变间距全息光栅记录光路的建模与优化
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摘要
衍射光栅是光谱仪器中重要的分光元件，衍射光栅的像差直接决定了光谱仪器的分辨率。随着对光谱性能要求的不断提高，具有自聚焦和消像差能力的变间距光栅已经成为高分辨率光谱仪器的核心器件。
相较于传统的机械刻划光栅，采用全息记录方法加工的变间距全息光栅具有加工效率高，杂散光小等诸多优点。目前，变间距全息光栅已经广泛应用于同步辐射、空间光谱、等离子体物理、表面干涉计量等领域。深入研究变间距全息光栅的设计、制造与检测技术，具有重要的理论价值与现实意义。
本文研究的重点是变间距全息光栅记录光路的设计问题，包括全息记录光路的建模与优化两方面。记录光路建模的目标是，建立记录参数与光栅参数之间的函数关系：记录光路优化的目标是，求取合适的记录参数，使得实际光栅参数尽可能的接近期望光栅参数。
本文在记录光路建模方面的主要工作是：针对使用辅助球面镜与辅助等间距平面光栅的两种记录光路，推导了四阶解析模型，给出了基于费马原理与局部搜索的光线追迹数值模型，并分析了解析模型的展开误差。
本文在记录光路优化方面的主要工作是：针对记录光路优化这一非线性、多极值、有约束的复杂优化问题，研究了基于演化算法的优化设计解决方案，包括：
一、考虑到目标函数的复杂性，研究了快速搜索算法。采用标准遗传算法与局部搜索相结合的混合优化策略，使用遗传算法进行初始搜索的预处理，在此基础上采用局部搜索算法进行精细搜索，兼顾了优化效果与优化效率。
二、考虑到目标函数的多极值特点，研究了多极值优化算法。讨论了受限演化算法的参数设置问题，并应用于使用辅助平面光栅的记录光路设计。将拥挤模型与聚类算法相结合，提出了一种全新的拥挤聚类遗传算法，研究了算法的收敛性质，并应用于使用辅助球面镜的记录光路设计。
三、考虑到容许误差对设计结果的影响，研究了鲁棒优化设计算法。针对记录光路鲁棒优化的特点，将其规划为单目标的确定性鲁棒优化模型。提出了在标准遗传算法及标准拥挤遗传算法框架下，利用演化策略计算近似鲁棒目标函数的层叠
Diffraction gratings are the important diffractive elements in spectral instruments and their aberrations directly decide the spectral resolution. With the increasing requirement of spectral performance, varied-line-spacing gratings have been the key elements of high-resolution spectral instruments due to the excellent self-focusing and aberration-correction ability.
Compared to the conventional mechanically ruled gratings, varied-line-spacing holographic gratings (VLSHGs) fabricated by holographic recording methods take the advantages of high fabrication efficiency and low stray light. Currently, VLSHGs have been widely applied to the areas such as synchrotron radiation, spatial spectrum, plasma physics, surface metrology, and so on. In both theoretical and practical aspects, it is a significant topic to study the design, fabrication and detection technologies of VLSHGs.
The key point of this thesis is the design of recording optics of VLSHGs, including modeling and optimization of recording optics. The objective of modeling is to establish the relationship between recording parameters and grating parameters, while the objective of optimization is to provide proper recording parameters to meet the requirement of grating parameters.
In the modeling of recording optics, the main contents of this thesis are: deriving the fourth-order analytical model for the recording optics with auxiliary spherical mirrors and auxiliary uniform-line-spacing plane gratings, providing the numerical ray-tracing models based on Fermat's principle and local search, and analyzing the expansion errors of analytical models.
In the optimization of recording optics, the main contents of this thesis are: studying several forms of optimal design problems based on evolutionary algorithms for these kinds of non-linear, multimodal, and constrained complicated optimization problems, including:
相较于传统的机械刻划光栅，采用全息记录方法加工的变间距全息光栅具有加工效率高，杂散光小等诸多优点。目前，变间距全息光栅已经广泛应用于同步辐射、空间光谱、等离子体物理、表面干涉计量等领域。深入研究变间距全息光栅的设计、制造与检测技术，具有重要的理论价值与现实意义。
本文研究的重点是变间距全息光栅记录光路的设计问题，包括全息记录光路的建模与优化两方面。记录光路建模的目标是，建立记录参数与光栅参数之间的函数关系：记录光路优化的目标是，求取合适的记录参数，使得实际光栅参数尽可能的接近期望光栅参数。
本文在记录光路建模方面的主要工作是：针对使用辅助球面镜与辅助等间距平面光栅的两种记录光路，推导了四阶解析模型，给出了基于费马原理与局部搜索的光线追迹数值模型，并分析了解析模型的展开误差。
本文在记录光路优化方面的主要工作是：针对记录光路优化这一非线性、多极值、有约束的复杂优化问题，研究了基于演化算法的优化设计解决方案，包括：
一、考虑到目标函数的复杂性，研究了快速搜索算法。采用标准遗传算法与局部搜索相结合的混合优化策略，使用遗传算法进行初始搜索的预处理，在此基础上采用局部搜索算法进行精细搜索，兼顾了优化效果与优化效率。
二、考虑到目标函数的多极值特点，研究了多极值优化算法。讨论了受限演化算法的参数设置问题，并应用于使用辅助平面光栅的记录光路设计。将拥挤模型与聚类算法相结合，提出了一种全新的拥挤聚类遗传算法，研究了算法的收敛性质，并应用于使用辅助球面镜的记录光路设计。
三、考虑到容许误差对设计结果的影响，研究了鲁棒优化设计算法。针对记录光路鲁棒优化的特点，将其规划为单目标的确定性鲁棒优化模型。提出了在标准遗传算法及标准拥挤遗传算法框架下，利用演化策略计算近似鲁棒目标函数的层叠
Diffraction gratings are the important diffractive elements in spectral instruments and their aberrations directly decide the spectral resolution. With the increasing requirement of spectral performance, varied-line-spacing gratings have been the key elements of high-resolution spectral instruments due to the excellent self-focusing and aberration-correction ability.
Compared to the conventional mechanically ruled gratings, varied-line-spacing holographic gratings (VLSHGs) fabricated by holographic recording methods take the advantages of high fabrication efficiency and low stray light. Currently, VLSHGs have been widely applied to the areas such as synchrotron radiation, spatial spectrum, plasma physics, surface metrology, and so on. In both theoretical and practical aspects, it is a significant topic to study the design, fabrication and detection technologies of VLSHGs.
The key point of this thesis is the design of recording optics of VLSHGs, including modeling and optimization of recording optics. The objective of modeling is to establish the relationship between recording parameters and grating parameters, while the objective of optimization is to provide proper recording parameters to meet the requirement of grating parameters.
In the modeling of recording optics, the main contents of this thesis are: deriving the fourth-order analytical model for the recording optics with auxiliary spherical mirrors and auxiliary uniform-line-spacing plane gratings, providing the numerical ray-tracing models based on Fermat's principle and local search, and analyzing the expansion errors of analytical models.
In the optimization of recording optics, the main contents of this thesis are: studying several forms of optimal design problems based on evolutionary algorithms for these kinds of non-linear, multimodal, and constrained complicated optimization problems, including:
引文
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