-Michel Tualle ◽  
Eric Tinet
Keyword(s):  
Refractive Index ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Scattering Media ◽  
Spatially Varying

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.

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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