基于小波和分形的KDP晶体形貌分析及对透光性能的研究
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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。
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.
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。
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.
引文
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66 P. Podsiadlo, G.W. Stachowiak. Fractal-wavelet based classification of tribological surfaces, Wear 254 (2003) 1189～198
67 G.W. Stachowiak, P. Podsiadlo. Classification of tribological surfaces. Tribology International 37 (2004): 211～217
68高玲玲,范勇,陈念年等.光学元件表面疵病快速检测分类方法研究.微计算机信息. 2008,24(9):306~307
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74 Lahaye Philippe, Chomont Christian, Dumont Pierre. Using a Design of Experiment Method to Improve KDP Crystal Machining Process. Proceedings of SPIE-the International Society for Optical Engineering. 1998, 34 92:814～820
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82高志山.光学表面轮廓功率谱密度对象质的影响及干涉测试研究.南京理工大学博士学位论文. 1999: 8~10
83沈正祥,王占山,马彬等.利用功率谱密度函数表征光学薄膜基底表面粗糙度.光学仪器. 2006,8(4): 141~145
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86刘世杰,麻健勇,沈自等.多层介质膜脉冲宽度压缩光栅与超短脉冲作用时的性能分析.物理学报. 2007, 56(8): 4542~4549
87唐雄贵,郭永康,杜惊雷.利用傅里叶模方法分析厚层光刻胶内衍射光场.光学学报. 2005, 25(2): 246~250
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65 Stachowiak GW, Podsiadlo P. Characterization and classification. of wear particles and surfaces. Wear 2001,243:194～200
66 P. Podsiadlo, G.W. Stachowiak. Fractal-wavelet based classification of tribological surfaces, Wear 254 (2003) 1189～198
67 G.W. Stachowiak, P. Podsiadlo. Classification of tribological surfaces. Tribology International 37 (2004): 211～217
68高玲玲,范勇,陈念年等.光学元件表面疵病快速检测分类方法研究.微计算机信息. 2008,24(9):306~307
69果宝智.光学零件表面疵病的标识.激光与红外. 2000,30(2): 123～127
70刘旭,杨甬英,刘东等.光学元件表面疵病检测扫描拼接的误差分析.光电子·激光. 2008,19(8): 1088~1093
71王雪,谢志江,孙红岩等.大口径精密光学元件表面疵病检测系统研究.仪器仪表学报. 2006,27(10):1262~1265
72刁立臣,张克从,常新安. KDP晶体激光损伤阈值研究的新进展.人工晶体学报. 2002,31(2): 99~103
73 Fuchs Baruch A, Hed P Paul, Baker Phillip C. Fine Diamond Turning of KDP Crystals. Applied Optics. 1986, 25:1733～1735
74 Lahaye Philippe, Chomont Christian, Dumont Pierre. Using a Design of Experiment Method to Improve KDP Crystal Machining Process. Proceedings of SPIE-the International Society for Optical Engineering. 1998, 34 92:814～820
75 Namba Yoshiharu, Katagiri Masanori, Nakatsuka Masahiro. Single point diamond turning of KDP inorganic optical crystals for laser fusion. Journal of the Japan Society Precision Engineering. 1998, 64(10):1487~1491
76赵光宙,舒勤.信号分析与处理.机械工业出版社,2001
77刘贵忠,邸双亮.小波分析及应用.西安电子科技大学出版社,1995
78李水根,吴纪桃.分形与小波.科学出版社, 2002
79 Jiang X, et al. Wavelets and their applications for surface metrology. CIRP Annals–Manufacturing Technology. 2008,57(1): 555~558
80 Xiangqian Jiang, Wenhan Zeng, Paul Scott et al. Linear feature extraction basedon complex ridgelet transform. Wear. 2008, 264:428~433
