基于粒子成像的水下流速场探测方法的研究
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摘要
水下成像目前已成为水下探测的一种常用手段。湍流作为一种重要的流动现象成为影响激光水下成像的重要因素。因此需要了解湍流场,掌握其流动特性才能进行相应的后续工作。为实现该目的,本论文通过粒子成像技术完成了对水下湍流流速场的测量。
粒子成像测量技术的工作原理是用激光薄片照亮流场中一个与流场流速平行的平面,在与激光面垂直方向上拍摄两个时刻流场中流动粒子的图像,对粒子图像进行处理就可以得到流场中的速度场分布。根据其工作原理,本论文从示踪粒子的选择、待测流场的建立、实验系统的选型和搭建及粒子图像处理四个部分进行了论述。
流场中加入的示踪粒子是正确反映流场流速的重要因素。本论文讨论了示踪粒子的跟随性和光散射特性。微小气泡作为无污染的微粒在本实验中做为示踪粒子添加到水体中,通过探测气泡的运动从而反映水体的流动。通过对两相流的模拟,计算了不同流速下不同直径的气泡的跟随性。
本论文提出了符合湍流条件的新的气泡模型-椭球模型并采用该模型对气泡的光散射进行了研究。在平面波入射的情况下,采用几何光学近似的方法计算了大尺寸气泡的光散射特性。其计算结果符合Mie散射理论的结果。同时分析了激光入射时,高斯光束照射下球形气泡的光散射分布。采用类似的方法计算得到的散射分布与扩展米散射理论进行了比较,通过各阶散射光强的分布与Debye序列的比较分析了产生差异的原因。
本论文建立了实验用待测湍流场。采用可实现κ-ε模型对两种结构简单的湍流场圆柱绕流模型和管道流动模型进行了二维模拟分析。选用了管道流动做为实验室流场模型。根据产生湍流场的条件,设计待测湍流场,并根据设计要求对各组件选件并组成了实验用待测流场。
本论文搭建整个粒子成像测量系统。根据流场的流速设计及相关要求,对激光器、扩束光路、成像光路及图像记录元件进行选件。搭建光路,选取双帧单曝光的方式记录流场粒子图像。
本论文对粒子图像对采用相关运算并得到了视场范围内的流场速度矢量分布图。考虑CCD的背景噪声,对粒子图像做了降噪及增强处理。选用合适的问询区,对两幅图像对应的区域做互相关运算,得到该区域的流速矢量。依次探询并得到整个图像的流速矢量分布。
Image underwater is a useful technique in the detection underwater. The turbulence as an important flow phenomena becomes an important factor for the laser imaging underwater. It is necessary to find out the properties of the turbulent flow. Aimed at this purpose, the thesis implemented measurement of the turbulent velocity field underwater using particle image velocimetry(PIV).
The principle of PIV is described as followed:A laser sheet illuminates a plane of the flow field, and the images of the fields are recorded in the perpendicular direction at two different times. Then velocity distribution of the flow field has been achieved using image processing. Based on the working principle, the thesis includes four parts:the selection of the tracer particles, the construction of the measured flow field, the establishment of the whole PIV system and the image processing of particle images.
The tracer particles seeding in the flow fields is an important factor to accurately measure the fluid velocity. The optical scattering and following properties of seeding particles are discussed. The small bubbles as non-polluting particles are seeded into the water in these experiments. The velocity of the flow field can be achieved with the measurement of the bubbles motion. Through the simulation of two phase flow, the following properties of the bubbles with different diameters are calculated in different flow velocities.
The thesis proposes a new spheroidal model to simulate the bubble's shape in the turbulent flow to research the optical properties of a bubble. With the plane wave incidence, the scattering distribution of the bubble is calculated by the geometrical optics approximation (GOA). The algorithm is verified using the Mie results for a spherical bubble, and the scattering patterns of the two methods agree well. The scattering properties of the spherical bubble with the Gaussian incidence are also calculated. The results of GOA and GLMT(Generalized Lorenz-Mie Theory) are compared, the scattering intensity distribution of different p orders rays are analyzed with Debye series in order to explain the differences between the two results.
