Chapter 10
Study of the Optical Characteristics
of Thin Layer of the Biological Sample
Abstract We construct the mathematical model, which makes it possible to vary
the characteristic sizes of roughness, the electrophysical parameters of the biological
sample under investigation, and its geometrical characteristics and to establish the
relations between these parameters and biological properties of the biological tissue
being modeled, as well as to calculate theoretically the absorption spectra of optically
thin biological samples placed into the cavity of an optical resonator.
10.1 Introduction
Most biological surfaces are rough to a certain extent. The roughness of the surface
affects the characteristics of wave propagation and scattering (namely, the characteristics of a wave propagating over such a surface differ from analogous characteristics
in the case of propagation over a smooth surface). A wave incident on a rough surface
not only reflects specularly, but is also scattered in all other directions. In analysis of
scattering from a rough surface, the extent of roughness of the surface is connected
with the wavelength of incident radiation and depends on the direction of wave
propagation and scattering. In this connection, it is important to study the effect of
roughness on the spectral characteristics of the biological structure being simulated.
It should be noted that using a resonator, it is possible to obtain more exact estimates of optical parameters of the medium taking into account the roughness, which
cannot be detected using conventional methods. Thus, it is expedient to consider
the problem of natural oscillations of a linear resonator loaded with an optically thin
layer simulating a certain biological structure. The biological structure is represented
by an optically thin layer with certain optical and geometrical characteristics, which
is illuminated by a laser beam.
The problem includes the following three consecutive stages. At the first stage, the
problem of scattering from the rough boundary had to be solved and the coefficient of
reflection of a plane wave from a smoothly irregular layer must be determined taking
into account the roughness of the boundary simulating the given biological medium.
At the second stage, the problem of reflection of a Gaussian beam with an arbitrary
cross section had to be solved. The problem was solved by expanding the fields
© Springer International Publishing AG, part of Springer Nature 2018
K. Kulikov and T. Koshlan, Laser Interaction with Heterogeneous
Biological Tissue, Biological and Medical Physics, Biomedical Engineering,
https://doi.org/10.1007/978-3-319-94114-1_10
161
Study of the Optical Characteristics
of Thin Layer of the Biological Sample
Abstract We construct the mathematical model, which makes it possible to vary
the characteristic sizes of roughness, the electrophysical parameters of the biological
sample under investigation, and its geometrical characteristics and to establish the
relations between these parameters and biological properties of the biological tissue
being modeled, as well as to calculate theoretically the absorption spectra of optically
thin biological samples placed into the cavity of an optical resonator.
10.1 Introduction
Most biological surfaces are rough to a certain extent. The roughness of the surface
affects the characteristics of wave propagation and scattering (namely, the characteristics of a wave propagating over such a surface differ from analogous characteristics
in the case of propagation over a smooth surface). A wave incident on a rough surface
not only reflects specularly, but is also scattered in all other directions. In analysis of
scattering from a rough surface, the extent of roughness of the surface is connected
with the wavelength of incident radiation and depends on the direction of wave
propagation and scattering. In this connection, it is important to study the effect of
roughness on the spectral characteristics of the biological structure being simulated.
It should be noted that using a resonator, it is possible to obtain more exact estimates of optical parameters of the medium taking into account the roughness, which
cannot be detected using conventional methods. Thus, it is expedient to consider
the problem of natural oscillations of a linear resonator loaded with an optically thin
layer simulating a certain biological structure. The biological structure is represented
by an optically thin layer with certain optical and geometrical characteristics, which
is illuminated by a laser beam.
The problem includes the following three consecutive stages. At the first stage, the
problem of scattering from the rough boundary had to be solved and the coefficient of
reflection of a plane wave from a smoothly irregular layer must be determined taking
into account the roughness of the boundary simulating the given biological medium.
At the second stage, the problem of reflection of a Gaussian beam with an arbitrary
cross section had to be solved. The problem was solved by expanding the fields
© Springer International Publishing AG, part of Springer Nature 2018
K. Kulikov and T. Koshlan, Laser Interaction with Heterogeneous
Biological Tissue, Biological and Medical Physics, Biomedical Engineering,
https://doi.org/10.1007/978-3-319-94114-1_10
161