4. The fundamental theory of bidirectional LIF

#### 4.1. Measurement equation of the species concentration profiles

A schematic of one-dimensional bidirectional LIF for molecular concentration measurement is shown in Figure 3. First we give a definition as described in the following. With ICCD camera for reference, the direction in which the laser beam traverses the flame from left to right is the backward direction, instead of reverse for the forward direction. The points x = 0 and x = L denote the boundaries for the concentration calculation.

The laser-induced fluorescence signal intensity at the point x is given by the following expression:

$$F\_b(\mathbf{x}) = \mathbb{CS}(\mathbf{x})\sigma\_0 \mathbf{N}(\mathbf{x}) I\_b(\mathbf{x}) \tag{6}$$

Ibð Þ¼ x Ib, <sup>0</sup>e

Ifð Þ¼ x If ,0e

R xð Þ¼ Ffð Þ<sup>x</sup>

Ibð Þx � �

Take the logarithm of the fluorescence ratio R(x); then one will obtain the following equation:

same height, the forward equation of the laser beam is given as

Figure 3. Schematic diagram for one-dimensional bidirectional LIF method.

ln ½ �¼ R xð Þ ln <sup>I</sup>fð Þ<sup>x</sup>

<sup>¼</sup> ln <sup>I</sup>f, <sup>0</sup> Ib,<sup>0</sup> þ ðx 0

<sup>¼</sup> ln <sup>I</sup>f, <sup>0</sup> Ib,<sup>0</sup> þ 2 ðx 0

� Ð x

Eq. (7) is established in the unsaturated condition. In Eq. (7), Ibð Þx is the laser intensity in the backward direction at point x, and Ib, <sup>0</sup> is the initial laser intensity of the backward beam at point x = 0. Similarly, if the laser propagates in the opposite direction from right to left, at the

> � Ð x

where Ifð Þx is the laser intensity in the forward direction at point x and If,<sup>0</sup> is the initial laser intensity of the forward beam. Note that the incident point of the forward beam is located at x = L. The ratio of fluorescence signals, R(x), is equal to the ratio between the laser intensities because the factors of C, i.e., S(x), σ0, and N(x), are canceled in the division expressed as

Fbð Þ<sup>x</sup> <sup>¼</sup> Ifð Þ<sup>x</sup>

σ0N yð Þdy �

σ0N yð Þdy �

ðL x

> ðL 0

σ0N yð Þdy

σ0N yð Þdy

<sup>0</sup> <sup>σ</sup>0N xð Þdy (7)

Quantitative Planar Laser-Induced Fluorescence Technology

http://dx.doi.org/10.5772/intechopen.79702

95

<sup>0</sup> <sup>σ</sup>0N xð Þdy (9)

Ibð Þ<sup>x</sup> (10)

(11)

Ffð Þ¼ x CS xð Þσ0N xð ÞIfð Þx (8)

where C is a constant depending on the collection angle of fluorescence signal and the detector sensitivity, S(x) denotes the fluorescent quantum yield which is only dependent on the spontaneous emission rate and the collisional quenching rate Q(x), σ<sup>0</sup> is the effective peak absorption cross section of molecules to be measured, and N(x) represents the particle number density at point x. Consider a laser beam propagating through the flame at a fixed height from left to right along the x-axis in Figure 1. The beam will be attenuated according to the Lambert-Beer law, and the intensity is given by the following equation:

Figure 3. Schematic diagram for one-dimensional bidirectional LIF method.

the quantitative measurements of OH concentration distributions in an opposed diffusion flame. Because the opposed diffusion flame belongs to a kind of symmetrical flame, they used only one beam to excite the OH radicals and combined the mirror symmetry method to achieve the quantitative measurements of one-dimensional OH concentration distributions. Their experimental results indicate that the OH concentration is about 7.8 � 1015 molecules/cm3 at the height of 1.8 mm from the burner nozzle. In addition, Tian et al. [20] also used bidirectional LIF to quantitatively measure the concentration of iron atoms in a premixed laminar propylene/oxygen/argon flat flames. However, the two opposite directional beams have not been employed in their experiments. Instead, the mirror symmetry method has been used to