The measured turbulence flow is constructed in this thesis. Using the RKE(realized κ-ε) model, two flow fields, including the flow around cylinder and the pipe flow, are simulated. The latter one is selected in the experiment. Based on the conditions of produceing turbulence, the equipments of the measured flow are designed and chosen, and the measured flow field in experiment is achieved.
The whole PIV system is established in this thesis. Based on the demands of velocity of flow and other corresponding conditions, the instruments of the laser, laser sheet optics, imaging optical path and image recordings are selected and assembled. The experiments are fulfilled and the images are achieved using the single frame-double exposed recording.
The pairs of particle images are calculated using the correlation algorithm to obtain the velocity vectorgraph of flow in the field of view. Considering the background noise of CCD, the particles images are reduced noise and enhanced. With the suitable interrogation windows, the images are processing using the cross-correlation in the corresponding grids to calculating the velocity of flow in this region. Then we yield the whole by analyze the image pairs point-by-point.
粒子成像测量技术的工作原理是用激光薄片照亮流场中一个与流场流速平行的平面,在与激光面垂直方向上拍摄两个时刻流场中流动粒子的图像,对粒子图像进行处理就可以得到流场中的速度场分布。根据其工作原理,本论文从示踪粒子的选择、待测流场的建立、实验系统的选型和搭建及粒子图像处理四个部分进行了论述。
流场中加入的示踪粒子是正确反映流场流速的重要因素。本论文讨论了示踪粒子的跟随性和光散射特性。微小气泡作为无污染的微粒在本实验中做为示踪粒子添加到水体中,通过探测气泡的运动从而反映水体的流动。通过对两相流的模拟,计算了不同流速下不同直径的气泡的跟随性。
本论文提出了符合湍流条件的新的气泡模型-椭球模型并采用该模型对气泡的光散射进行了研究。在平面波入射的情况下,采用几何光学近似的方法计算了大尺寸气泡的光散射特性。其计算结果符合Mie散射理论的结果。同时分析了激光入射时,高斯光束照射下球形气泡的光散射分布。采用类似的方法计算得到的散射分布与扩展米散射理论进行了比较,通过各阶散射光强的分布与Debye序列的比较分析了产生差异的原因。
本论文建立了实验用待测湍流场。采用可实现κ-ε模型对两种结构简单的湍流场圆柱绕流模型和管道流动模型进行了二维模拟分析。选用了管道流动做为实验室流场模型。根据产生湍流场的条件,设计待测湍流场,并根据设计要求对各组件选件并组成了实验用待测流场。
本论文搭建整个粒子成像测量系统。根据流场的流速设计及相关要求,对激光器、扩束光路、成像光路及图像记录元件进行选件。搭建光路,选取双帧单曝光的方式记录流场粒子图像。
本论文对粒子图像对采用相关运算并得到了视场范围内的流场速度矢量分布图。考虑CCD的背景噪声,对粒子图像做了降噪及增强处理。选用合适的问询区,对两幅图像对应的区域做互相关运算,得到该区域的流速矢量。依次探询并得到整个图像的流速矢量分布。
Image underwater is a useful technique in the detection underwater. The turbulence as an important flow phenomena becomes an important factor for the laser imaging underwater. It is necessary to find out the properties of the turbulent flow. Aimed at this purpose, the thesis implemented measurement of the turbulent velocity field underwater using particle image velocimetry(PIV).
The principle of PIV is described as followed:A laser sheet illuminates a plane of the flow field, and the images of the fields are recorded in the perpendicular direction at two different times. Then velocity distribution of the flow field has been achieved using image processing. Based on the working principle, the thesis includes four parts:the selection of the tracer particles, the construction of the measured flow field, the establishment of the whole PIV system and the image processing of particle images.
