2.1. Textured surface models

mask etching [11], mask growing [12], electro-chemical corrosion [13], electrical discharge machining [14]. These methods have positive influence on improving photoelectric conversion

At present, wet etching is the most mature method to fabricate the light trapping structure on the surface of silicon solar cells. Because of the isotropy of polycrystalline silicon, the morphology of porous silicon can be etched on the surface of polycrystalline silicon solar cells by acid etching. Compared with pyramidal textured surface, the light trapping efficiency of porous silicon is lower, and the optical reflectance is higher. As for monocrystalline silicon solar cells, pyramidal textured surface can be formed due to the anisotropy of material by alkaline etching. However, the limitation of crystal structure makes the largest base angle of the pyramid is 54.74, some experimental studies believe that the angle is closer to 50–52. The reflectance shown dependence on the base angle, with larger base angle size resulting in reduced reflectance. The lowest reflectance of the pyramidal textured surface formed by

Etching with alkaline solution such as NaOH, KOH, the texture obtained is a generally welldistributed pyramidal texture with solid top angle of 70 due to the different corrosion rate in different crystal orientation [13]. Reflectance of light when propagating from one media to another media with different refractive indices is determined by incidence, wavelength and polarization of light. Some researchers studied the effects of pyramidal structure with different top angles fabricated by mechanical way on weighted reflectance. The reflectance can reach 6% when the top angle is 60 and the reflectance is less than 10% when the incident angle of light is less than 30. When the incident angle of light is larger than top angle, the structure tends to be a primary reflection area [15], in the light of Fresnel equations, the results could be considerably not precise. Hua et al. [16] proposed four different structures including triangular pyramid, rectangular pyramid, hexangular pyramid and cone structure. Ray-Tracing technology was employed to investigate the influence of many factors like geometrical shape, density and the top angle of the unit structure on sunlight absorption. In addition, mechanical tools develop in a trend of miniaturization and facilitation presently, Dehong et al. [17], Choong et al. [18], Rusnaldy et al. [19] have investigated and proved that single-crystalline silicon can be removed by micro machining in the ductile mode under the condition of appropriate parameters of mechanical grooving. Because of isotropy of polycrystalline silicon surface, pyramidal structure with large ratio of depth to diameter cannot be fabricated by alkaline corrosion, which appear to be a limit of this dominant fabrication method. Recently, the metal assisted chemical etching method [20–22] has been utilized to prepare SiNW(Silicon Nanowire) or nanopore structure in silicon crystalline surface called "black silicon", which has a relatively low reflectance at all angles, but the trade-off between low reflectance and low PCE (Power Conversion Efficiency) resulting from surface recombination efficiency caused by high surfaceto-volume ratio of SiNW arrays is a problem [23]. Besides, preparing a homogeneous and dense light trapping structure is difficult for chemical etching way, and the acid etching and alkaline corrosion produce contaminative water and cause pollution on the surface of the finished products, the quality could be influenced. The aim of this paper is to investigate the reflectance of arc-shaped and rectangular-shaped groove structure prepared by common cutting tools, while mentioned by few papers(for our knowledge). The reflectance of light trapping structure on rectangular groove can reach 3% and even lower without ARC (Antireflection Coatings).

efficiency.

48 Solar Panels and Photovoltaic Materials

alkaline etching is about 10.5%.

The normal pyramidal textured surface morphology depicted in Figure 1.

The size-independent behavior of the reflectance was clearly explained by a simple mathematical model in the perspective of geometric-optical. A profile was shown schematically in Figure 2. The orange (second reflection) and green (third reflection) areas play the role of light trapping efficiency. When the model size changes, if the ratio of the orange area to the green area does not change, the reflectance will not change. This principle also applied to the threedimensional pyramid structure. Therefore, the height of the structure was defined as a unit length. The reflectance of the whole wafer was not affected by the change of the parameters in the subsequent stage.

The schematics of cross-sectional views for ideal model with no fillet on the included angle and the model with a fillet on the included angle were depicted in Figure 3(a) and (b), respectively. If there exists a fillet on the included angle between neighboring pyramidal structures fabricated by mechanical way, the second model was proposed. The height of structure was set to a unit length in the algorithm. The size and angle of the structure was shown in Figure 3.

