90
5 Study of the Optical Characteristics of a Biotissue …
in [1]. The case of coarse roughness was considered, when the parameters (standard
deviation and correlation radius) are much larger than the wavelength. In [3], light
scattering from an anisotropic rough surface was also considered. Scattering of light
from a rough cylindrical surface was studied in [4]. In [2], scattering of light from a
rough dielectric surface was analyzed (both theoretically and numerically).
Here, we construct an electrodynamic model which makes it possible to vary the
electrophysical parameters of a biological structure in calculations with allowance
for roughness (real and imaginary parts of the refractive index of the epidermis, the
upper layer of the derma, and blood) and to establish the dependences between these
parameters and the biological properties of blood under the action of laser radiation
for case in vivo. The problem consists of three consecutive stages. At the first stage,
the problem of light scattering from a rough boundary is solved and the coefficient
of reflection of a plane wave from a smoothly irregular layer simulating the given
biological medium is determined taking into account the roughness of the interface
in the case when the size of the roughness is larger than the wavelength of radiation
illuminating them.
At the second stage, we solve the problem of reflection of a Gaussian beam with
an arbitrary cross section. The problem is solved by expanding the fields of counter
propagating waves in plane waves in the domain of medium 1 and their reflection
by layer 2 and inverse transformation followed by the Huygens-Fresnel integral
transformation to obtain the field in the initial reference cross section (see Chap. 4).
At the third stage, the dependence of the radiation intensity on the refractive index
is determined for a system of blood vessels in the upper layer of the dermis and the
effect of roughness on the electrophysical characteristics of the biological sample
being simulated is analyzed. The structure simulated consists of three regions with
different refractive indices (epidermis, upper layer of the dermis, and blood vessel)
illuminated by a laser beam for case in vivo.
The chapter is based on the results of the [5, 6].
5.2 Scattering of a Plane Wave from the Rough Surface
The surfaces of real bodies (in particular, in biology) are not perfectly smooth to a
certain extent. For this reason, reflection and refraction of the waves at these surfaces
are accompanied by the effects which are not observed for smooth surfaces. Rigorous
methods for solving the problem in the case of a rough surface do not exist. The
problem can be solved only approximately under certain constraints imposed on the
size and shape of roughness. For calculating the scattered field, the small-perturbation
method and the Kirchhoff (tangential plane) method are used. In this work, we will
use the Kirchhoff method for calculating the scattered field. To solve the formulated
problem, we will use the Kirchhoff approximation. To apply the Kirchhoff method
correctly, we make the assumption concerning the smoothness of inhomogeneities.
At each point, the wave field can be represented as the sum of incident field (E inc )
and reflected field (E re f ).
5 Study of the Optical Characteristics of a Biotissue …
in [1]. The case of coarse roughness was considered, when the parameters (standard
deviation and correlation radius) are much larger than the wavelength. In [3], light
scattering from an anisotropic rough surface was also considered. Scattering of light
from a rough cylindrical surface was studied in [4]. In [2], scattering of light from a
rough dielectric surface was analyzed (both theoretically and numerically).
Here, we construct an electrodynamic model which makes it possible to vary the
electrophysical parameters of a biological structure in calculations with allowance
for roughness (real and imaginary parts of the refractive index of the epidermis, the
upper layer of the derma, and blood) and to establish the dependences between these
parameters and the biological properties of blood under the action of laser radiation
for case in vivo. The problem consists of three consecutive stages. At the first stage,
the problem of light scattering from a rough boundary is solved and the coefficient
of reflection of a plane wave from a smoothly irregular layer simulating the given
biological medium is determined taking into account the roughness of the interface
in the case when the size of the roughness is larger than the wavelength of radiation
illuminating them.
At the second stage, we solve the problem of reflection of a Gaussian beam with
an arbitrary cross section. The problem is solved by expanding the fields of counter
propagating waves in plane waves in the domain of medium 1 and their reflection
by layer 2 and inverse transformation followed by the Huygens-Fresnel integral
transformation to obtain the field in the initial reference cross section (see Chap. 4).
At the third stage, the dependence of the radiation intensity on the refractive index
is determined for a system of blood vessels in the upper layer of the dermis and the
effect of roughness on the electrophysical characteristics of the biological sample
being simulated is analyzed. The structure simulated consists of three regions with
different refractive indices (epidermis, upper layer of the dermis, and blood vessel)
illuminated by a laser beam for case in vivo.
The chapter is based on the results of the [5, 6].
5.2 Scattering of a Plane Wave from the Rough Surface
The surfaces of real bodies (in particular, in biology) are not perfectly smooth to a
certain extent. For this reason, reflection and refraction of the waves at these surfaces
are accompanied by the effects which are not observed for smooth surfaces. Rigorous
methods for solving the problem in the case of a rough surface do not exist. The
problem can be solved only approximately under certain constraints imposed on the
size and shape of roughness. For calculating the scattered field, the small-perturbation
method and the Kirchhoff (tangential plane) method are used. In this work, we will
use the Kirchhoff method for calculating the scattered field. To solve the formulated
problem, we will use the Kirchhoff approximation. To apply the Kirchhoff method
correctly, we make the assumption concerning the smoothness of inhomogeneities.
At each point, the wave field can be represented as the sum of incident field (E inc )
and reflected field (E re f ).