The tracer particles seeding in the flow fields is an important factor to accurately measure the fluid velocity. The optical scattering and following properties of seeding particles are discussed. The small bubbles as non-polluting particles are seeded into the water in these experiments. The velocity of the flow field can be achieved with the measurement of the bubbles motion. Through the simulation of two phase flow, the following properties of the bubbles with different diameters are calculated in different flow velocities.
The thesis proposes a new spheroidal model to simulate the bubble's shape in the turbulent flow to research the optical properties of a bubble. With the plane wave incidence, the scattering distribution of the bubble is calculated by the geometrical optics approximation (GOA). The algorithm is verified using the Mie results for a spherical bubble, and the scattering patterns of the two methods agree well. The scattering properties of the spherical bubble with the Gaussian incidence are also calculated. The results of GOA and GLMT(Generalized Lorenz-Mie Theory) are compared, the scattering intensity distribution of different p orders rays are analyzed with Debye series in order to explain the differences between the two results.
The measured turbulence flow is constructed in this thesis. Using the RKE(realized κ-ε) model, two flow fields, including the flow around cylinder and the pipe flow, are simulated. The latter one is selected in the experiment. Based on the conditions of produceing turbulence, the equipments of the measured flow are designed and chosen, and the measured flow field in experiment is achieved.
The whole PIV system is established in this thesis. Based on the demands of velocity of flow and other corresponding conditions, the instruments of the laser, laser sheet optics, imaging optical path and image recordings are selected and assembled. The experiments are fulfilled and the images are achieved using the single frame-double exposed recording.
The pairs of particle images are calculated using the correlation algorithm to obtain the velocity vectorgraph of flow in the field of view. Considering the background noise of CCD, the particles images are reduced noise and enhanced. With the suitable interrogation windows, the images are processing using the cross-correlation in the corresponding grids to calculating the velocity of flow in this region. Then we yield the whole by analyze the image pairs point-by-point.
引文
[1]D. M. Farmer, J. R. Gemmrich. Measurements of temperature fluctuations in breaking surface waves. Journal of physical oceanography,1996,26 (5):816-825
[2]徐世昌,张亮.潜艇尾流的空间演化及与自由面的相互作用.哈尔滨工程大学学报,2007,27(6)：802-805
[3]罗浩,李杨,都思丹等.数字式大气湍流探测仪及其数据可靠性研究.交通与计算机,2004,22(4)：44-47
[4]张慧敏,李新阳.热风式大气湍流模拟装置的哈特曼测量.光电工程,2004,31(S1)：4-7
[5]苏毅勇,白洁,王洪芳.利用多普勒技术识别探测大气湍流研究进展.第26届中国气象学会年会第三届气象综合探测技术研讨会分会场.中国浙江杭州,2009.156-161
[6]G. Billet, V. Giovangigli, G. de Gassowski. Impact of volume viscosity on a shock-Hydrogen-bubble interaction. Combustion Theory and Modelling,2008,12 (2): 221-248
[7]戴阳,林兆祥,张文艳等.激光雷达大气湍流测量方法研究.强激光与粒子束,2006,18(11)：1769-1773
[8]张守川,吴毅,侯再红等.激光雷达测量大气湍流廓线.强激光与粒子束,2009,21(12)：1795-1798
[9]陈栋,李红刚,倪志波等.海洋大气湍流对激光通信系统性能的影响分析.大气与环境光学学报,2009,4(3)：178-182