For convenience of calculation, a simplified two-dimensional model of arc-shaped groove structure formed under ideal mechanical condition (without uncut part, and will be mentioned below) is depicted in Figure 4. As Figure 5 shows, θ<sup>p</sup> is the primary incidence angle of light projects on arc-shaped groove trap of cell, θi1, θi2, and θi3 are the incidence angle of rays at

Figure 1. Normal pyramidal textured surface morphology.

of the groove. After one reflection in microstructure, the ratio of reflected light intensity to incident light intensity is defined as primary reflectance R, and after t reflections, the ratio of

As depicted in Figure 6, a beam of parallel light projects into the light trapping microstructure. This beam of parallel light can be evenly divided into n rays in the direction of horizontal

<sup>β</sup> <sup>¼</sup> <sup>R</sup><sup>t</sup> (1)

http://dx.doi.org/10.5772/intechopen.74972

, and the ratio of total escaped light intensity to incident light

Effects of the Novel Micro-Structure on the Reflectance of Photovoltaic Silicon Solar Cell

th ray is noted

51

reflected light intensity to incident light intensity is defined as exitance β:

as tj, then the exitance <sup>β</sup> <sup>¼</sup> Rtj

intensity is defined as weighted reflectance γ:

Figure 6. Multi-reflection schematic of parallel light in trap.

Figure 5. Schematic of arc-shaped groove structure model.

width (AB). It is assumed n is large enough, and the number of reflections of the i

Figure 2. A simplified two-dimensional model of multiple reflections.

Figure 3. Schematic of (a) ideal model with no fillet on the included angle and (b) the model with a fillet on the included angle.

Figure 4. Simplified two-dimensional arc-shaped groove model.

each point of reflection, r is radius of arc-shaped light trap. The height of groove H is defined as the dimensionless unit length in this model.

#### 2.2. Calculated model and numerical algorithm

To analyze light trapping efficiency of ideal arc-shaped grooved microstructure, curve equation of microstructure should be obtained first, which is determined by radius r and height H of the groove. After one reflection in microstructure, the ratio of reflected light intensity to incident light intensity is defined as primary reflectance R, and after t reflections, the ratio of reflected light intensity to incident light intensity is defined as exitance β:

$$
\beta = \mathbb{R}^t \tag{1}
$$

As depicted in Figure 6, a beam of parallel light projects into the light trapping microstructure. This beam of parallel light can be evenly divided into n rays in the direction of horizontal width (AB). It is assumed n is large enough, and the number of reflections of the i th ray is noted as tj, then the exitance <sup>β</sup> <sup>¼</sup> Rtj , and the ratio of total escaped light intensity to incident light intensity is defined as weighted reflectance γ:

Figure 5. Schematic of arc-shaped groove structure model.

Figure 6. Multi-reflection schematic of parallel light in trap.

each point of reflection, r is radius of arc-shaped light trap. The height of groove H is defined as

Figure 3. Schematic of (a) ideal model with no fillet on the included angle and (b) the model with a fillet on the included

To analyze light trapping efficiency of ideal arc-shaped grooved microstructure, curve equation of microstructure should be obtained first, which is determined by radius r and height H

the dimensionless unit length in this model.

angle.

2.2. Calculated model and numerical algorithm

Figure 4. Simplified two-dimensional arc-shaped groove model.

Figure 2. A simplified two-dimensional model of multiple reflections.

50 Solar Panels and Photovoltaic Materials

$$\gamma = \frac{1}{n} \sum\_{j=1}^{n} \beta\_j = \frac{1}{n} \sum\_{j=1}^{n} R^{t\_j} \tag{2}$$

the number of rays after tj reflections is noted as ni (1 ≤ ni ≤ n, i = tj), hence the Eq. (2) can be shown as following:

$$\mathcal{V} = \frac{1}{n} \sum\_{j=1}^{n} \mathcal{R}^{t\_j} = \sum\_{i=1}^{\infty} \zeta\_i \mathcal{R}^i \tag{3}$$

where ζ<sup>i</sup> is the proportion of rays after i reflections relative to total rays, which can be depicted as following:

$$\sum\_{i=1}^{n} \zeta\_i = 1, \zeta\_i = \frac{n\_i}{n}, i = 1, 2, \cdots \tag{4}$$

