180
12 Determination of the Optical Parameters …
allows monitoring the effectiveness of the patient’s treatment and evaluating the effect
of various individual treatment procedures. Therefore, non-invasive laser diagnostics
(spectrophotometry) in medicine can be effective in a wide variety of fields, from
oncology and dermatology to occupational pathology, physiotherapy and other areas
of medicine. In clinical medical practice, spectrophotometry is used to diagnose the
functional state of biological tissues and organs. The method has such advantages as
non-invasiveness and a significant depth of penetration of probing radiation in the
red and near-infrared range.
Spectrophotometry as a method is based on a transmission of radiation through
the sample under study and recording backscattered radiation. The recorded attenuated radiation contains information about the properties of the bio-object, primarily
about the absorption and scattering of radiation in the tissue. In the modern technical implementation, the method makes it possible to quantify the optical parameters
(refractive index and absorption coefficient) of biological tissue. Thus, having information on the spectral dependence of these parameters, one can reveal the dynamics
of the physiological, morphological and biochemical characteristics of biological
tissues. In particular, the analysis of the absorption coefficient spectra of biological
tissues makes it possible to determine the concentration of endogenous chromophores
(melanin, hemoglobin, bilirubin, etc.).
In this chapter, we solve the following problem: on the basis of spectrophotometric
data of reflection R(λ) for n measurements intensity of the reflected waves to develop
a numerical method (for all the investigated diapason wavelength) for determination
n j ( refractive index) jth layer etc. Note that this task is a the inverse problem.
12.2 Algorithm for Solving the Inverse Problem
An algorithm for solving the inverse problem consist of approximation the imaginary
part the dielectric constant linear combination of basis functions and the use of the
Kramers–Kronig relation for the calculation of the real part this function.
ε j = ε 0 j +
n
i=1
A i j exp[−(ω − ω i j )
2
/Δ i j ], ε j = 1 +
1
π
v. p.
+∞
−∞
ε j
ω ∗ − ω
dω
∗
,
where ε 0 j , ω i j , Δ i j , A i j are desired parameters, by which optimization is performed.
(ε j ) =
λ
n
i=1
[R i (λ) − R i (λ, ε j )]
2 dλ −→ min,
where R i (λ, ε j ) is coefficient reflection of the simulated biological tissue (see
Chaps. 3–7), ε j determined from the relations Kramers–Kronig. Thus, it is possible
to determine from the measured intensities the reflected waves, the complex refractive index of the jth layer of the simulated biological tissue. Since the absorption
12 Determination of the Optical Parameters …
allows monitoring the effectiveness of the patient’s treatment and evaluating the effect
of various individual treatment procedures. Therefore, non-invasive laser diagnostics
(spectrophotometry) in medicine can be effective in a wide variety of fields, from
oncology and dermatology to occupational pathology, physiotherapy and other areas
of medicine. In clinical medical practice, spectrophotometry is used to diagnose the
functional state of biological tissues and organs. The method has such advantages as
non-invasiveness and a significant depth of penetration of probing radiation in the
red and near-infrared range.
Spectrophotometry as a method is based on a transmission of radiation through
the sample under study and recording backscattered radiation. The recorded attenuated radiation contains information about the properties of the bio-object, primarily
about the absorption and scattering of radiation in the tissue. In the modern technical implementation, the method makes it possible to quantify the optical parameters
(refractive index and absorption coefficient) of biological tissue. Thus, having information on the spectral dependence of these parameters, one can reveal the dynamics
of the physiological, morphological and biochemical characteristics of biological
tissues. In particular, the analysis of the absorption coefficient spectra of biological
tissues makes it possible to determine the concentration of endogenous chromophores
(melanin, hemoglobin, bilirubin, etc.).
In this chapter, we solve the following problem: on the basis of spectrophotometric
data of reflection R(λ) for n measurements intensity of the reflected waves to develop
a numerical method (for all the investigated diapason wavelength) for determination
n j ( refractive index) jth layer etc. Note that this task is a the inverse problem.
12.2 Algorithm for Solving the Inverse Problem
An algorithm for solving the inverse problem consist of approximation the imaginary
part the dielectric constant linear combination of basis functions and the use of the
Kramers–Kronig relation for the calculation of the real part this function.
ε j = ε 0 j +
n
i=1
A i j exp[−(ω − ω i j )
2
/Δ i j ], ε j = 1 +
1
π
v. p.
+∞
−∞
ε j
ω ∗ − ω
dω
∗
,
where ε 0 j , ω i j , Δ i j , A i j are desired parameters, by which optimization is performed.
(ε j ) =
λ
n
i=1
[R i (λ) − R i (λ, ε j )]
2 dλ −→ min,
where R i (λ, ε j ) is coefficient reflection of the simulated biological tissue (see
Chaps. 3–7), ε j determined from the relations Kramers–Kronig. Thus, it is possible
to determine from the measured intensities the reflected waves, the complex refractive index of the jth layer of the simulated biological tissue. Since the absorption