[10]胡月宏,强希文,冯建伟等.基于气象参数戈壁沙漠地区近地面大气湍流建模.强激光与粒子束,2010,22(12)：2799-2802
[11]杨迪.大气湍流闪烁效应对激光通信系统影响及补偿技术研究：[硕士学位论文].长春：长春理工大学,2009
[12]朱文越,马晓珊,饶瑞中.大气光学湍流对光电探测器性能的影响.红外与激光工程,2006,35(3)：354-358
[13]张晓芳,俞信,阎吉祥.大气湍流对光学系统图像分辨力的影响.光学技术,2005,31(2)：263-265
[14]孙昭晨,梁书秀,沈永明等.三维海洋紊流模型对杭州湾附近潮流场数值模拟.大连理工大学学报,2000,40(5)：609-612
[15]魏皓,武建平,张平.海洋湍流模式应用研究.青岛海洋大学学报(自然科学版),2001,31(1)：7-13
[16]邱辽原.潜艇粘性流场的数值模拟及其阻力预报的方法研究：[博士学位论文].武汉：华中科技大学,2006
[17]C. Foias, D. D. Holm, E. S. Titi. The Navier-Stokes-alpha model of fluid turbulence. Physica D:Nonlinear Phenomena,2001,152-153:505-519
[18]D. J. Webb. An ocean model code for array processor computers. Computers & Geosciences,1996,22 (5):569-578
[19]G. N. Ivey, K. B. Winters, J. R. Koseff. Density Stratification, Turbulence, but How Much Mixing? Annual Review of Fluid Mechanics,2008,40 (1):169-184
[20]A. H. H. Renner, K. J. Heywood, S. E. Thorpe. Validation of three global ocean models in the Weddell Sea. Ocean Modelling,2009,30 (1):1-15
[21]M. P. Strand. Imaging model for underwater range-gated imaging systems. Proc.SPIE 1537,1991.151-160
[22]J. S. Jaffe. Monte Carlo modeling of underwater-image formation:validity of the linear and small-angle approximations. Applied Optics,1995,34 (24):5413-5421
[23]G. L. Mellor, T. Yamada. A hierarchy of turbulence closure models for planetary boundary layers. Journal of the Atmospheric Sciences,1974,31 (7):1791-1806
[24]A. Rosati, K. Miyakoda. A general circulation model for upper ocean simulation. J Phys Oceanogr,1988,18 (11):1601-1626
[25]B. E. Launder, D. B. Spalding. Lectures in mathematical models of turbulence. London, England:Academic Press,1972
[26]G. L. Mellor, T. Yamada. Development of a turbulence closure model for geophysical fluid problems. Reviews of geophysics and space physics,1982,20 (4):851-875
[27]H. Burchard. Applied Turbulence Modelling in Marine Waters. New York:Springer-Verlag Berlin Heidelberg,2002.1-5
[28]H. Burchard, O. Petersen. Models of turbulence in the marine environment --a comparative study of two-equation turbulence models. Journal of Marine Systems, 1999,21 (1-4):29-53
[29]H. Burchard, K. Bolding, M. R. Villarreal, et al. GOTM, a general ocean turbulence model:Theory, implementation and test cases. Tech. Rep. EUR 18745 EN. European Commission:Space Applications Institute,1999.103-106
[30]R. J. Adrian. Twenty years of particle image velocimetry. Experiments in Fluids,2005, 39(2):159-169
[31]M. R. Dhanak, K. Holappa. An Autonomous Ocean Turbulence Measurement Platform. Journal of Atmospheric and Oceanic Technology,1999,16 (11):1506-1518
[32]S. A. Thorpe, T. R. Osborn, J. F. E. Jackson, et al. Measurements of Turbulence in the Upper-Ocean Mixing Layer Using Autosub. Journal of Physical Oceanography,2003, 33 (1):122-145
[33]朱红钧,林元华,谢龙汉.FLUENT流体分析及仿真实用教程.北京：人民邮电出版社,2010.1-131
[34]B. Ruth. Superposition of Two Dynamic Speckle Patterns. Journal of Modern Optics, 1987,34(2):257-273
[35]R. Theunissen, M. Riethmuller. Particle image velocimetry in lung bifurcation models- Particle Image Velocimetry. Springer Berlin/Heidelberg,2008,112:73-101
[36]S. Groβe, W. Schroder, M. Klaas. Time-resolved PIV measurements of vortical structures in the upper human airways-Particle Image Velocimetry:New Developments and Recent Applications (Topics in Applied Physics Volume 112). Springer Berlin/Heidelberg,2008.35-53