Rs <sup>¼</sup> <sup>n</sup><sup>1</sup> cos <sup>θ</sup><sup>i</sup> � <sup>n</sup><sup>2</sup> cos <sup>θ</sup><sup>t</sup> n<sup>1</sup> cos θ<sup>i</sup> þ n<sup>2</sup> cos θ<sup>t</sup>

Rp <sup>¼</sup> <sup>n</sup><sup>1</sup> cos <sup>θ</sup><sup>t</sup> � <sup>n</sup><sup>2</sup> cos <sup>θ</sup><sup>i</sup> n<sup>1</sup> cos θ<sup>t</sup> þ n<sup>2</sup> cos θ<sup>i</sup>

as unpolarized light, the reflectance for unpolarized light

order polynomial function and exponential function.

� � � � 2 ¼

� � � � 2 ¼ n1

<sup>R</sup> <sup>¼</sup> <sup>1</sup> 2 n1

Sun light consists of short wave trains with equal mixture of polarizations, which can be seen

To derive the reflectance at each reflected point in light trap on silicon cell, we need to know refractive index of air and silicon and incidence angle at each reflected point on the interface, the refractive index of light for air is seen as 1 here, refractive index for silicon differing with wavelength of ray is shown in Figure 9. We used numerical software to pick out points from original refractive index curve [26], and the curve in Figure 8 can fit original curve well by 4th

Figure 9 shows the reflectance for different wavelength rays of various incidence angles, the curve follows a trend similar to Figure 8 when wavelength increases, the curve of incidence equal to 75� shows a lower descending gradient comparing with other smaller incidence angles, and wavelength seem to have more significant influence than incidence on reflectance of light. By analyzing the calculated results of reflectance, the maximal value of reflectance for silicon is approximately obtained at wavelength 380 nm, Rmax = 0.535, After 20 reflections, the exitance

Rs þ Rp

� � � � � � � �

� � � � � � � �

n<sup>1</sup> cos θ<sup>i</sup> � n<sup>2</sup>

n<sup>1</sup> cos θ<sup>i</sup> þ n<sup>2</sup>

<sup>1</sup> � <sup>n</sup><sup>1</sup>

<sup>1</sup> � <sup>n</sup><sup>1</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Effects of the Novel Micro-Structure on the Reflectance of Photovoltaic Silicon Solar Cell

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>n</sup><sup>2</sup> sin θ<sup>i</sup> � �<sup>2</sup> <sup>r</sup>

<sup>n</sup><sup>2</sup> sin θ<sup>i</sup> � �<sup>2</sup> <sup>r</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>n</sup><sup>2</sup> sin θ<sup>i</sup> � �<sup>2</sup> <sup>r</sup>

� � � � � � � �

http://dx.doi.org/10.5772/intechopen.74972

� � � � � � � �

2

2

(8)

53

(9)

<sup>n</sup><sup>2</sup> sin θ<sup>i</sup> � �<sup>2</sup> <sup>r</sup>

� n<sup>2</sup> cos θ<sup>i</sup>

þ n<sup>2</sup> cos θ<sup>i</sup>

� � (10)

<sup>1</sup> � <sup>n</sup><sup>1</sup>

<sup>1</sup> � <sup>n</sup><sup>1</sup>

� � � �

Figure 7. Variables used in the Fresnel equations.

the reflectance for p-polarized light becomes

� � � �

The reflectance R of ordinary silicon wafer is about 0.33 [24], which can be considerably not precise for the weighted reflectance calculation. On the basis of Fresnel equations, the reflectance for s-polarized light (the component of the electric field of photons perpendicular to the plane of incidence) is explained by [25]:

$$R\_s = \left| \frac{Z\_2 \cos \theta\_i - Z\_1 \cos \theta\_t}{Z\_2 \cos \theta\_i + Z\_1 \cos \theta\_t} \right|^2 = \left| \frac{\sqrt{\frac{\mu\_2}{\varepsilon\_2}} \cos \theta\_i - \sqrt{\frac{\mu\_1}{\varepsilon\_1}} \cos \theta\_t}{\sqrt{\frac{\mu\_2}{\varepsilon\_2}} \cos \theta\_i + \sqrt{\frac{\mu\_1}{\varepsilon\_1}} \cos \theta\_t} \right|^2 \tag{5}$$

