铝基微结构光栅几何参数反演

孙双成; 齐宏; 孙建平; 阮世庭; 吕中原; 阮立明

doi:10.13700/j.bh.1001-5965.2017.0055

铝基微结构光栅几何参数反演

doi: 10.13700/j.bh.1001-5965.2017.0055

1.
哈尔滨工业大学能源科学与工程学院, 哈尔滨 150001
2.
上海卫星工程研究所, 上海 201100

基金项目:

国家自然科学基金 51476043

详细信息

作者简介:
孙双成男, 博士研究生。主要研究方向:辐射传输逆问题及智能优化算法

齐宏男, 博士, 教授, 博士生导师。主要研究方向:热辐射传输与耦合换热、高温弥散颗粒辐射物性及温度测量、辐射传输逆问题及智能优化算法、微藻新能源利用

通讯作者:
齐宏, E-mail: qihong@hit.edu.cn

中图分类号: TK121
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- 被引次数: 0
出版历程
- 收稿日期: 2017-02-13
- 录用日期: 2017-06-07
- 网络出版日期: 2017-11-20

Inverse estimation of geometric parameters of aluminum matrix microscale structure grating

1.
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
2.
Shanghai Satellite Engineering Research Institute, Shanghai 201100, China

Funds:

National Natural Science Foundation of China 51476043

More Information

Corresponding author: QI Hong, E-mail: qihong@hit.edu.cn

摘要

摘要:
微结构光栅是一种广泛应用的电子元件。采用随机微粒群优化（SPSO）算法反演了一维铝基衬底矩形光栅的几何结构参数。首先介绍了严格耦合波分析（RCWA）法和微粒群优化算法的基本原理，并采用RCWA法求解了光栅内电磁场问题；然后根据正问题求得的光栅光谱反射率建立目标函数，并采用SPSO算法优化目标函数，反演得到单槽和双槽矩形光栅的周期、凸脊宽度和凹槽深度；最后分析了种群大小和搜索区间对反演结果的影响。结果表明，SPSO算法可以准确地反演光栅几何结构参数，并推荐种群数取30。
- 光栅结构反演 /
- 随机微粒群优化(SPSO)算法 /
- 严格耦合波分析(RCWA)法 /
- 光谱反射率 /
- 辐射特性
Abstract:
Micro structure grating is a widely used electronic component. The geometric parameters of one-dimensional rectangular aluminum matrix grating are inversely estimated using stochastic particle swarm optimization (SPSO) algorithm. The theoretical overview of rigorous coupled wave analysis (RCWA) algorithm and particle swarm optimization algorithm is introduced, and RCWA algorithm is employed to solve the electromagnetic field problem within grating. The objective function is formulated based on the spectral reflectance obtained by the direct problem, and then the SPSO algorithm is used to optimize the objective function. The geometric parameters such as the grating period, ridge width and groove depth are retrieved simultaneously. The effects of population size and searching space on the inverse estimation results are also investigated. The retrieval results show that SPSO algorithm is effective and robust for estimating geometric parameters of grating and the population size is suggested as 30.

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图 1 TE波入射矩形光栅示意图

Figure 1. Schematic of rectangular grating with a TE wave irradiation

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图 2 PSO算法计算流程图

Figure 2. Calculation flowchart of PSO algorithm

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图 3 单槽光栅光谱反射率

Figure 3. Spectral reflectance of single-slot grating

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图 4 单槽光栅几何参数反演结果

Figure 4. Inverse estimation results of single-slot grating geometry parameters

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图 5 4种PSO算法目标函数值变化曲线

Figure 5. Changing curves of objective function values of four PSO algorithms

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图 6 不同种群大小下目标函数值变化曲线

Figure 6. Changing curves of objective function values under different population sizes

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图 7 双槽矩形光栅示意图

Figure 7. Schematic of rectangular double-slot grating

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图 8 双槽光栅光谱反射率

Figure 8. Spectral reflectance of double-slot grating

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图 9 双槽光栅几何参数反演结果

Figure 9. Inverse estimation results of double-slot grating geometry parameters

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表 1 SPSO算法参数设置

Table 1. Parameter setting of SPSO algorithm

参数	数值
M	50
V_max	3.0
C₁	1.2
C₂	0.8
t_max	100
ε₁	10^-6
λ₁/μm	0.1
λ₂/μm	5.0
n	100

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表 2 不同入射角度下反演结果

Table 2. Inverse estimation results with different incident angles

入射角度/(°)	a_est/μm	平均相对误差/%	最大相对误差/%
0	[1.000 6±1.26×10^－3, 0.899 2±3.61×10^－3, 0.600 4±2.51×10^－3]	0.380 5	2.852 6
30	[0.999 3±3.09×10^－3, 0.899 3±4.59×10^－3, 0.599 2±2.99×10^－3]	0.368 9	2.863 1
60	[0.999 4±2.90×10^－3, 0.900 5±3.23×10^－3, 0.599 3±3.02×10^－3]	0.376 6	2.799 9

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表 3 不同结构参数下反演结果

Table 3. Inverse estimation results with different structure parameters

a_exa/μm	a_est/μm	平均相对误差/%	最大相对误差/%
[1.0, 0.9, 0.6]	[0.999 3±3.09×10^－3, 0.899 3±4.59×10^－3, 0.599 2±2.99×10^－3]	0.368 9	2.863 1
[3.0, 2.5, 1.5]	[2.999 1±3.11×10^－3, 2.500 5±1.19×10^－3, 1.499 4±2.95×10^－3]	0.359 6	2.904 0
[5.0, 4.0, 2.0]	[5.000 6±3.33×10^－3, 3.999 2±4.14×10^－3, 2.000 6±3.20×10^－3]	0.331 5	2.882 3

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表 4 不同搜索区间下反演结果

Table 4. Inverse estimation results with different searching spaces

算例	Λ /μm	l /μm	d/μm	迭代次数	目标函数值	平均相对误差/%
算例1	[0.9, 1.1]	[0.8, 1.0]	[0.5, 0.7]	59	3.25×10^-7	0.020 9
算例2	[0.8, 1.2]	[0.7, 1.1]	[0.4, 0.8]	71	9.19×10^-7	0.115 5
算例3	[0.5, 1.5]	[0.4, 1.4]	[0.1, 1.1]	100	8.11×10^-6	0.206 4

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