[37]L. Araneo, A. Coghe, F. Cozzi, et al. Natural Gas Burners for Domestic and Industrial Appliances-Particle Image Velocimetry. Springer Berlin/Heidelberg, 2008.245-257
[38]N. G. Deen, J. Westerweel, E. Delnoij. Two-phase PIV in bubbly flows:Status and trends. Chemical Engineering & Technology,2002,25 (1):97-101
[39]钱广强,董治宝,王洪涛等.粒子图像测速(PIV)技术在风沙环境风洞中的应用.中国沙漠,2006,26(6)：890-893
[40]F. Scarano. Overview of PIV in supersonic flows-Particle Image Velocimetry. Springer Berlin/Heidelberg,2008.445-463
[41]F. Felice, F. Pereira. Developments and Applications of PIV in Naval Hydrodynamics-Particle Image Velocimetry. Springer Berlin/Heidelberg,2008.475-503
[42]徐斌.湍流的现代实验研究方法.沿海企业与科技,2009,9(9)：13-15
[43]M. T. Milbocker. Laser Doppler velocimetry stabilized in one dimension. Biomedical Engineering, IEEE Transactions on,1991,38 (9):928-930
[44]S. So, H. Morikita, S. Takagi, et al. Laser Doppler velocimetry measurement of turbulent bubbly channel flow. Experiments in Fluids,2002,33(1):135-142
[45]A. L. Tassin, D. E. Nikitopoulos. Non-intrusive measurements of bubble size and velocity. Experiments in Fluids,1995,19 (2):121-132
[46]X. Liu, W. H. Doub, C. Guo. Evaluation of droplet velocity and size from nasal spray devices using phase Doppler anemometry (PDA). International journal of pharmaceutics,2010,388 (1-2):82-87
[47]A. B. Parthasarathy, E. L. Weber, L. M. Richards, et al. Cerebral Blood Flow Imaging during Neurosurgery with Laser Speckle Contrast Imaging. Biomedical Optics: Optical Society of America,2010. JMA991-3
[48]D. Tarlet, C. Bendicks, C. Roloff, et al. Gas Flow Measurements by 3D Particle Tracking Velocimetry Using Coloured Tracer Particles. Flow, Turbulence and Combustion,2010,88 (3):343-365
[49]D. Broder, M. Sommerfeld. A PIV/PTV system for analysing turbulent bubbly flows. Proceedings of the 10th International Symposium Application of Laser Techniques to Fluid Mechanics Lisbon,2000.10.1-10.11
[50]M. Kreizer, D. Ratner, A. Liberzon. Real-time image processing for particle tracking velocimetry. Experiments in Fluids,2010,48 (1):105-110
[51]N. Damaschke, H. Nobach, T. I. Nonn, et al. Size and velocity measurements with the global phase Doppler technique. In:11th international symposium on application of laser techniques to fluid mechanics, Lisbon,2002.1-11
[52]S. Kruger, G. Grunefeld. Stereoscopic flow-tagging velocimetry. Applied Physics B: Lasers and Optics,1999,69 (5):509-512
[53]C. Elkins, M. Alley. Magnetic resonance velocimetry:applications of magnetic resonance imaging in the measurement of fluid motion. Experiments in Fluids,2007, 43 (6):823-858
[54]R. J. Adrian. Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow:speckle velocimetry vs particle image velocimetry. Appl Opt,1984,23 (11):1690-1691
[55]C. J. D. Pickering, N. A. Halliwell. Laser speckle photography and particle image velocimetry:photographic film noise. Appl Opt,1984,23 (17):2961-2969
[56]R. D. Keane, R. J. Adrian. Optimization of particle image velcimeters:1.double pulsed systems. Measurement Science & Technology,1990,1 (11):1202-1215
[57]N. Farrugia, S. Kanne, D. A. Greenhalgh. Three-pulse digital particle image velocimetry. Opt Lett,1995,20 (17):1827-1829