Judging from the existing literature statistics, the current species concentration measurements based on bidirectional LIF/PLIF technology are still fairly scarce. Although the bidirectional LIF/PLIF has great advantages beyond other quantitative LIF/PLIF technologies, such as no collisional quenching effect, no special excitation conditions (e.g., large energy, short pulses, etc.) and no additional calibration, it has a high requirement for the spatial coincidence of the beams and the SNR of the fluorescence signal. In addition, the experimental expression of effective peak absorption cross section provided by Versluis et al. has a limitation, which is not applicable to the case of weak absorption. In view of this problem, we have supplemented and corrected the experimental measurement equation in this chapter. These difficulties have resulted in the fact that the research of species concentration measurement based on the bidirectional PLIF is almost at a standstill. Therefore, it is necessary to conduct the in-depth

research in order to promote the further development of the bidirectional LIF/PLIF.

A schematic of one-dimensional bidirectional LIF for molecular concentration measurement is shown in Figure 3. First we give a definition as described in the following. With ICCD camera for reference, the direction in which the laser beam traverses the flame from left to right is the backward direction, instead of reverse for the forward direction. The points x = 0 and x = L

The laser-induced fluorescence signal intensity at the point x is given by the following expression:

where C is a constant depending on the collection angle of fluorescence signal and the detector sensitivity, S(x) denotes the fluorescent quantum yield which is only dependent on the spontaneous emission rate and the collisional quenching rate Q(x), σ<sup>0</sup> is the effective peak absorption cross section of molecules to be measured, and N(x) represents the particle number density at point x. Consider a laser beam propagating through the flame at a fixed height from left to right along the x-axis in Figure 1. The beam will be attenuated according to the Lambert-Beer

Fbð Þ¼ x CS xð Þσ0N xð ÞIbð Þx (6)

4. The fundamental theory of bidirectional LIF

denote the boundaries for the concentration calculation.

law, and the intensity is given by the following equation:

4.1. Measurement equation of the species concentration profiles

obtain the variations of the iron atom concentration with the axial heights.

94 Laser Technology and its Applications

$$I\_b(\mathbf{x}) = I\_{b,0}e^{-\int\_0^{\mathbf{x}} \phi \circ N(\mathbf{x}) dy} \tag{7}$$

Eq. (7) is established in the unsaturated condition. In Eq. (7), Ibð Þx is the laser intensity in the backward direction at point x, and Ib, <sup>0</sup> is the initial laser intensity of the backward beam at point x = 0. Similarly, if the laser propagates in the opposite direction from right to left, at the same height, the forward equation of the laser beam is given as

$$F\_f(\mathbf{x}) = \mathbb{C}\mathbf{S}(\mathbf{x})\sigma\_0 \mathbf{N}(\mathbf{x}) I\_f(\mathbf{x}) \tag{8}$$

$$I\_f(\mathbf{x}) = I\_{f,0} \mathbf{e}^{-\int\_0^{\mathbf{x}} \sigma\_0 N(\mathbf{x}) dy} \tag{9}$$

where Ifð Þx is the laser intensity in the forward direction at point x and If,<sup>0</sup> is the initial laser intensity of the forward beam. Note that the incident point of the forward beam is located at x = L. The ratio of fluorescence signals, R(x), is equal to the ratio between the laser intensities because the factors of C, i.e., S(x), σ0, and N(x), are canceled in the division expressed as

$$R(\mathbf{x}) = \frac{F\_f(\mathbf{x})}{F\_b(\mathbf{x})} = \frac{I\_f(\mathbf{x})}{I\_b(\mathbf{x})} \tag{10}$$

Take the logarithm of the fluorescence ratio R(x); then one will obtain the following equation:

$$\begin{aligned} \ln\left[R(\mathbf{x})\right] &= \ln\left[\frac{I\_{\mathbf{f}}(\mathbf{x})}{I\_{\mathbf{b}}(\mathbf{x})}\right] \\ &= \ln\frac{I\_{\mathbf{f},0}}{I\_{\mathbf{b},0}} + \int\_{0}^{\mathbf{x}} \sigma\_{0}N(\mathbf{y})d\mathbf{y} - \int\_{\mathbf{x}}^{\mathbf{L}} \sigma\_{0}N(\mathbf{y})d\mathbf{y} \\ &= \ln\frac{I\_{\mathbf{f},0}}{I\_{\mathbf{b},0}} + 2\int\_{0}^{\mathbf{x}} \sigma\_{0}N(\mathbf{y})d\mathbf{y} - \int\_{0}^{\mathbf{L}} \sigma\_{0}N(\mathbf{y})d\mathbf{y} \end{aligned} \tag{11}$$

