vol - Radiative Transfer in the presence of Participating...

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Radiative Transfer in the presence of Participating Media
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Light transport Light transport Main Assumption So Far Radiance does not change with distance.
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Light transport through participating Light transport through participating media media Main processes that affect light passing through Absorption Emission Scattering
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Absorption • Described by absorption cross section σ σ a σ σ a : the probability density that light is absorbed per unit distance traveled in the medium. varies with position spectral dependence unit is reciprocal distance (m -1 ) dt t L dL a ) ( ) ( ) ( σ ϖ - =
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- = = = + - = - = - = - = T a dt t o T t t a a a a e L L c dt t L t L dt d t L dt dL dt t L dL 0 ) ( 0 ) ( ) ( ) ( ) ( ln ) ( ) ( ln ) ( ) ( 1 ) ( ) ( ) ( ) ( σ ϖ - = T a dt t o e L L 0 ) ( ) ( ) ( Absorption
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Emission Emission adds to the radiance Emitted light is independent of the incoming radiance is the emitted radiance per unit distance. dt dL ) ( ) ( ϖ ε ϖ= ) (
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Emission dt dL ) ( ) ( ϖ ε ϖ= = = = T t t dt L 0 ) ( ) (
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Emission Emitted light also undergoes absorption as it passes through the participating medium dt e t L T t a dt t T = - ' ) ' ( 0 ) , ( ) ( σ ϖ ε
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Absorption only Absorption plus Emission Emission + Absorption dt e t e L L T t a T a dt t T dt t o + = - - ' ) ' ( 0 ) ( ) , ( ) ( ) ( 0 σ ϖ ε
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Scattering Light collides with particles in the medium and is scattered in different directions loss due to out-scatter : reduces the radiance entering the medium from a given direction dt t L dL s ) ( ) ( ) ( σ ϖ - = [ ] + - = T s a dt t t o e L L 0 ) ( ) ( ) ( ) ( Optical Thickness Transmittance Special case: Homogeneous medium (Beer’s Law) T o e L L - = ) ( ) (
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Scattering Light collides with particles in the medium and is scattered in different directions loss due to out-scatter : reduces the radiance entering the medium from a given direction gain due to in-scatter : Increase in radiance due to scattering from all other directions.
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Scattering gain due to in-scatter : Increase in radiance due to scattering from all other directions. Phase function: Describes angular distribution of scattered radiation at a point. The probability distribution of scattering. ) ' , ( ϖ p 1 ' ) ' , ( = Sphere d p
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InScattering Total amount added at any point due to inscattering: = Sphere s inScatter d L t p dt t dL ' ) ' ( ) , ' , ( ) ( ) ( ϖ σ
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Source Function Total amount added at any point due to volume emission and in-scattering: dt d L t p t t dL dL dt t S Sphere s inScatter emission + = + = ' ) ' ( ) , ' , ( ) ( ) ( ) ( ) ( ) , ( ϖ σ ε )
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Light Transport Equation in Participating Medium dt e x S e L L T s a T a dt t T dt t o - - + = ) ( 0 ) ( ) , ( ) ( ) ( 0 σ ϖ
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Isotropic Phase Function : Equally scattering in all directions. Equivalent of Lambertian surface. π ϖ 4 1 ) ' , ( = ISO p Examples of Phase Functions
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In most naturally occurring media the phase functions are simple functions of angle Θ between the two directions.
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This note was uploaded on 08/22/2010 for the course CAP 6701 taught by Professor Staff during the Spring '10 term at University of Central Florida.

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vol - Radiative Transfer in the presence of Participating...

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