[58]R. D. Keane, R. J. Adrian. Optimization of particle image velcimeters:2.multiple pulsed systems. Measurement Science & Technology,1991,2 (10):963-974
[59]M. Sutton, W. Wolters, W. Peters, et al. Determination of displacements using an improved digital correlation method. Image and Vision Computing,1983,1 (3): 133-139
[60]R. D. Keane, R. J. Adrian. Theory of cross-correlation analysis of PIV images. Applied Scientific Research,1992,49 (3):191-215
[61]C. Willert, M. Gharib. Digital particle image velocimetry. Experiments in Fluids,1991, 10(4):181-193
[62]J. Westerweel. Analysis of PIV interrogation with low-pixel resolution. In:Soyoung SC, James DT, editors:SPIE,1993.624-635
[63]R. J. Adrian. Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry. Applied Optics,1986,25 (21):3855-3858
[64]C. Meinhart, S. Wereley, J. Santiago. PIV measurements of a microchannel flow. Experiments in Fluids,1999,27 (5):414-419
[65]R. Lima, S. Wada, S. Tanaka, et al. In vitro blood flow in a rectangular PDMS microchannel:experimental observations using a confocal micro-PIV system. Biomedical Microdevices,2008,10 (2):153-167
[66]M. R. Bown, J. M. Maclnnes, R. W. K. Allen, et al.. Three-dimensional, three-component velocity measurements using stereoscopic micro-PIV and PTV. Measurement Science and Technology,2006,17 (8):2175-2185
[67]S. Coudert, J. Foucaut, J. Kostas, et al. Double large field stereoscopic PIV in a high Reynolds number turbulent boundary layer. Experiments in Fluids,2011,50 (1):1-12
[68]R. C. Chen, L. S. Fan. Particle image velocimetry for characterizing the flow structure in three-dimensional gas-liquid-solid fluidized beds. Chem Eng Sci,1992,47 (13-14):3615-3622
[69]L. Gui, R. Lindken, W. Merzkirch. Phase-separated PIV measurements of the flow around systems of bubbles rising in water. FEDSM'97:ASME Fluids Engineering Division Summer Meeting(June),1997.1-6
[70]A. Tokuhiro, M. Maekawa, K. Iizuka, et al. Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques. Int J Multiph Flow,1998,24 (8): 1383-1406
[71]R. Lindken, W. Merzkirch. Velocity measurements of liquid and gaseous phase for a system of bubbles rising in water. Experiments in Fluids,2000,29 (Suppl):S194-S201
[72]R. Lindken, W. Merzkirch. A novel PIV technique for measurements in multiphase flows and its application to two-phase bubbly flows. Experiments in Fluids,2002,33 (6):814-825
[73]E. Delnoij, J. A. M. Kuipers, W. P. M. van Swaaij, et al. Measurement of gas-liquid two-phase flow in bubble columns using ensemble correlation PIV. Chem Eng Sci, 2000,55 (17):3385-3395
[74]A. Fujiwara, Y. Danmoto, K. Hishida, et al. Bubble deformation and flow structure measured by double shadow images and PIV/LIF. Experiments in Fluids,2004,36 (1):157-165
[75]D. Broder, M. Sommerfeld. Combined PIV/PTV-measurements for the analysis of bubble interactions and coalescence in a turbulent flow. Can J Chem Eng,2003,81 (3-4):756-763
[76]M. J. Sathe, I. H. Thaker, T. E. Strand, et al. Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows. Chem Eng Sci,2010,65 (8):2431-2442
[77]M. Raffel, C. E. Willert, J. Kompenhans. Particle image velocimetry:a practical guide. Springer-Verlag Berlin Heidelberg,1998.1-11
[78]C. F. Boliren, D. R. Huffman. Absorption and scattering of light by small particles. J New York:Wiley & Sons,1983.165-183