Finally taking the differential operation on Eq. (11), one can obtain

$$\mathbf{N}(\mathbf{x}) = \frac{1}{2\sigma\_0} \frac{\mathbf{d}}{\mathbf{dx}} \ln \left[ \frac{F\_f(\mathbf{x})}{F\_b(\mathbf{x})} \right] \tag{12}$$

where <sup>I</sup>νð Þ<sup>x</sup> is the intensity of laser at x point, <sup>ν</sup> represents the wave number (cm�<sup>1</sup>

As long as the laser energy is not too high and the molecular number density is not too large, the absorption cross section can be considered directly proportional to the linear absorption

where σtot is the integral absorption cross section (cm) and the line-shape function satisfies the

ð∞ �∞

It can be seen that σtot is only related to the nature of the molecule but has no relationship with external environmental conditions. The integral absorption cross section is directly related to

> mec<sup>2</sup> <sup>f</sup> <sup>υ</sup><sup>0</sup> υ00J 0 J

where e is the electronic charge (esu), me is the mass of electron (g), c is the speed of light (cm/s),

<sup>υ</sup><sup>00</sup> υ<sup>0</sup> ; υ � �<sup>00</sup> 4

the vibrational quantum number in the lower vibrational level; is the vibrator strength, SJ

In the actual experiment, the measured absorption line shape is not normalized, and thus

For this reason, it is necessary to normalize it for obtaining the experimental expression of the

the rotational transition probability, that is, the Honl-London factor; and TJ

vibrational and rotational correction factor. The detailed values of f <sup>υ</sup><sup>0</sup>

ð∞ �∞

<sup>00</sup> is the molecular oscillator strength in the given oscillator transition, expressing as [23]

SJ 0 J 00

2J 00 þ 1 TJ 0 J

<sup>00</sup> is the vibrational quantum number in the upper vibrational energy level; J" is

ð∞ �∞

σtot ¼

<sup>σ</sup>tot <sup>¼</sup> <sup>π</sup>e<sup>2</sup>

the oscillator strength of the molecule, with the expression of [22]

f υ0 υ00J 0 J <sup>00</sup> <sup>¼</sup> <sup>f</sup> <sup>υ</sup><sup>0</sup>

pressure (atm), N(x) denotes the number density (cm�<sup>3</sup>

phenomenological physical definition of the absorption cross section.

and <sup>σ</sup>ð Þ<sup>ν</sup> is the absorption cross section (cm2

function (cm) [21]:

and f <sup>υ</sup><sup>0</sup> υ00J 0 J

where υ

found in the LIFBASE software.

effective peak absorption cross section.

normalization condition:

To integrate Eq. (15), one can obtain

), P is the

97

) of the excited molecules at the point x,

http://dx.doi.org/10.5772/intechopen.79702

) of the molecules. Eq. (14) is thought to be the

Quantitative Planar Laser-Induced Fluorescence Technology

σð Þ¼ ν σtotgð Þ ν (15)

gð Þ ν dν ¼ 1 (16)

σð Þ ν dν (17)

<sup>00</sup> (18)

<sup>00</sup> (19)

0 J

υ00J 0 J <sup>00</sup> , SJ 0 J <sup>00</sup> and TJ 0 J <sup>00</sup> can be

ϕð Þν dν 6¼ 1 (20)

0 J <sup>00</sup> is

<sup>00</sup> represents the

which is a measurement equation of the species concentration profiles, representing the quantitative functional relationship between particle number density and LIF fluorescence intensity. Eq. (12) clearly shows that the particle number density is only associated with the forward and backward fluorescence intensities and the effective peak absorption cross section of particles under the linear excitation, independent of the temperature, pressure, quenching rate, laser energy, etc. It also suggests that the derivative of the fluorescence ratio R(x) is very sensitive to noise in the LIF signal.

