18
2 Overview of Theoretical Approaches to the Analysis of Light Scattering
We assume that the scattering takes place only when, ξ 4 < a is where optical
albedo,
a =
μ s
μ a + μ s
.
if ξ 4 < a photon is absorbed, which is analogous to step 4.
4. Destruction. This step is used only when assigning a weight to each photon in
step 3. When the weight reaches a certain value, the photon is eliminated. Then
a new photon emits and the program continues with step 1.
5. Registration. After repeating steps 1–4 for a sufficient number of photons, a map
of the trajectories is calculated and accumulated in the computer. Thus, it may
be obtained by a statistical report on portions of the incident photons absorbed
by the medium, and the spatial and angular distribution of the photons emerging
from it.
We consider one of the variants of the construction algorithm of the Monte-Carlo
method. The modeling medium is defined by the following parameters: L ave is the
thickness, μ s is the scattering coefficient and μ a is the absorption coefficient, g is
the cosine of the scattering angle, n is the relative refractive index.
The incident impulse consists of one million photons within the medium along
the z-axis perpendicular to the surface (x, y) at the point (0, 0, 0). Calculations are
made in a three-dimensional Cartesian coordinate system. After entry of the photon
the mean free path of a photon in the medium, and the scattering angles θ and ϕ are
determined. The scattering angle p(θ ) is defined by the scattering phase function. In
the general case p(s, s
) = p(θ ) p(ϕ) where s is incident direction, s
is scattering
direction of photon. Note, particles of medium are spherically symmetrical particles,
when we have absorption and scattering. This approximation is used in similar cases,
and based on the fact that in the process of passage through a medium with strong
scattering of a photon interacts with particles from different angles. We can therefore
use the average of the scattering indicatrix.
Thus, if you use this approach, we have p(ϕ) =
1
2π
. In the case of tissue with
strong scattering as a function of the phase of the scattering phase function p(θ )
Henie-Greenstein can be applied, from which we obtain an expression for the angle
θ :
θ = cos
−1
⎡
⎢
⎣
1 + g
2
−
1−g
2
1+g 2 −2g Random
2
2g
⎤
⎥
⎦ ,
where Random is random number uniformly distributed in the range (0,1). At each
step θ angle is relative to the old direction of propagation, the angle ϕ is in a
plane perpendicular to the new direction of movement.
The free path of photon is:
p(L) =
1
l ph
l
e
l ph ,
2 Overview of Theoretical Approaches to the Analysis of Light Scattering
We assume that the scattering takes place only when, ξ 4 < a is where optical
albedo,
a =
μ s
μ a + μ s
.
if ξ 4 < a photon is absorbed, which is analogous to step 4.
4. Destruction. This step is used only when assigning a weight to each photon in
step 3. When the weight reaches a certain value, the photon is eliminated. Then
a new photon emits and the program continues with step 1.
5. Registration. After repeating steps 1–4 for a sufficient number of photons, a map
of the trajectories is calculated and accumulated in the computer. Thus, it may
be obtained by a statistical report on portions of the incident photons absorbed
by the medium, and the spatial and angular distribution of the photons emerging
from it.
We consider one of the variants of the construction algorithm of the Monte-Carlo
method. The modeling medium is defined by the following parameters: L ave is the
thickness, μ s is the scattering coefficient and μ a is the absorption coefficient, g is
the cosine of the scattering angle, n is the relative refractive index.
The incident impulse consists of one million photons within the medium along
the z-axis perpendicular to the surface (x, y) at the point (0, 0, 0). Calculations are
made in a three-dimensional Cartesian coordinate system. After entry of the photon
the mean free path of a photon in the medium, and the scattering angles θ and ϕ are
determined. The scattering angle p(θ ) is defined by the scattering phase function. In
the general case p(s, s
) = p(θ ) p(ϕ) where s is incident direction, s
is scattering
direction of photon. Note, particles of medium are spherically symmetrical particles,
when we have absorption and scattering. This approximation is used in similar cases,
and based on the fact that in the process of passage through a medium with strong
scattering of a photon interacts with particles from different angles. We can therefore
use the average of the scattering indicatrix.
Thus, if you use this approach, we have p(ϕ) =
1
2π
. In the case of tissue with
strong scattering as a function of the phase of the scattering phase function p(θ )
Henie-Greenstein can be applied, from which we obtain an expression for the angle
θ :
θ = cos
−1
⎡
⎢
⎣
1 + g
2
−
1−g
2
1+g 2 −2g Random
2
2g
⎤
⎥
⎦ ,
where Random is random number uniformly distributed in the range (0,1). At each
step θ angle is relative to the old direction of propagation, the angle ϕ is in a
plane perpendicular to the new direction of movement.
The free path of photon is:
p(L) =
1
l ph
l
e
l ph ,