[79]C. Matzle. MATLAB Functions for Mie Scattering and Absorption. Report Number 2002-8:Institute of Applied Physics, University of Bern,2002.1-20
[80]G. E. Davis. Scattering of Light by an Air Bubble in Water. J Opt Soc Am,1955,45 (7):572-581
[81]H. C. van de Hulst. Light scattering by small particles. New York:John Wiley & Sons, 1957.203-209
[82]P. L. Marston. Critical angle scattering by a bubble:physical-optics approximation and observations. J Opt Soc Am,1979,69 (9):1205-1211
[83]P. L. Marston, D. L. Kingsbury. Scattering by a bubble in water near the critical angle: interference effects. J Opt Soc Am,1981,71 (2):192-196
[84]L. Wu, H. Yang, X. Li, et al. Scattering by large bubbles:Comparisons between geometrical-optics theory and Debye series. Journal of Quantitative Spectroscopy and Radiative Transfer,2007,108 (1):54-64
[85]H. Yu, J. Shen, Y. Wei. Geometrical optics approximation of light scattering by large air bubbles. Particuology,2008,6 (5):340-346
[86]K. Arai. Phase function of relatively large aerosol particles containing bubbles by means of a ray tracing. Advances in Space Research,2002,29 (11):1813-1818
[87]W. Li. Computation of the scattering intensity distribution for natural light scattered by an air bubble in water. Journal of Optics A:Pure and Applied Optics,2006,8 (1): 93-99
[88]J. Shen, H. Wang, B. Wang, et al. Stability in Debye series calculation for light scattering by absorbing particles and bubbles. Journal of Quantitative Spectroscopy and Radiative Transfer,2010,111 (5):772-781
[89]S. Asano, G. Yamamoto. Light Scattering by a Spheroidal Particle. Appl Opt,1975,14 (1):29-49
[90]S. Asano. Light scattering properties of spheroidal particles. Appl Opt,1979,18 (5):712-723
[91]S. Asano, M. Sato. Light scattering by randomly oriented spheroidal particles. Appl Opt,1980,19(6):962-974
[92]P. C. Waterman. Symmetry, Unitarity, and Geometry in Electromagnetic Scattering. Physical Review D,1971,3 (4):825-839
[93]P. Barber, C. Yeh. Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies. Appl Opt,1975,14 (12):2864-2872
[94]M. I. Mishchenko, L. D. Travis, D. W. Mackowski. T-matrix computations of light scattering by nonspherical particles:A review. J Quant Spectrosc Radiat Transfer, 1996,55 (5):535-575
[95]M. I. Mishchenko, Travis, L.D. Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers. J Quant Spectrosc Radiat Transfer,1998,60:309-324
[96]M. I. Mishchenko, L. D. Travis, A. A. Lacis. Scattering, Absorption, and Emission of Light by Small Particles.3rd revised electronic edition ed. Cambridge:Cambridge University Press,2002.115-186
[97]J. C. Ravey, P. Mazeron. Light scattering in the physical optics approximation; application to large spheroids. Journal of Optics,1982,13 (5):273-282
[98]K. Muinonen, K. Lumme, J. Peltoniemi, et al. Light scattering by randomly oriented crystals. Appl Opt,1989,28 (15):3051-3060
[99]A. Macke, M. I. Mishchenko, K. Muinonen, et al. Scattering of light by large nonspherical particles:ray-tracing approximation versus T-matrix method. Opt Lett, 1995,20(19):1934-1936
[100]J. C. Ravey, P. Mazeron. Light scattering by large spheroids in the Physical Optics Approximation:numerical comparison with other approximate and exact results. Journal of Optics,1983,14 (1):29-41
