Theory for Radiation in Participating Media
Radiation and Participating Media Interactions
Figure 4-12: Example of interactions between participating media and radiation.
In some applications the medium is not completely transparent and the radiation rays interact with the medium.
Let I(Ω) denote the radiative intensity traveling in a given direction, Ω . Different kinds of interactions are observed:
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Absorption: The medium absorbs a fraction of the incident radiation. The amount of absorbed radiation is κI(Ω), where κ is the absorption coefficient.
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Emission: The medium emits radiation in all directions. The amount of emitted radiative intensity is equal to κIb, where Ib is the blackbody radiation intensity.
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Scattering: Part of the radiation coming from a given direction is scattered in other directions. The scattering properties of the medium are described by the scattering phase function φ(Ω′, Ω), which gives the probability that a ray coming from one direction Ω′ is scattered into the direction Ω. The phase function φ(Ω′, Ω) satisfies:
Radiative intensity in a given direction is attenuated and augmented by scattering:
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It is attenuated because a part of the incident radiation in this direction is scattered into other directions. The amount of radiation attenuated by scattering is σsI(Ω).
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It is augmented because a part of the radiative intensity coming from other directions is scattered in all direction, including the direction we are looking at. The amount of radiation augmented by scattering is obtained by integrating scattering coming from all directions Ω′: