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基于小波和分形的KDP晶体形貌分析及对透光性能的研究

Wavelet and Fractal Analysis about Surface Topography of KDP Crystal and Its Effect on Transparent Performance

【作者】 庞启龙

【导师】 程凯; 陈明君;

【作者基本信息】 哈尔滨工业大学 , 机械制造及其自动化, 2009, 博士

【摘要】 KDP晶体元件是惯性约束核聚变(ICF)中的关键性部件,其光学性能的优良与否是制约惯性约束核聚变项目发展的关键性问题。惯性约束聚变中固体激光驱动器对KDP晶体光学零件表面形貌的基本要求是:高精度的面形质量(透射波前λ/6 PV)、高激光损伤阈值(15J/cm~2)、良好的表面粗糙度rms(≤5nm)。目前,表面形貌特征对KDP晶体光学性能的影响,还未有系统性的研究。全面的表征和分析KDP晶体元件的表面形貌特征,是研究表面形貌对光学性能影响的前提。研究各种表面形貌特征对其光学性能的影响,对优化KDP晶体的加工工艺、提高KDP晶体元件的光学性能,有重要的借鉴意义。基于以上原因,本文针对KDP晶体表面形貌特征的分析与表征及其与加工工艺和光学性能的关系展开研究。为能够比较全面的分析和表征KDP晶体的已加工表面形貌特征,本文选择分形方法、小波方法和功率谱密度方法对KDP晶体已加工表面形貌进行分析。分形方法区别于传统粗糙度表征方法的主要特征是不依赖于测量尺度,即表面的分形维数值不随测量尺度的变化而变化,而且能够充分利用测量数据,可以用于反映表面形貌的本质属性。功率谱密度方法可以全面的反映测量区间中的所有小尺度波纹特征对表面形貌的影响,并且与小波方法相结合可以提取和分析表面形貌中任意小尺度波纹特征的三维空间分布状态。文中使用傅立叶模方法分析了表面小尺度波纹特征对近场光电场强度的影响规律;通过计算表面形貌对入射光束的偏移量,理论分析了表面分形维数与晶体元件二倍频效率和近场光场强度的关系。为充分分析表面形貌特征,文中使用二维小波方法实现对KDP晶体三维已加工表面形貌的多尺度分解;使用一维及二维功率谱密度方法,分析KDP晶体已加工表面上的频率状态分布;使用功率谱密度方法与二维小波变换相结合提取出表面上特定空间频率特别是小尺度波纹的三维表面形貌,并且通过对功率谱密度的计算,可以得到特定空间频率的三维形貌对原始表面形貌的影响程度,从而能够分析影响表面形貌或光学性能的各种频率因素。同时使用分形方法分析了KDP晶体表面形貌的分形维数特征和各向异性特征;分形维数特征的分析包括分形维数值的计算及其与表面粗糙度的关系,表面各向异性特征通过计算表面形貌各个方向轮廓的一维分形维数分布状态来进行分析。通过对KDP晶体进行切削实验,得到与不同加工参数相关的已加工表面形貌。对切削试验所得到的表面进行分形、小波和功率谱密度分析,可以得到进给量、主轴转速和背吃刀量等加工工艺参数对表面分形特征及频率特征的影响规律。各种不同工艺参数对表面形貌的影响为:进给量对已加工表面形貌的分形维数和频率特征影响的规律性最为明显;背吃刀量只对表面分形维数特征影响的规律比较明显,而对表面频率特征无明显的影响;主轴转速则对表面形貌分形维数和频率特征的影响均不明显。最后,对具有不同形貌特征的KDP晶体元件进行激光透过率的光学实验,并通过结合表面分析方法可以分别得到不同表面形貌的分形特征和频率特征对KDP元件光学性能的影响规律,其结果基本与理论分析结果相一致。通过光学试验表明,表面形貌的分形特征和频率特征对KDP晶体元件的透光性能均有比较明显的影响,其中频率特征对透光性能的影响要大于分形特征对透光性能的影响。在分析不同形貌特征对透光性能影响的基础上,结合切削工艺的不同加工参数对表面形貌分形特征和频率特征的影响规律,提出了可以得到具有较好光学性能表面形貌的KDP晶体加工工艺参数的优化方案。

【Abstract】 In the Inertial Confinement Fusion (ICF) project, KDP crystal component is very important and the optical performance of it directly impacts on the development of ICF. The basic requirements to the KDP crystal optics of ICF solid laser driver are: high accuracy face shape quality (Transmission wave frontλ/6 PV), high laser damage threshold value (15J/cm~2), good surface roughness (≤5nm). But the relation between the surface topography and oprical performace has never been studied completely. Therefore completely evaluating the surface topography of KDP and analyzing the influence on the optical performance are very important to optimize the machining process of KDP and enhance the optical performance of it. Based on these reasons, the relations of surface topography with machining process and optical performance are studied in this thesis.After completely analyzing the different analytic methods of surface topography, the wavelet, fractal and power spectral density (PSD) are selected to analyze the surface topography of machined KDP crystal. The ability to characterize surface roughness using scale-independent parameters is a specific feature of fractal approach; because fractal dimension is never changed for a certain surface and can completely use the measurement data, fractal dimension is a substance property of surface topography. The PSD method could sufficiently use the measured data and completely reflect the influence of frequency information on the surface topography. The composition of wavelet and PSD could extract the information of any micro-scale waveness from the machined surfaces.Through the Fourier model method, the relation between the surface frenquency and intensity of optical field is analyzed. And through calculation of influence of surface topography on optical deviation, the regularity between fractal dimension and efficiency of secondary harmonic is obtained. The 2D wavelet method is used to realize multi-scale decomposition of original machined KDP surface in the thesis. 1D and 2D PSD methods are adopted to reflect the frequency information of machined KDP surface. Com PSD and 2D continuous wavelet transform (CWT2D) will be used together to achieve the extraction of the spacial frequency. And the PSD method could calculate the impact degree of the particular spacial frequency on the surface morphology. Then find out the frequency information what is the main factor impacting the quality of the surface and optical performance. Fractal method is used to analyze fractal and anisotropic features. Fractal features include the calculation of fractal dimension and the relation between fractal dimension and surface roughness. The anisotropic features can be analyzed through the circle profile fractal dimension distribution method.The influence of feed rate, cutting depth and spindle speed on the fractal features and frequency features of surface topography could be analyzed in the different topography obtained by the cutting experiments. Through analysis of machined surfaces by wavelet, fractal and PSD methods, the feed rate has the obvious influence on the fractal dimension and frequency feature of machined surfaces. The cutting depth has only the obvious influence on the fractal dimension but no influence on the frequency feature. The spindle speed has no obvious influence on the fractal dimension and frequency feature.At last the influence of different surface topography on the optical performance can be obtained by optical experiments. Combining the surface analysis method, the influence of fractal and frequency features on the optical performance can be obtained, and both of them have the obvious influence on the optical performance. The results are nearly accordant with the theoretical analysis. Through the optical experiments, fractal and frequency features can impact optical performance of KDP crystal, and frequency features have larger effect than fractal features. And though the analysis results of influence of different cutting parameters on the fractal and frequency features, optimized plan of machining process parameters that could be obtained to improve surface topography and enhance optical performance of KDP crystal component.

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