6715_Lecture8 - Lecture VIII 1. 2. 3. 4. 5. 6. VIII1 The...

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1 PHYS 6715 - Lecture VIII 1 Lecture VIII The Diffusion Model 1. The diffusion approximation 2. A boundary-value problem 3. The Green function method 4. Similarity principle 5. Boundary condition 6. Solving the BVP PHYS 6715 - Lecture VIII 2 Different components of light • The light radiance L in a turbid medium can be separated into two major components: one with unscattered light Æ the primary component L p one with scattered light Æ L s • The distribution of the primary component L p is correlated with the incident light on the turbid medium but reduces exponentially as exp{- μ t d} with d as the pathlength Æ for μ t =10(mm -1 ), only about 10% photons from an incident light beam or internal light source belong to the primary component after traveling over a distance of d c =0.23mm VIII–1 Diffusion Approximation PHYS 6715 - Lecture VIII 3 Different components of light • The scattered component has a much more complicated distribution so we further divide it into two sub-components: those being scattering only a few times Æ “snake” sub-component those being scattered many times Æ diffuse sub-component • The snake sub-component still has a strong correlation with the incident light and can be detected using the coherence technique Æ Optical coherence tomography (OCT) • The diffuse sub-component essentially lost its correlation with the incident light and can be well described by a diffusion approximation to the radiative transfer equation Æ Diffuse Optical Tomography (DOT) VIII–1 Diffusion Approximation PHYS 6715 - Lecture VIII 4 VIII–1 Diffusion Approximation Different components of light Diffusion approximation of radiative transfer equation – neglect the portion of light scattered only a few time or less. Diffuse component Snake component absorbed component incident light tissue primary component PHYS 6715 - Lecture VIII 5 VIII–1 Diffusion Approximation Separation of RTE Let L( r , s )=L p ( r , s ) + L s ( r , s ) and denote as 4 (, ) ( )( ,) (,' ,' ) ' ( sa s e L Lp L d s π μμ μ ε =− + + Ω+ rs ss (,) p tp L L s 4 ) (,' ) ' s ts s s p e L L d s + Ω + + L s ⋅∇ s A. Ishimaru, Wave propagation and scattering in random media , vol.1 (1978) 4 ) ' ps p pL d εμ PHYS 6715 - Lecture VIII 6 VIII–1 Diffusion Approximation The scattered component •T h e 2 nd equation containing both of the primary and scattered components is much harder to solve • The way out is to replace the scattered component with its diffuse sub-component or ignore the snake sub-component L p ( r , s ) Φ s ( r )
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2 PHYS 6715 - Lecture VIII 7 VIII–1 Diffusion Approximation The diffusion approximation • The diffuse sub-component does not correlated with incident light and its distribution in the turbid medium will not have a preferred direction • Mathematically, this can be expressed by a diffusion approximation: 1 () (,) () () 4 l m s sl m l s lom l La Y c π == Φ =≈ + ∑∑ r rs r s F r s 4 ss Ld Φ= Ω rr s 4 Fr rss Æ net scattered power flux vector Æ net scattered energy fluence rate PHYS 6715 - Lecture VIII 8
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This note was uploaded on 01/21/2012 for the course PHYS 6720 taught by Professor Hu during the Spring '10 term at East Carolina University .

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6715_Lecture8 - Lecture VIII 1. 2. 3. 4. 5. 6. VIII1 The...

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