81 R. A. Jones. Computer simulation of smoothing during computer-controlled optial polishing. Appl Opt, 1995, 34:1162~1169
82高志山.光学表面轮廓功率谱密度对象质的影响及干涉测试研究.南京理工大学博士学位论文. 1999: 8~10
83沈正祥,王占山,马彬等.利用功率谱密度函数表征光学薄膜基底表面粗糙度.光学仪器. 2006,8(4): 141~145
84 Janeczko D J. Power spectrum standard for surface roughness: part I. SPIE,1989,1165:175～18
85姚欣,高福华,李剑峰等.光束取样光栅强激光近场调制及诱导损伤研究.物理学报. 2008, 57(8): 4891~4897
86刘世杰,麻健勇,沈自等.多层介质膜脉冲宽度压缩光栅与超短脉冲作用时的性能分析.物理学报. 2007, 56(8): 4542~4549
87唐雄贵,郭永康,杜惊雷.利用傅里叶模方法分析厚层光刻胶内衍射光场.光学学报. 2005, 25(2): 246~250
88刘洋.三角形面形亚波长光栅的衍射特性研究.四川大学硕士学位论文,2004
89 Anisimov S I, Kapeliovich B L, Perelman T L. Electron emission from metal surfaces exposed 10 ultra-short laser pulses. Soviet Physics Joumal of Experimental and Theoretical Physics Letters. 1974,39(2) :375~377
90费斌,王海容,蒋庄德.机械加工表面分形特性的研究.西安交通大学学报. 1998, 32(5): 83~86
91 B.B. Mandelbrot. The fractal geometry of nature. New York: Freeman, 1982
92张济忠.分形.清华大学出版社,1995
93谢和平,薛秀谦.分形应用中的数学基础与方法.北京,科学出版社,1997
94幸厚文.分形理论及其应用.中国科学技术大学出版社,1993
95 J. Schmahlinga, F.A. Hamprechtb, D.M.P. Hoffmann. A three-dimensional measure of surface roughness based on mathematical morphology. International Journal of Machine Tools & Manufacture. 2006, 46: 1764~1769
96 Chenggui Li, Shen Dong, Guoxiong Zhang. Evaluation of the Root-mean-square Slope of 3D Surface Topography. International Journal of Machine Tools & Manufacture. 2000, 40: 445~454
97 Zhuangde Jiang, Hairong Wang, Bin Fei. Research into the Application of Fractal Geometry in Characterising Machined Surfaces. International Journal ofMachine Tools & Manufacture. 2001, 41: 2179～2185
98肯尼斯?法尔科内.分形几何-数学基础及其应用.曾文曲译.沈阳:东北大学出版社. 1991: 191～206
99 A. Majumdar, B. Bhushan. Role of fractal geometry in roughness characterization and contact mechanics of surface. ASME Jounal of Tribology. 1990,172: 205～216
100 J Chadwick. Calculation of the fractal dimension of grain boundaries in nanocrystalline Pd. J. Phys: Condens Matter, 11 (1999) 129～133
101 V.I. Trefilov, V.V. Kartuzov, N.V. Minakov. Fractal dimension of fracture surfaces. Metal Science and Heat Treatment, 2001(43): 95～98
102 J.M. Li, L. Lu, Y. Su et al. Self-affine nature of thin film surface. Applied Surface Science, 2000, 161:187～193
103 J.R. Carr. Statistical self-affine, fractal dimension, and geologic interpretation. Engineering Geology. 1997,48: 269～282
104 J. C. Russ. Fractal Dimension Measurement of Engineering surfaces, Int. J. Mach. Tools Manufact, 38(1998): 567～571
105 D. Blackmore, G. Zhou. A New Fractal Model for Anisotropic Surfaces, Int. J. Mach. Tools Manufact, 38(1998): 551～557
106 A. Othmani, C. Kaminsky. Three Dimension Fractal Analysis of Sheet Metal Surface, Wear, 214(1998): 147～150
107李成贵.三维表面微观形貌的表征及微纳米表面和表层的完整性评价探讨.哈尔滨:哈尔滨工业大学, 1999: 13～22
108石顺祥,陈国夫,赵卫等.非线性光学.西安电子科技大学出版社. 2003
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