2.1 Introduction
11
describes the spatial configuration and the optical properties of lenses If the excited
field is found, further analysis concerns the calculation from the scattered fields of
individual particles and the addition of these fields with phase shifts. Since we are
considering random fields, calculating the observed photometric is needed to use
the correlation analysis. In the theory of multiple scattering of waves the theory of
coherent radiation propagation in a medium close-packed lenses has been developed
in detail, the main result of which is the output of the dispersion equation for the
effective wave number describing the propagation of a coherent field in a medium
different from the wave number of free space. This dispersion equation takes into
account the optical properties of the scatterers and the statistical properties of their
spatial location. Note that in the derivation of the dispersion equation simplifying
assumptions are made. For example, the use of quasi-crystalline approximation to
decouple the infinite chain of equations of multiple scattering, and to describe the
pairing correlations in the positions of the particles using the Percus-Yevick. A fundamental feature of the theory of MSW is that the optical properties of interacting
particles differ from those characteristics which are obtained by solving the scattering problem for an isolated particle. For example, the extinction cross-section of the
particles in the cluster do not coincide with the usual calculation of Mie theory. Even
in the simplest case of two completely identical spheres in the contact cross section
of each particle depends on the orientation of the bisfery in relation to the incident
plane wave. Effects of this type are said to be “collective” or “cooperative” effects of
the scattering of interacting particles. In general, the cooperative effects of multiple
scattering are the two components and their calculation is rather complex. However,
for biological systems the situation is simplified by the fact that the optical properties
of interacting particles are usually not much different from those of the environment.
The analysis of the conditions for the applicability of a specific version of the theory
of light scattering is a nontrivial problem, which requires taking into account the
coherence properties of the incident light, the size, concentration, and optical properties of the particles, the time of stability of the microstructure of the medium (i.e.,
the characteristic relaxation times of fluctuations), the geometric parameters of the
scattering sample, the characteristics of the photodetector, etc. Note that in this paper
we consider only the first two of the main approaches in the theory of scattering for
highly scattering tissue.
2.2 Optical Properties of Tissues with Multiple Scattering
In this section we consider light scattering methods for the quantitative study of the
optical characteristics of the tissue, and the results of theoretical and experimental
studies of photon transport in biological tissues. The theoretical analysis is based on
a stationary or non-stationary radiation transfer theory for strongly scattering media,
as well as numerical Monte-Carlo method, which is used to solve the problems of
scattering in multilayered biological tissues with complex boundary conditions.
11
describes the spatial configuration and the optical properties of lenses If the excited
field is found, further analysis concerns the calculation from the scattered fields of
individual particles and the addition of these fields with phase shifts. Since we are
considering random fields, calculating the observed photometric is needed to use
the correlation analysis. In the theory of multiple scattering of waves the theory of
coherent radiation propagation in a medium close-packed lenses has been developed
in detail, the main result of which is the output of the dispersion equation for the
effective wave number describing the propagation of a coherent field in a medium
different from the wave number of free space. This dispersion equation takes into
account the optical properties of the scatterers and the statistical properties of their
spatial location. Note that in the derivation of the dispersion equation simplifying
assumptions are made. For example, the use of quasi-crystalline approximation to
decouple the infinite chain of equations of multiple scattering, and to describe the
pairing correlations in the positions of the particles using the Percus-Yevick. A fundamental feature of the theory of MSW is that the optical properties of interacting
particles differ from those characteristics which are obtained by solving the scattering problem for an isolated particle. For example, the extinction cross-section of the
particles in the cluster do not coincide with the usual calculation of Mie theory. Even
in the simplest case of two completely identical spheres in the contact cross section
of each particle depends on the orientation of the bisfery in relation to the incident
plane wave. Effects of this type are said to be “collective” or “cooperative” effects of
the scattering of interacting particles. In general, the cooperative effects of multiple
scattering are the two components and their calculation is rather complex. However,
for biological systems the situation is simplified by the fact that the optical properties
of interacting particles are usually not much different from those of the environment.
The analysis of the conditions for the applicability of a specific version of the theory
of light scattering is a nontrivial problem, which requires taking into account the
coherence properties of the incident light, the size, concentration, and optical properties of the particles, the time of stability of the microstructure of the medium (i.e.,
the characteristic relaxation times of fluctuations), the geometric parameters of the
scattering sample, the characteristics of the photodetector, etc. Note that in this paper
we consider only the first two of the main approaches in the theory of scattering for
highly scattering tissue.
2.2 Optical Properties of Tissues with Multiple Scattering
In this section we consider light scattering methods for the quantitative study of the
optical characteristics of the tissue, and the results of theoretical and experimental
studies of photon transport in biological tissues. The theoretical analysis is based on
a stationary or non-stationary radiation transfer theory for strongly scattering media,
as well as numerical Monte-Carlo method, which is used to solve the problems of
scattering in multilayered biological tissues with complex boundary conditions.