104
6 Light Scattering by Dielectric Bodies of Irregular …
the scatterer. We have constructed a mathematical model that makes it possible to
vary the electrophysical and geometrical parameters (thickness of the layers) of the
biological structure being simulated and to represent the result in the form of a graph
describing the dependence of the laser radiation intensity on the electrophysical
characteristics of the model structure for each version being analyzed.
The problem consists of several steps. At the first step, it is necessary to find the
coefficient of reflection of a plane wave from a smoothly irregular layer simulating a
given biological structure which consist of two continuous layers and the third layer
containing inhomogeneous inclusions simulating blood cells with different refractive
indices.
At the second step, it is necessary to solve the problem of reflection of a Gaussian
beam with an arbitrary cross section for the above conditions (see Chap. 4). The
construction of these parts is auxiliary. In this study, we precisely solve the problem
of light scattering from particles of irregular shapes, which simulate erythrocytes
oriented arbitrarily in free space, taking into account their multiple scattering, as
well as the problem of simulating the efficiency of light absorption by the main
derivatives of hemoglobin: oxyhemoglobin (HbO 2 ) and deoxyhemoglobin (Hb) of
human blood in the upper layers of human dermis.
Chapter is based on the results of the [7–9].
6.2 Matrix Formulation of Scattering for the j th Particle
of an Arbitrary Shape
From the standpoint of biomedical optics, whole blood is a highly concentrated
turbid medium, whose scattering and absorption properties are mainly determined by
erythrocytes. For this reason, we will consider in this section erythrocytes present in
blood and their optical properties, disregarding the effect of other blood corpuscles on
light scattering; this does not affect the generality and correctness of the formulation
of the problem.
In some publications, an erythrocyte is considered as a homogeneous sphere
whose volume is the same as that of the erythrocyte [10, 11]; this can be treated as
the first approximation (see Chap. 3), and it is expedient to consider the erythrocyte
as a body of an irregular shape.
Let us suppose that a plane linearly polarized electromagnetic wave is incident on
a group of homogeneous particles simulating erythrocytes with radii a
j and refractive
indices N
j , where j are the numbers of particles. The direction of the incident wave is
arbitrary. The group of particles is considered in the 3D system of coordinates with the
origin at the center of a particle with certain number j 0 . We denote by r j 0 , j the radius
vector of any other jth particle. We always assume that the surface (denoted by s) of a
particle is quite regular and satisfies the Green theorem, and surface s of the scatterer
has a continuous single-valued normal n at each point. We consider only the simple
harmonic time dependence with circular frequency ω, omitting factor exp(−iωt)
6 Light Scattering by Dielectric Bodies of Irregular …
the scatterer. We have constructed a mathematical model that makes it possible to
vary the electrophysical and geometrical parameters (thickness of the layers) of the
biological structure being simulated and to represent the result in the form of a graph
describing the dependence of the laser radiation intensity on the electrophysical
characteristics of the model structure for each version being analyzed.
The problem consists of several steps. At the first step, it is necessary to find the
coefficient of reflection of a plane wave from a smoothly irregular layer simulating a
given biological structure which consist of two continuous layers and the third layer
containing inhomogeneous inclusions simulating blood cells with different refractive
indices.
At the second step, it is necessary to solve the problem of reflection of a Gaussian
beam with an arbitrary cross section for the above conditions (see Chap. 4). The
construction of these parts is auxiliary. In this study, we precisely solve the problem
of light scattering from particles of irregular shapes, which simulate erythrocytes
oriented arbitrarily in free space, taking into account their multiple scattering, as
well as the problem of simulating the efficiency of light absorption by the main
derivatives of hemoglobin: oxyhemoglobin (HbO 2 ) and deoxyhemoglobin (Hb) of
human blood in the upper layers of human dermis.
Chapter is based on the results of the [7–9].
6.2 Matrix Formulation of Scattering for the j th Particle
of an Arbitrary Shape
From the standpoint of biomedical optics, whole blood is a highly concentrated
turbid medium, whose scattering and absorption properties are mainly determined by
erythrocytes. For this reason, we will consider in this section erythrocytes present in
blood and their optical properties, disregarding the effect of other blood corpuscles on
light scattering; this does not affect the generality and correctness of the formulation
of the problem.
In some publications, an erythrocyte is considered as a homogeneous sphere
whose volume is the same as that of the erythrocyte [10, 11]; this can be treated as
the first approximation (see Chap. 3), and it is expedient to consider the erythrocyte
as a body of an irregular shape.
Let us suppose that a plane linearly polarized electromagnetic wave is incident on
a group of homogeneous particles simulating erythrocytes with radii a
j and refractive
indices N
j , where j are the numbers of particles. The direction of the incident wave is
arbitrary. The group of particles is considered in the 3D system of coordinates with the
origin at the center of a particle with certain number j 0 . We denote by r j 0 , j the radius
vector of any other jth particle. We always assume that the surface (denoted by s) of a
particle is quite regular and satisfies the Green theorem, and surface s of the scatterer
has a continuous single-valued normal n at each point. We consider only the simple
harmonic time dependence with circular frequency ω, omitting factor exp(−iωt)