2.7 Methods for Solving Inverse Problems of Scattering Theory
23
2.7 Methods for Solving Inverse Problems of Scattering
Theory
One method of solving the inverse scattering problem is the inversion method of
adding-doubling [28]. The inversion method of adding-doubling includes the following steps:
1. assignment of expected optical parameters;
2. calculation of reflection and transmission using the method of adding-doubling;
3. comparison of the calculated values of the reflection and transmission with the
measured;
4. repetition of the procedure to obtain coherent data with a given precision.
The method is used with the following assumptions: the distribution of light is
independent of time, the samples have homogeneous optical properties, the geometry
of the samples is an infinite plane-parallel layer final thickness, tissue has a homogeneous index of refraction, internal reflection at the boundaries is described by
Fresnel law and the light is not polarized The inversion method of adding-doubling
was successfully used in finding the optical parameters of the dermis [29].
2.8 Resume
This chapter describes methods for modeling the interaction of light with biological
tissue: the diffusion approximation, the theory of radiative transfer, various multi-flux
theories and the Monte-Carlo method.
Note the most significant limitations and disadvantages of these methods:
1. The theory of radiative transfer is true for sufficiently distant scatterers.
2. The diffusion approximation can not be applied at a wavelength λ = 0.514 µm.
It also is not applicable near the surface of the object at the input of the light
beam, where single scattering is predominant.
3. A major shortcoming of the Monte-Carlo method is that in order to obtain precise
results with help program must be passed a large number of photons.
4. Modeling of Monte-Carlo does not account for the details of the distribution of
radiation inside a single cell.
These reasons have defined the development of a new approach of mathematical
modeling of the interaction of light with biological particles and biological tissue
through the application of asymptotic methods in the theory of diffraction.
This approach enabled:
1. the investigation of the optical properties of an ensemble of randomly oriented
spherical particles (hemocytes) in the cavity optical linear resonator;
2. the calculation of the refractive index of the blood and to determine the speed
blood of an flow in the capillary at a wavelength λ = 0.63 µm for the case in
vivo;
23
2.7 Methods for Solving Inverse Problems of Scattering
Theory
One method of solving the inverse scattering problem is the inversion method of
adding-doubling [28]. The inversion method of adding-doubling includes the following steps:
1. assignment of expected optical parameters;
2. calculation of reflection and transmission using the method of adding-doubling;
3. comparison of the calculated values of the reflection and transmission with the
measured;
4. repetition of the procedure to obtain coherent data with a given precision.
The method is used with the following assumptions: the distribution of light is
independent of time, the samples have homogeneous optical properties, the geometry
of the samples is an infinite plane-parallel layer final thickness, tissue has a homogeneous index of refraction, internal reflection at the boundaries is described by
Fresnel law and the light is not polarized The inversion method of adding-doubling
was successfully used in finding the optical parameters of the dermis [29].
2.8 Resume
This chapter describes methods for modeling the interaction of light with biological
tissue: the diffusion approximation, the theory of radiative transfer, various multi-flux
theories and the Monte-Carlo method.
Note the most significant limitations and disadvantages of these methods:
1. The theory of radiative transfer is true for sufficiently distant scatterers.
2. The diffusion approximation can not be applied at a wavelength λ = 0.514 µm.
It also is not applicable near the surface of the object at the input of the light
beam, where single scattering is predominant.
3. A major shortcoming of the Monte-Carlo method is that in order to obtain precise
results with help program must be passed a large number of photons.
4. Modeling of Monte-Carlo does not account for the details of the distribution of
radiation inside a single cell.
These reasons have defined the development of a new approach of mathematical
modeling of the interaction of light with biological particles and biological tissue
through the application of asymptotic methods in the theory of diffraction.
This approach enabled:
1. the investigation of the optical properties of an ensemble of randomly oriented
spherical particles (hemocytes) in the cavity optical linear resonator;
2. the calculation of the refractive index of the blood and to determine the speed
blood of an flow in the capillary at a wavelength λ = 0.63 µm for the case in
vivo;