【作者】 刘光宏；

【导师】 吴刚；

【作者基本信息】 中国科学技术大学 ， 控制理论与控制工程， 2011， 博士

【摘要】 成像光谱仪是一种可同时采集目标光谱特征和空间特征的光学设备,可以实现图、谱合一,从而解决传统科学领域“成像无光谱”和“光谱不成像”的问题。相比于基于平面或凹面光栅的成像光谱仪,采用凸面光栅做分光元件的Offner成像光谱仪具有数值孔径大、无谱线弯曲、色畸变小、结构紧凑和加工装配相对简单等诸多优点。目前,Offner成像光谱仪已经广泛应用于卫星遥感、地质探测、精准农业、生产制造和军事侦察等领域。现有设计方法主要为数值光线追迹法和基于单光栅像差理论的解析设计方法。深入研究Offner成像光谱仪的成像特性及设计方法,具有重要的理论价值与现实意义。本文的研究重点是Offner成像光谱仪光学系统的建模与优化设计。建模的目标是建立起像点与物点、系统参数之间的解析函数关系;优化的目标是,求取合适的系统结构参数和元件参数,使得系统的性能满足应用要求。主要研究内容包括以下几个方面:(1)针对Offner成像光谱仪光学系统,基于费马原理,利用光线追迹法得到光学系统的数值模型,然后运用级数展开方法,推导出系统的3阶解析模型,亦即3阶像差理论。解析模型提供了像差系数关于结构参数、光栅参数和元件参数的解析函数关系。通过数值实验验证了解析模型的精度并分析了模型误差的来源。利用解析的像差系数分析了系统中彗差、球差和像散等主要像差的几何特征,丰富多元件光学系统的像差理论,加深对系统成像特性的理解,为Offner系统优化设计提供理论指导。(2)结合理想成像条件,利用像差理论建立起光学系统优化设计问题的单目标优化模型。引入具有全局搜索功能的遗传算法进行优化,设计结果表明,遗传算法能够较好的解决Offner光学系统的优化设计问题。从光谱分辨率、谱线弯曲、色畸变和调制传递函数截止频率等方面验证了设计结果的性能。(3)针对目标函数的计算复杂性,将复杂模型近似技术Kriging模型引入Offner光学系统的优化设计问题,提高优化设计效率。讨论了采样方法对Kriging模型精度的影响,及Kriging模型在非线性建模方面的性能。通过在设计空间中采集训练样本,建立起多个波长处像差系数和目标函数的Kriging模型。实验结果表明,在优化过程中,有机结合Kriging模型和精确解析模型,同时考虑多个波长处的系统性能,既可以提高优化设计的时间效率,又可以保证设计结果在全光谱范围内的最优性。(4)针对优化问题的多目标特点,研究适合工程应用的多目标优化算法及其在Offner光学系统优化设计中的应用。为了提高多目标优化算法的效率和优化结果的实用性,提出了结合决策者偏好的多加权和优化算法与多加权和鲁棒优化算法,可以有效地缩小搜索空间,使优化结果分布在决策者感兴趣的区域,提高了解的分辨率。数值试验和设计实例验证了算法的性能。这些研究工作不仅对Offner光学系统设计具有重要意义,也对将进化算法用于求解复杂工程优化问题具有重要的意义。更多还原

【Abstract】 Imaging spectrometers are the optical instruments, which can simultaneously acquire the spectral and spatial characteristics of an object, and combine them into one image cube. It solves the problem of "no spectral imaging" and "non-spectral imaging" in the traditional fields of optical science.Compared to the flat or concave grating-based imaging spectrometer, the Offner imaging spectrometer which utilizes a convex grating as the diffractive element takes the advantages of large numerical aperture, no Smile, small spectral Keystone, compact volume, relatively easy processing and assembly, and so on. Currently, Offner imaging spectrometers have been widely applied to the areas such as satellite remote sensing, geological exploration, precision agriculture, manufacturing, and military reconnaissance. The main design methods include the numerical ray-tracing and the analytical design based on the aberration theory of the signal grating. In both theoretical and practical aspects, it is a significant topic to study the imaging properties and optimal design of the Offner imaging spectrometer.This thesis mainly focuses on modeling and optimization of the optical system in Offner imaging spectrometer. The goal of modeling is to build the analytical function among image point, object point and system parameters; and the goal of optimization is to provide the appropriate system parameters to meet application requirements. The main research works in this thesis are as follows:(1) For the Offner optical system, the numerical model is derived using numerical ray-tracing method according to Fermat’s principle, and then a third order analytical model is obtained using series expansion method, which is also a third order aberration theory of the optical system. Analytical model provides aberration coefficients in analytical form, which are the analytical functions among structural parameters, grating parameters and element parameters. The accuracy of the analytical model is verified and the sources of model error are analyzed through numerical experiments. With the analytical aberration coefficients Coma, spherical aberration, and astigmatism and distortion are discussed in detail. This fills the gap in the aberration theory of multi-element optical system, makes a deeper understanding of the imaging properties of the system, and provides theoretical guidance for system optimization design. (2) Considering the ideal imaging condition, a single optimization model is constructed using the third order aberration theory. Genetic algorithm is applied to determine the system parameters. The results show that genetic algorithm is capable of solving the optimal design problem with high performance. The optimal design results are validated from the aspects of spectral resolution, Smile, spectral Keystone, the cut-off frequency of modulation transfer function, and so on.(3) Taking into account the computational complexity of the objective function, application of Kriging model which is an approximate technique for complex model speeds up the optimal design process of Offner optimal system. First, discusses the effect of different sampling methods on the accuracy of Kriging model, and then discusses the performance of Kriging model in non-linear modeling area. The Kriging models of aberration coefficients and merit functions at multiple design wavelengths are established through training data sampled from design space. Experimental results show that in the optimization process, the combination of Kriging model and the exact analytical model, taking into account the system performance at multiple wavelengths, can enhance the time efficiency of optimal design, but also ensure the optimality of design results in the whole spectral range.(4) Considering the multi-objective properties of the design problem, multi-objective optimization algorithms suitable for engineering application are developed and applied to the Offner optical system design problem. To enhance the efficiency of the algorithms and the practicality of optimal results, decision maker’preference based on multiple weighted sums is incorporated into multi-objective evolutionary algorithms and robust algorithms. These two novel methods can effectively reduce the search space, make the optimal results located only in the region of decision-maker’s interest, so that improve the resolution of the resulting solutions. Both numerical experiments and design examples demonstrate the algorithm performance.These studies are conducted for optimal design of Offner optical system, but they are also of great significance when applying evolutionary algorithm to solve other complex engineering optimization problems.更多还原