The solution of the radiative transfer equation for polarized light by the Chandrasekhar's discrete ordinate method

Barman, S. K.

doi:10.1016/s0022-4073(99)00178-8

Cited by 5 publications

(2 citation statements)

References 4 publications

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“…Tanaka 2003Tanaka , 2005. Similar problems have been addressed by Chandrasekhar himself, and solved later in several ways, as shown for example in Liou (1973); Chalhoub (2005); Barman (2000). The discrete ordinates method, in particular, gives a solution by expanding the phase function in Legendre polynomials.…”

Section: Radiative Transfer Inside a Cloudmentioning

confidence: 79%

Radiative Transfer in a Translucent Cloud Illuminated by an Extended Background Source

Biganzoli

Potenza

Robberto

2017

ApJ

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We discuss the radiative transfer theory for translucent clouds illuminated by an extended background source. First we derive a rigorous solution based on the assumption that multiple scattering produce an isotropic flux. Then we derive a more manageable analytic approximation showing that it nicely matches the results of the rigorous approach. To validate our model, we compare our predictions with accurate laboratory measurements for various types of well characterized grains, including purely dielectric and strongly absorbing materials representative of astronomical icy and metallic grains, respectively, finding excellent agreement without the need of adding free parameters. We use our model to explore the behavior of an astrophysical cloud illuminated by a diffuse source with dust grains having parameters typical of the classic ISM grains of Draine & Lee (1984) and protoplanetary disks, with an application to the dark silhouette disk 114-426 in Orion Nebula. We find that the scattering term modifies the transmitted radiation, both in terms of intensity (extinction) and shape (reddening) of the spectral distribution. In particular, for small optical thickness our results show that scattering makes reddening almost negligible at visible wavelengths. Once the optical thickness increases enough and the probability of scattering events become close to or larger than 1, reddening becomes present but appreciably modified with respect to the standard expression for line-of-sight absorption. Moreover, variations of the grain refractive index, in particular the amount of absorption, also play an important role changing the shape of the spectral transmission curve, with dielectric grain showing the minimum amount of reddening.

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Section: Radiative Transfer Inside a Cloudmentioning

confidence: 79%

Radiative Transfer in a Translucent Cloud Illuminated by an Extended Background Source

Biganzoli

Potenza

Robberto

2017

ApJ

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“…The random distribution of the scattering elements makes it impossible to solve these systems analytically; instead Monte Carlo methods are often used requiring a long computational time to obtain accurate results. Also, the radiative transfer problem for diffused light has been presented in the framework of Chandrasekhar's equation [5] solving the problem for different incident angles [6][7][8][9] which give accurate solutions for diffused light. On the other hand, methods based on flux balance equations usually present a much faster way to obtain results [10][11][12]; two-flux models assume fully diffused fluxes propagating in opposite directions, among those there is the well known Kubelka-Munk theory [13,14], which has been intensively used and researched [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Extending the applicability of the four-flux radiative transfer method

et al. 2017

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A generalized four-flux method capable of modeling and tuning the spectral reflectance of a diverse range of complex composite coatings is presented. An example application is exploring and maximizing the visible and near-infrared (IR) spectral reflectance available from the diverse structures arising from combinations of the many practical paint ingredients that are available or can be made when applied to different substrates. This requires consideration of scatterers that can differ in composition, particle size, size distribution, and fill factor, and are held in place by a variety of organic binders, which typically partially absorb in the near IR. This extended model is further enhanced by an explicit matrix algorithm that allows analysis of diverse multilayer stacks. This is applied to a multilayer and is designed to model useful changes that result from varying the pigment fill factor as a function of depth within a layer. What we believe is a novel feature is the way the scattering affects matrix absorptance. The model includes contributions to total absorptance from the scattering pigments and from the paint binder that can arise in different bands or simultaneously at the same wavelengths. Model accuracy is demonstrated by example results when compared to experimental data on dried single layer paint profiles using imaged cross sections. The model input covering the actual pigment and binder properties used are material, shape, size, and size distributions, mass added, and the measured optical constants from 400 nm to 2,500 nm of the undoped binder resin layer. One interesting result is the comparison of a two-layered stack, with bigger particles in the first layer and smaller ones in the second, to one with the opposite depth profile.

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Effects of polarization on radiation absorption in one-dimensional semitransparent slab exposed to collimated irradiation

Liu

Tan

2002

Journal of Quantitative Spectroscopy and Radiative Transfer

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The solution of the radiative transfer equation for polarized light by the Chandrasekhar's discrete ordinate method

Cited by 5 publications

References 4 publications

Radiative Transfer in a Translucent Cloud Illuminated by an Extended Background Source

Radiative Transfer in a Translucent Cloud Illuminated by an Extended Background Source

Extending the applicability of the four-flux radiative transfer method

Effects of polarization on radiation absorption in one-dimensional semitransparent slab exposed to collimated irradiation

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