NUMERICAL TREATMENT OF HIGHLY FORWARD SCATTERING ON RADIATIVE TRANSFER USING THE DELTA-M APPROXIMATION AND GALERKIN QUADRATURE METHOD

2019 ◽  
Author(s):  
Hiroyuki Fujii ◽  
Go Chiba ◽  
Yukio Yamada ◽  
Yoko Hoshi ◽  
Kazumichi Kobayashi ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Forward Scattering ◽  
Quadrature Method ◽  
Numerical Treatment

scholarly journals Chromospheric diagnosis with forward scattering polarization

2014 ◽  
Vol 10 (S305) ◽  
pp. 146-153
Author(s):  
E. S. Carlin
Keyword(s):  
Radiative Transfer ◽  
Solar Disk ◽  
Disk Center ◽  
Forward Scattering ◽  
Dynamic Effects ◽  
Polarity Inversion ◽  
Physical Context ◽  
Hanle Effect ◽  
Definition Of ◽  
Spatial Maps

AbstractIs it physically feasible to perform the chromospheric diagnosis using spatial maps of scattering polarization at the solar disk center? To investigate it we synthesized polarization maps (in 8542 Å) resulting from MHD solar models and NLTE radiative transfer calculations that consider Hanle effect and vertical macroscopic motions. After explaining the physical context of forward scattering and presenting our results, we arrive at the definition of Hanle polarity inversion lines. We show how such features can give support for a clearer chromospheric diagnosis in which the magnetic and dynamic effects in the scattering polarization could be disentangled.

scholarly journals An Improved Small-Angle Approximation for Forward Scattering and Its Use in a Fast Two-Component Radiative Transfer Method

2017 ◽  
Vol 74 (6) ◽  
pp. 1959-1987 ◽  
Author(s):  
Bingqiang Sun ◽  
George W. Kattawar ◽  
Ping Yang ◽  
Eli Mlawer
Keyword(s):  
Radiative Transfer ◽  
Small Angle ◽  
Delta Function ◽  
Computational Effort ◽  
Forward Scattering ◽  
Scattering Method ◽  
Diffuse Component ◽  
Dirac Delta ◽  
Small Angle Approximation ◽  
Two Component

Abstract The vector radiative transfer equation is decomposed into two components: a forward component and a diffuse component. The forward component is analytically solved with a small-angle approximation. The solution of the forward component becomes the source for the diffuse component. In the present study, the diffuse component is solved using the successive order of scattering method. The strong anisotropy of the scattering of radiation by a medium is confined to the forward component for which a semianalytical solution is given; consequently, the diffuse component slowly varies as a function of scattering angle once the forward-scattering peak is removed. Moreover, the effect on the diffuse component induced by the forward component can be interpreted by including the low orders of the generalized spherical function expansion of the forward component or even replaced by the Dirac delta function. As a result, the computational effort can be significantly reduced. The present two-component method is validated using the benchmarks related to predefined aerosol and cloud layers with a totally absorbing underlying surface. As a canonical application, the optical properties of water clouds and ice clouds used for the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 6 cloud-property retrieval products are used for radiative transfer simulations under cloudy conditions.

scholarly journals Characteristic Length and Time Scales of the Highly Forward Scattering of Photons in Random Media

2019 ◽  
Vol 10 (1) ◽  
pp. 93 ◽  
Author(s):  
Hiroyuki Fujii ◽  
Moegi Ueno ◽  
Kazumichi Kobayashi ◽  
Masao Watanabe
Keyword(s):  
Radiative Transfer ◽  
Time Scales ◽  
Analytical Solutions ◽  
Random Media ◽  
Three Dimensional ◽  
Forward Scattering ◽  
Diffusion Equations ◽  
Transport Models ◽  
Photon Diffusion ◽  
Photon Transport

Background: Elucidation of the highly forward scattering of photons in random media such as biological tissue is crucial for further developments of optical imaging using photon transport models. We evaluated length and time scales of the photon scattering in three-dimensional media. Methods: We employed analytical solutions of the time-dependent radiative transfer, M-th order delta-Eddington, and photon diffusion equations (RTE, dEM, and PDE). We calculated the fluence rates at different source-detector distances and optical properties. Results: We found that the zeroth order dEM and PDE, which approximate the highly forward scattering to the isotropic scattering, are valid in longer length and time scales than approximately 10 / μ t ′ and 40 / μ t ′ v , respectively, where μ t ′ is the reduced transport coefficient and v the speed of light in a medium. The first and second order dEM, which approximate the highly forward-peaked phase function by the first two and three Legendre moments, are valid in the longer scales than approximately 4.0 / μ t ′ and 6.3 / μ t ′ v ; 2.8 / μ t ′ and 3.5 / μ t ′ v , respectively. The boundary conditions less influence the length scales, while they reduce the times scales from those for bulk at the longer length scale than approximately 4.0 / μ t ′ . Conclusion: Our findings are useful for constructions of accurate and efficient photon transport models. We evaluated length and time scales of the highly forward scattering of photons in various kinds of three-dimensional random media by analytical solutions of the radiative transfer, M-th order delta-Eddington, and photon diffusion equations.

Numerical Treatment of Radiative Transfer

2005 ◽  
Vol 298 (1-2) ◽  
pp. 357-362 ◽  
Author(s):  
Matthias González ◽  
Edouard Audit
Keyword(s):  
Radiative Transfer ◽  
Numerical Treatment
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