It is important to note that the N(x) in Eq. (12) refers to the molecular number density in the excited level for the low rotational level J". However, the total number density of the molecules to be measured N<sup>0</sup> is often concerned in the experiments. Therefore, it needs to be converted to N<sup>0</sup> after obtaining the experimental value of N(x). In the state of thermal equilibrium, the relationship between the number density N υ; J " ; T in the excited molecule and the total number density N<sup>0</sup> of the molecules is linked by the Boltzmann fraction f <sup>B</sup> υ; J " ; T , and the mathematical expression is given as follows:

$$f\_B(\nu, \boldsymbol{f}', T) = \frac{N(\nu, \boldsymbol{f}', T)}{N\_0} = \frac{\{2\boldsymbol{f}'' + 1\}}{Q\_{vib} Q\_{rot} Q\_{elcc}} e^{-(\mathcal{E}\_{nb} + \mathcal{E}\_{nt})/k\_B T} \tag{13}$$

where k<sup>B</sup> is the Boltzmann constant; T is the temperature; the vibrational quantum number J" represents the rotational quantum number at the low energy level; Evib and Erot are vibrational and rotational energies, respectively; and Qvib, Qrot, and Qelec are vibrational, rotational, and electronic partition functions, respectively.

Overall, the bidirectional LIF/PLIF is thought to be a no-calibration and no quenching effect LIF/PLIF technique, based on the combination of the traditional linear LIF/PLIF and absorption spectroscopy. It not only preserves the advantages of high spatial resolution of traditional LIF/PLIF but also absorbs the superiority of no quenching effect from absorption spectroscopy. It is of great significance to solve the problem of traditional quantitative LIF/PLIF technology.

#### 4.2. Effective peak absorption cross section

From the view of the quantum mechanics, the absorption cross section describes the probability that the incident photon is absorbed by the target nucleus, and its unit usually has the dimension of area (cm<sup>2</sup> ). When the laser propagating along the x direction passes through the medium, the molecules will be attenuated by absorption, following the Lambert Bill absorption law. The differential form is expressed as

$$\frac{1}{I\_{\overline{\mathcal{V}}}(\mathbf{x})} \frac{dI\_{\overline{\mathcal{V}}}(\mathbf{x})}{d\mathbf{x}} = -N(\mathbf{x})\sigma(\overline{\mathbf{v}})P\tag{14}$$

where <sup>I</sup>νð Þ<sup>x</sup> is the intensity of laser at x point, <sup>ν</sup> represents the wave number (cm�<sup>1</sup> ), P is the pressure (atm), N(x) denotes the number density (cm�<sup>3</sup> ) of the excited molecules at the point x, and <sup>σ</sup>ð Þ<sup>ν</sup> is the absorption cross section (cm2 ) of the molecules. Eq. (14) is thought to be the phenomenological physical definition of the absorption cross section.

As long as the laser energy is not too high and the molecular number density is not too large, the absorption cross section can be considered directly proportional to the linear absorption function (cm) [21]:

$$
\sigma(\overline{\mathbf{v}}) = \sigma\_{\text{tot}} \mathbf{g}(\overline{\mathbf{v}}) \tag{15}
$$

where σtot is the integral absorption cross section (cm) and the line-shape function satisfies the normalization condition:

$$\int\_{-\infty}^{\infty} \mathbf{g}(\overline{\mathbf{v}}) d\overline{\mathbf{v}} = 1 \tag{16}$$

To integrate Eq. (15), one can obtain

Finally taking the differential operation on Eq. (11), one can obtain

noise in the LIF signal.

96 Laser Technology and its Applications

relationship between the number density N υ; J

mathematical expression is given as follows:

electronic partition functions, respectively.

4.2. Effective peak absorption cross section

tion law. The differential form is expressed as

dimension of area (cm<sup>2</sup>

f <sup>B</sup> υ; J " ; <sup>T</sup> <sup>¼</sup> <sup>N</sup> <sup>υ</sup>; <sup>J</sup>

Nð Þ¼ x

1 2σ<sup>0</sup> d dx ln

which is a measurement equation of the species concentration profiles, representing the quantitative functional relationship between particle number density and LIF fluorescence intensity. Eq. (12) clearly shows that the particle number density is only associated with the forward and backward fluorescence intensities and the effective peak absorption cross section of particles under the linear excitation, independent of the temperature, pressure, quenching rate, laser energy, etc. It also suggests that the derivative of the fluorescence ratio R(x) is very sensitive to