the reflectance for p-polarized light (the component of the electric field of photons parallel to the plane of incidence):

$$R\_p = \left| \frac{Z\_2 \cos \theta\_t - Z\_1 \cos \theta\_i}{Z\_2 \cos \theta\_t + Z\_1 \cos \theta\_i} \right|^2 = \left| \frac{\sqrt{\frac{\mu\_2}{\varepsilon\_2}} \cos \theta\_t - \sqrt{\frac{\mu\_1}{\varepsilon\_1}} \cos \theta\_i}{\sqrt{\frac{\mu\_2}{\varepsilon\_2}} \cos \theta\_t + \sqrt{\frac{\mu\_1}{\varepsilon\_1}} \cos \theta\_i} \right|^2 \tag{6}$$

where Z1 and Z2 are the wave impedances of media 1 and media 2, respectively, μ<sup>1</sup> and μ<sup>2</sup> are the magnetic permeability of two materials, ε<sup>1</sup> and ε<sup>2</sup> are the electric permeability of two materials. θ<sup>i</sup> and θ<sup>t</sup> are the incident and refracted angle of rays respectively, they are showed in Figure 7.

For non-magnetic materials such as silicon (i.e. materials for which μ<sup>1</sup> ≈ μ<sup>2</sup> ≈ μ0, where μ<sup>0</sup> is the permeability of free space), we have

$$Z\_1 = \frac{Z\_0}{n\_1}, Z\_2 = \frac{Z\_0}{n\_2} \tag{7}$$

The parameters n1 and n2 are the refractive index of media 1 and media 2 respectively. Using Snell's law and trigonometric identities, by eliminating θ<sup>t</sup> in Fresnel equations, the reflectance for s-polarized light becomes

Effects of the Novel Micro-Structure on the Reflectance of Photovoltaic Silicon Solar Cell http://dx.doi.org/10.5772/intechopen.74972 53

Figure 7. Variables used in the Fresnel equations.

<sup>γ</sup> <sup>¼</sup> <sup>1</sup> n Xn j¼1

<sup>γ</sup> <sup>¼</sup> <sup>1</sup> n Xn j¼1

X∞ i¼1

Rs <sup>¼</sup> <sup>Z</sup><sup>2</sup> cos <sup>θ</sup><sup>i</sup> � <sup>Z</sup><sup>1</sup> cos <sup>θ</sup><sup>t</sup> Z<sup>2</sup> cos θ<sup>i</sup> þ Z<sup>1</sup> cos θ<sup>t</sup>

Rp <sup>¼</sup> <sup>Z</sup><sup>2</sup> cos <sup>θ</sup><sup>t</sup> � <sup>Z</sup><sup>1</sup> cos <sup>θ</sup><sup>i</sup> Z<sup>2</sup> cos θ<sup>t</sup> þ Z<sup>1</sup> cos θ<sup>i</sup>

shown as following:

52 Solar Panels and Photovoltaic Materials

as following:

plane of incidence) is explained by [25]:

the plane of incidence):

in Figure 7.

� � � �

> � � � �

permeability of free space), we have

for s-polarized light becomes

<sup>β</sup><sup>j</sup> <sup>¼</sup> <sup>1</sup> n Xn j¼1

the number of rays after tj reflections is noted as ni (1 ≤ ni ≤ n, i = tj), hence the Eq. (2) can be

where ζ<sup>i</sup> is the proportion of rays after i reflections relative to total rays, which can be depicted

n

The reflectance R of ordinary silicon wafer is about 0.33 [24], which can be considerably not precise for the weighted reflectance calculation. On the basis of Fresnel equations, the reflectance for s-polarized light (the component of the electric field of photons perpendicular to the

> � � � � 2 ¼

the reflectance for p-polarized light (the component of the electric field of photons parallel to

� � � � 2 ¼

where Z1 and Z2 are the wave impedances of media 1 and media 2, respectively, μ<sup>1</sup> and μ<sup>2</sup> are the magnetic permeability of two materials, ε<sup>1</sup> and ε<sup>2</sup> are the electric permeability of two materials. θ<sup>i</sup> and θ<sup>t</sup> are the incident and refracted angle of rays respectively, they are showed

For non-magnetic materials such as silicon (i.e. materials for which μ<sup>1</sup> ≈ μ<sup>2</sup> ≈ μ0, where μ<sup>0</sup> is the

