6.5 Reflection of a Plane Wave from a Layer with a Slowly Varying Thickness
123
E 3 = exp
i
ε
τ 3elap (ξ 1 , ξ 2 , ξ 3 )
C
+
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y )+
+ exp
i
ε
τ 4re f (ξ 1 , ξ 2 , ξ 3 )
C
−
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y ),
(6.80)
E 4 = exp
i
ε
τ 4elap (ξ 1 , ξ 2 , ξ 3 )
D
+
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y )+
exp
i
ε
τ 5re f (ξ 1 , ξ 2 , ξ 3 )
D
−
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y )+
+ E 4θscat (ξ 1 , ξ 2 , ξ 3 )
(6.81)
E 5 = exp
i
ε
τ 5elap (ξ 1 , ξ 2 , ξ 3 )
E(ξ 1 , ξ 2 , ξ 3 , ε x , ε y ),
(6.82)
where E 4θscat is defined by formula (6.76) and τ 1inc ,τ 1re f , τ 2elap , τ 3re f , τ 3elap , τ 4re f ,
τ 4elap are defined in Chap. 4. Amplitudes A, B
± , C
± , D
± , E are sought in the form of
power series in small parameter ε x , ε y , the expressions for the amplitudes are defined
analogously to the method described in Chap. 4.
Substitution of expressions (8.1)−(8.5) into (4.6)−(4.11) generates a recurrence
system of equations. For the reflected field, this system leads to reflection coefficient
A. The expression for the reflection of a Gaussian beam with an arbitrary cross
section is defined analogously to the method described in Chap. 4.
6.6 Spectrum of Action of Laser Radiation
on the Hemoglobin Derivatives
Let us consider the mathematical simulation of the spectral efficiency of light absorption by the main blood hemoglobin derivatives: oxyhemoglobin(HbO 2 ) and deoxyhemoglobin(Hb) of human blood in the upper layers of the human dermis.
It should be noted that the mechanism of action of laser radiation on biological
structures are not completely clear as yet; several processes (namely, photoinduced
dissociation of oxyhemoglobin of blood, which is accompanied by the molecular
oxygen liberation and a local increase in its concentration in blood [20, 21]); as
a result of this photochemical reaction, deoxyhemoglobin is formed, and an optooxygen effect is observed [20–22], which is responsible for the liberation of singlet
oxygen from triplet oxygen dissolved in the cells. It should be noted that the above
processes depend on the efficiency of light absorption by blood and, hence, on the
radiation wavelength and the radiation power density at a given depth.
123
E 3 = exp
i
ε
τ 3elap (ξ 1 , ξ 2 , ξ 3 )
C
+
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y )+
+ exp
i
ε
τ 4re f (ξ 1 , ξ 2 , ξ 3 )
C
−
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y ),
(6.80)
E 4 = exp
i
ε
τ 4elap (ξ 1 , ξ 2 , ξ 3 )
D
+
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y )+
exp
i
ε
τ 5re f (ξ 1 , ξ 2 , ξ 3 )
D
−
(ξ 1 , ξ 2 , ξ 3 , ε x , ε y )+
+ E 4θscat (ξ 1 , ξ 2 , ξ 3 )
(6.81)
E 5 = exp
i
ε
τ 5elap (ξ 1 , ξ 2 , ξ 3 )
E(ξ 1 , ξ 2 , ξ 3 , ε x , ε y ),
(6.82)
where E 4θscat is defined by formula (6.76) and τ 1inc ,τ 1re f , τ 2elap , τ 3re f , τ 3elap , τ 4re f ,
τ 4elap are defined in Chap. 4. Amplitudes A, B
± , C
± , D
± , E are sought in the form of
power series in small parameter ε x , ε y , the expressions for the amplitudes are defined
analogously to the method described in Chap. 4.
Substitution of expressions (8.1)−(8.5) into (4.6)−(4.11) generates a recurrence
system of equations. For the reflected field, this system leads to reflection coefficient
A. The expression for the reflection of a Gaussian beam with an arbitrary cross
section is defined analogously to the method described in Chap. 4.
6.6 Spectrum of Action of Laser Radiation
on the Hemoglobin Derivatives
Let us consider the mathematical simulation of the spectral efficiency of light absorption by the main blood hemoglobin derivatives: oxyhemoglobin(HbO 2 ) and deoxyhemoglobin(Hb) of human blood in the upper layers of the human dermis.
It should be noted that the mechanism of action of laser radiation on biological
structures are not completely clear as yet; several processes (namely, photoinduced
dissociation of oxyhemoglobin of blood, which is accompanied by the molecular
oxygen liberation and a local increase in its concentration in blood [20, 21]); as
a result of this photochemical reaction, deoxyhemoglobin is formed, and an optooxygen effect is observed [20–22], which is responsible for the liberation of singlet
oxygen from triplet oxygen dissolved in the cells. It should be noted that the above
processes depend on the efficiency of light absorption by blood and, hence, on the
radiation wavelength and the radiation power density at a given depth.