膜系光谱系数对膜层参数的一阶和二阶偏导数的计算模型
Calculation model for spectral coefficient’s first and second order partial derivatives of multilayer optical coatings with respect to layer parameters
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摘要: 为了寻找一种膜系深入分析与设计的有力辅助计算工具，从光学薄膜光谱系数的矩阵计算理论出发，基于对矩阵求迹运算的巧妙运用，从数学上建立了准确计算膜系光谱系数关于膜层几何厚度、实际折射率和消光系数等膜层参数的一阶和二阶偏导数的解析模型。这一偏导数计算模型物理上与矩阵理论具有一致的通用性和普适性，适用于任何各向同性的均匀膜系统。在数学上也严格成立，数值编程计算不存在差分近似，精度达到了计算机浮点运算的极限精度。而且算法运算费时少，计算速度快，取得了高度准确性和便于实时化的双重优越性能，非常有利于应用于膜系设计领域来提高膜层数较大时的设计速度和效率。同时，这一模型能非常便捷和准确地给出膜系许多实用的导数信息，对膜系分析、测量和膜厚监控等领域中的相关应用具有重要的参考意义。
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关键词:
- 薄膜光学 /
- 光谱系数导数计算模型 /
- 矩阵法 /
- 膜层参数
Abstract: In order to find a powerful assistant computation tool for further analysis and design of multilayer optical coatings, an analytical model is mathematically established for accurate calculation of the first and second derivatives of the spectral coefficients of multilayer optical coatings with respect to layer parameters like thickness, real refractive index and extinction coefficient. It is based on the matrix theory of calculating the spectral coefficients of multilayer optical coatings and is achieved by perfectly using the trace operation of matrix. This partial derivative computation model characterizes the same applicable condition and universality in physics with the matrix theory mentioned above. Thus it can also be applied to any homogenous and isotropic layered multilayer system. -
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