The parameters n1 and n2 are the refractive index of media 1 and media 2 respectively. Using Snell's law and trigonometric identities, by eliminating θ<sup>t</sup> in Fresnel equations, the reflectance

, Z<sup>2</sup> <sup>¼</sup> <sup>Z</sup><sup>0</sup> n2

<sup>Z</sup><sup>1</sup> <sup>¼</sup> <sup>Z</sup><sup>0</sup> n1

ffiffiffiffi μ2 ε2 q

� � � � � � �

ffiffiffiffi μ2 ε2 q

ffiffiffiffi μ2 ε2 q

� � � � � � �

ffiffiffiffi μ2 ε2 q

cos θ<sup>i</sup> �

cos θ<sup>i</sup> þ

cos θ<sup>t</sup> �

cos θ<sup>t</sup> þ

ffiffiffiffi μ1 ε1 q

ffiffiffiffi μ1 ε1 q

ffiffiffiffi μ1 ε1 q

ffiffiffiffi μ1 ε1 q

cos θ<sup>t</sup>

� � � � � � �

2

(5)

(6)

(7)

cos θ<sup>t</sup>

cos θ<sup>i</sup>

� � � � � � �

2

cos θ<sup>i</sup>

<sup>ζ</sup><sup>i</sup> <sup>¼</sup> <sup>1</sup>, <sup>ζ</sup><sup>i</sup> <sup>¼</sup> ni

Rtj <sup>¼</sup> <sup>X</sup><sup>∞</sup> i¼1

Rtj (2)

ζiRi (3)

, i ¼ 1, 2, ⋯ (4)

$$R\_s = \frac{\left| n\_1 \cos \theta\_i - n\_2 \cos \theta\_i \right|^2}{\left| n\_1 \cos \theta\_i + n\_2 \cos \theta\_i \right|} = \left| \frac{n\_1 \cos \theta\_i - n\_2 \sqrt{1 - \left(\frac{n\_1}{n\_2} \sin \theta\_i\right)^2}}{n\_1 \cos \theta\_i + n\_2 \sqrt{1 - \left(\frac{n\_1}{n\_2} \sin \theta\_i\right)^2}} \right|^2 \tag{8}$$

the reflectance for p-polarized light becomes

$$R\_p = \left| \frac{n\_1 \cos \theta\_l - n\_2 \cos \theta\_i}{n\_1 \cos \theta\_l + n\_2 \cos \theta\_i} \right|^2 = \left| \frac{n\_1 \sqrt{1 - \left(\frac{n\_1}{n\_2} \sin \theta\_i\right)^2} - n\_2 \cos \theta\_i}{n\_1 \sqrt{1 - \left(\frac{n\_1}{n\_2} \sin \theta\_i\right)^2} + n\_2 \cos \theta\_i} \right|^2 \tag{9}$$

Sun light consists of short wave trains with equal mixture of polarizations, which can be seen as unpolarized light, the reflectance for unpolarized light

$$R = \frac{1}{2} \left( R\_s + R\_p \right) \tag{10}$$

To derive the reflectance at each reflected point in light trap on silicon cell, we need to know refractive index of air and silicon and incidence angle at each reflected point on the interface, the refractive index of light for air is seen as 1 here, refractive index for silicon differing with wavelength of ray is shown in Figure 9. We used numerical software to pick out points from original refractive index curve [26], and the curve in Figure 8 can fit original curve well by 4th order polynomial function and exponential function.

Figure 9 shows the reflectance for different wavelength rays of various incidence angles, the curve follows a trend similar to Figure 8 when wavelength increases, the curve of incidence equal to 75� shows a lower descending gradient comparing with other smaller incidence angles, and wavelength seem to have more significant influence than incidence on reflectance of light.

By analyzing the calculated results of reflectance, the maximal value of reflectance for silicon is approximately obtained at wavelength 380 nm, Rmax = 0.535, After 20 reflections, the exitance

Figure 8. Refractive index for silicon to different wavelength rays.

Figure 9. Reflectance for different wavelength rays.