It is important to note that the N(x) in Eq. (12) refers to the molecular number density in the excited level for the low rotational level J". However, the total number density of the molecules to be measured N<sup>0</sup> is often concerned in the experiments. Therefore, it needs to be converted to N<sup>0</sup> after obtaining the experimental value of N(x). In the state of thermal equilibrium, the

number density N<sup>0</sup> of the molecules is linked by the Boltzmann fraction f <sup>B</sup> υ; J

" ; T N<sup>0</sup>

"

<sup>¼</sup> <sup>2</sup><sup>J</sup>

where k<sup>B</sup> is the Boltzmann constant; T is the temperature; the vibrational quantum number J" represents the rotational quantum number at the low energy level; Evib and Erot are vibrational and rotational energies, respectively; and Qvib, Qrot, and Qelec are vibrational, rotational, and

Overall, the bidirectional LIF/PLIF is thought to be a no-calibration and no quenching effect LIF/PLIF technique, based on the combination of the traditional linear LIF/PLIF and absorption spectroscopy. It not only preserves the advantages of high spatial resolution of traditional LIF/PLIF but also absorbs the superiority of no quenching effect from absorption spectroscopy. It is of great significance to solve the problem of traditional quantitative LIF/PLIF technology.

From the view of the quantum mechanics, the absorption cross section describes the probability that the incident photon is absorbed by the target nucleus, and its unit usually has the

medium, the molecules will be attenuated by absorption, following the Lambert Bill absorp-

1 Iνð Þx dIνð Þx

" <sup>þ</sup> <sup>1</sup> QvibQrotQelec

e

). When the laser propagating along the x direction passes through the

dx ¼ �N xð Þσð Þ<sup>ν</sup> <sup>P</sup> (14)

; T in the excited molecule and the total

" ; T , and the

�ð Þ EvibþErot <sup>=</sup>kBT (13)

Ffð Þx Fbð Þx 

(12)

$$
\sigma\_{\rm tot} = \int\_{-\infty}^{\infty} \sigma(\overline{\mathbf{v}}) d\overline{\mathbf{v}} \tag{17}
$$

It can be seen that σtot is only related to the nature of the molecule but has no relationship with external environmental conditions. The integral absorption cross section is directly related to the oscillator strength of the molecule, with the expression of [22]

$$
\sigma\_{\text{tot}} = \frac{\pi e^2}{m\_\text{e} c^2} f\_{\nu' v'} '\!\!/\!/\!/ \tag{18}
$$

where e is the electronic charge (esu), me is the mass of electron (g), c is the speed of light (cm/s), and f <sup>υ</sup><sup>0</sup> υ00J 0 J <sup>00</sup> is the molecular oscillator strength in the given oscillator transition, expressing as [23]

$$f\_{\left(\upsilon'\upsilon''\right)'\!\!/\!\!/}^{\prime} = \frac{f\_{\upsilon'\upsilon''}\left(\upsilon',\upsilon''\right)}{4} \frac{\mathcal{S}\_{\left[\!\!\!/\!\!/\!\!/]}}{\mathcal{D}\_{\left[\!\!\!/\!\!/]}^{\prime} + 1} T\_{\left[\!\!\!\!/\!\!/]}\right) \tag{19}$$

where υ <sup>00</sup> is the vibrational quantum number in the upper vibrational energy level; J" is the vibrational quantum number in the lower vibrational level; is the vibrator strength, SJ 0 J <sup>00</sup> is the rotational transition probability, that is, the Honl-London factor; and TJ 0 J <sup>00</sup> represents the vibrational and rotational correction factor. The detailed values of f <sup>υ</sup><sup>0</sup> υ00J 0 J <sup>00</sup> , SJ 0 J <sup>00</sup> and TJ 0 J <sup>00</sup> can be found in the LIFBASE software.

In the actual experiment, the measured absorption line shape is not normalized, and thus

$$\int\_{-\infty}^{\infty} \phi(\overline{\nu}) d\overline{\nu} \neq 1 \tag{20}$$

For this reason, it is necessary to normalize it for obtaining the experimental expression of the effective peak absorption cross section.

The integral on the left side of Eq. (15) is defined as the relative integral absorption area Int. Normalizing above integral, one will obtain

$$\int\_{-\infty}^{\infty} \frac{\phi(\overline{\mathbf{v}})}{Int} d\overline{\mathbf{v}} = \int\_{-\infty}^{\infty} g(\overline{\mathbf{v}}) d\overline{\mathbf{v}} = 1 \tag{21}$$

5. Concentration profiles in a laminar flame by bidirectional PLIF

methane/air flat flame

and 5.

(c) Φ = 0.9, (d) Φ = 1.0.

5.1. Measurements for the absolute OH concentration profiles in a partially premixed

The temperature distribution of CH4/O2/N2 partially premixed flame is first measured by UV absorption spectrometry. The average temperature of the premixed flame of methane/air is 1772 K, with the statistical uncertainty of 10.4%. Then, the axial distributions of OH effective peak absorption cross section for Q1(8) line (the corresponding wavelength of 309.240 nm) in the band (0,0) are determined by using the wavelength scanning method. The statistical average of the OH effective peak absorption cross section on the axial direction is 1.10 <sup>10</sup><sup>15</sup> cm<sup>2</sup> with the relative statistical uncertainty, which is 9.9%. The standard flat flame burner, designed by Hartung et al. [24], in the experiments is employed. More detailed experimental parameters can be found in the literature [25]. The variations of two-dimensional OH concentration fields with the equivalence ratios Φ (from 0.7 to 1.4) have been obtained in CH4/O2/N2 partially premixed flat flame by using bidirectional PLIF, as shown in Figures 4

Quantitative Planar Laser-Induced Fluorescence Technology

http://dx.doi.org/10.5772/intechopen.79702

99

Figures 4 and 5 show the two-dimensional spatial distributions of OH concentration in the methane/air partially premixed flame and its variations with the equivalence ratios, respectively. The actual size of each image is 15 mm 46 mm, and the spatial resolution is 87.6 μm. As can be seen from Figure 4, when the flame is burned in the lean-burn condition, the OH radicals are mainly distributed in a narrow band above the burner surface. With the increase of the axial distance, the OH concentration will decrease rapidly. On the other hand, the OH

Figure 4. Variations of two-dimensional OH concentrations with equivalence ratios (Φ = 0.7–1.0). (a) Φ = 0.7, (b) Φ = 0.8,

Meanwhile, it is noted that if the first-term integral of Eq. (21) is multiplied on the left side of Eq. (17), one will get

$$\int\_{-\infty}^{\infty} \sigma(\overline{\mathbf{v}}) d\overline{\mathbf{v}} = \sigma\_{\text{tot}} \int\_{-\infty}^{\infty} \frac{\phi(\overline{\mathbf{v}})}{Int} d\overline{\mathbf{v}} \tag{22}$$

That is

$$\sigma(\overline{\nu}) = \frac{\sigma\_{\text{tot}} \phi(\overline{\nu})}{\text{Int}} \tag{23}$$

Eq. (23) is the relationship between the absorption cross section and the molecular absorption line profile measured experimentally.

In particular, if ν ¼ ν0, then

$$
\sigma\_0 = \sigma(\overline{\nu}\_0) = \frac{\sigma\_{\text{tot}} \phi(\overline{\nu}\_0)}{\text{Int}} \tag{24}
$$

where σ<sup>0</sup> is the effective peak absorption cross section; the numerical value of σtot can be calculated by Eq. (18). Eq. (24) is thought to be the experimental expression for measuring the effective peak absorption cross section of the molecule. Eq. (24) indicates that the effective peak absorption cross section of the molecule is related to the molecular absorption line shape and the relative integral absorption area.

As Versluis et al. have not clearly pointed out that the effective peak absorption cross section associates with the peak value ϕð Þ ν<sup>0</sup> of absorption line-shape, there is a difference between the effective peak absorption cross section and the actual value, if using the measurement equation given by Versluis et al. The difference is not obvious for the absorption band (0,0) of OH radical. However, this discrepancy will manifest significantly for the weak absorption band of (1,0). Therefore, the measurement equation of effective peak absorption cross section given by Versluis et al. is not applicable to the condition of weak absorption. To solve this problem, we revised the experimental equation. The corrected effective peak absorption cross section measurement equation is shown in Eq. (24). To confirm the validity of the modified measurement equation, the effective peak absorption cross section of the band (0,0) and band (1,0) within the Q1(8) line for the OH radical is measured, respectively. The experimental results show that the OH effective peak absorption cross section of the Q1(8) line for band (0,0) turns out to be about 5.5 times higher than that of band (1,0), while the theoretical calculation given by the LIFBASE simulation is about 6 times. The experimental result has been proven to be in good agreement with the simulation results.