<sup>β</sup><sup>20</sup> <sup>¼</sup> <sup>R</sup>max<sup>20</sup> <sup>¼</sup> <sup>3</sup>:<sup>69</sup> � <sup>10</sup>�<sup>6</sup> , and ζ<sup>i</sup> < 1 (in Eq. (4)), hence the calculations can be ignored when i>20, and the weighted reflectance γ can be shown as:

$$\mathcal{V} = \sum\_{i=1}^{20} \mathbb{zeta}\_i \mathbb{R}^i \tag{11}$$

3. Results and discussions

3.1. Beam number determination

light beam increased a distance of <sup>2</sup><sup>H</sup>

under the model with no fillet (<sup>θ</sup> <sup>¼</sup> <sup>55</sup><sup>∘</sup>

respectively which can meet the needs of engineering completely.

3.2. Effects of base angle size on optical reflectance

different base angle size θ (from 30<sup>∘</sup> to 75<sup>∘</sup>

The irregular curve can be discussed as follows:

, i.e., <sup>α</sup> <sup>¼</sup> <sup>180</sup>

reflection area starting occurrence when θ reached 30<sup>∘</sup>

n ∘

efficiency when θ ≤ 30<sup>∘</sup>

, i.e., <sup>α</sup> <sup>¼</sup> <sup>360</sup>

, 72<sup>∘</sup>

angle θ reached 90<sup>n</sup>�<sup>1</sup>

one time when θ ≤ 30<sup>∘</sup>

, 67:5<sup>∘</sup>

2n�1 ∘

n ∘

, and 75<sup>∘</sup>

Table 1. Calculated result and analysis by different n (<sup>θ</sup> <sup>¼</sup> <sup>55</sup><sup>∘</sup>

Table 2. Calculated result and analysis by different n (<sup>θ</sup> <sup>¼</sup> <sup>55</sup> <sup>∘</sup>

reflected light.

180n�270 2n�1 ∘

45<sup>∘</sup> , 60<sup>∘</sup>

(<sup>θ</sup> <sup>¼</sup> <sup>55</sup><sup>∘</sup>

As shown in Figure 4, the incident light starting point was selected at point A, and then each

weighted reflectance γ according to the flow chart were carried out when n was set to different values. γ can achieve exact value when n is larger than a certain value. The calculation results

A satisfactory result was obtained at n ¼ 200, following works were carried out at the condition of n ¼ 200. At n ¼ 200, the relative errors between the adjacent dates were 0.148% and �0.491%

As depicted in Figure 4 (a), the calculation results were shown as curve (a) in Figure 10 with

The variation of reflection times changed with the base angle size was obtained after a rigorous geometric calculation: the nth reflection area started occurrence when the base angle θ reached

and the whole light trapping area became 2nd, 3rd, 4th, 5th, 6th reflection area when θ reached

n 10 20 100 200 500 2000 5000 10,000 γ/% 9.630 10.370 9.926 10.000 9.985 9.985 9.984 9.986 relative error/% �7.143 4.478 �0.741 0.148 0 0.010 �0.014 0

n 10 20 100 200 500 2000 5000 10,000 γ/% 9.630 11.111 11.852 12.000 12.059 12.052 12.050 12.050 relative error/% �13.333 �6.250 �1.235 �0.491 0.061 0.012 0 0

,r ¼ 0).

,r ¼ H=10).

, r ¼ H=10) on the included angle were shown in Table 1 and Table 2 respectively.

<sup>n</sup> tan <sup>α</sup> at x-axis direction, and ended at point C. Different

http://dx.doi.org/10.5772/intechopen.74972

55

Effects of the Novel Micro-Structure on the Reflectance of Photovoltaic Silicon Solar Cell

, r ¼ 0) on the included angle and the model with a fillet

). It is notable that the structure lost light trapping

, according to the geometric relationship between the incident and

; the whole light trapping area became nth reflection area when the base

, and the reflectance was stable at 33.333%; the 2nd, 3rd, 4th, 5th, 6th

, 54<sup>∘</sup>

. Specifically speaking, all the incident lights reflected only

, 64:286<sup>∘</sup>

, respectively. And the weighted reflection γ maintained constants

, 70<sup>∘</sup>

, 73:636<sup>∘</sup> respectively,

where Ri in formula (11) becomes

$$R^i = \prod\_{j=1}^i R\_j \tag{12}$$

where Rj is the reflectance of monochromatic ray at j th reflection.