[101]P. Latimer. Light scattering by ellipsoids. Journal of Colloid and Interface Science, 1975,53 (1):102-109
[102]P. Latimer, P. Barber. Scattering by ellipsoids of revolution a comparison of theoretical methods. Journal of Colloid and Interface Science,1978,63 (2):310-316
[103]C. F. Bohren, G. Koh. Forward-scattering corrected extinction by nonspherical particles. Appl Opt,1985,24 (7):1023-1029
[104]M. V. Berry, C. Upstill, E. Wolf. IV Catastrophe Optics:Morphologies of Caustics and Their Diffraction Patterns. Progress in Optics:Elsevier,1980.257-346
[105]J. A. Lock. Ray scattering by an arbitrarily oriented spheroid. Ⅰ. Diffraction and specular reflection. Appl Opt,1996,35 (3):500-514
[106]J. A. Lock. Ray scattering by an arbitrarily oriented spheroid. Ⅱ. Transmission and cross-polarization effects. Appl Opt,1996,35 (3):515-531
[107]B. T. Draine, P. J. Flatau. Discrete-dipole approximation for scattering calculations. J Opt Soc Am A,1994,11 (4):1491-1499
[108]M. A. Yurkin, V. P. Maltsev, A. G. Hoekstra. The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength. J Quant Spectrosc Radiat Transf,2007,106 (1-3):546-557
[109]M. A. Yurkin, A. G. Hoekstra. The discrete dipole approximation:An overview and recent development. J Quant Spectrosc Radiat Transf,2007,106 (1-3):558-589
[110]F. Xu, K. F. Ren, X. Cai, et al. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. Ⅱ. By a spheroidal particle with end-on incidence. Appl Opt,2006,45 (20):5000-5009
[111]E. A. Hovenac. Calculation of far-field scattering from nonspherical particles using a geometrical optics approach. Appl Opt,1991,30 (33):4739-4746
[112]G. Gouesbet, B. Maheu, G. Grehanan. Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation. J Opt Soc Am A,1988,5 (9):1427-1443
[113]J. A. Lock, G. Gouesbet. Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. Ⅰ. On-axis beams. J Opt Soc Am A,1994,11 (9):2503-2515
[114]J. A. Lock, G. Gouesbet. Generalized Lorenz-Mie theory and applications. Journal of Quantitative Spectroscopy and Radiative Transfer,2009,110 (11):800-807
[115]J. P. Chevaillier, J. Fabre, P. Hamelin. Forward scattered light intensities by a sphere located anywhere in a Gaussian beam. Appl Opt,1986,25 (7):1222-1225
[116]J. P. Chevaillier, J. Fabre, G. Grehan, et al. Comparison of diffraction theory and generalized Lorenz-Mie theory for a sphere located on the axis of a laser beam. Appl Opt,1990,29(9):1293-1298
[117]F. Xu, K. F. Ren, X. Cai. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle. Appl Opt,2006,45 (20): 4990-4999
[118]P. Laven. A computer program for scattering of light from a sphere using Mie theory & the Debye series. Switzerland:Geneva,2012.1-5
[119]M. Morkovin. Flow around circular cylinder-a kaleidoscope of challenging fluid phenomena. In:Hansen, A.G. (Ed), ASME Symposium on Fully Separated Flows. Philadelphia, ASME, New York,1964.102-118
[120]M. Raffel, C. Willert, S. Wereley, et al. Image Evaluation Methods for PIV-Particle Image Velocimetry. Springer-Verlag Berlin Heidelberg,2007.123-176
[2]徐世昌,张亮.潜艇尾流的空间演化及与自由面的相互作用.哈尔滨工程大学学报,2007,27(6)：802-805
[3]罗浩,李杨,都思丹等.数字式大气湍流探测仪及其数据可靠性研究.交通与计算机,2004,22(4)：44-47
[4]张慧敏,李新阳.热风式大气湍流模拟装置的哈特曼测量.光电工程,2004,31(S1)：4-7
[5]苏毅勇,白洁,王洪芳.利用多普勒技术识别探测大气湍流研究进展.第26届中国气象学会年会第三届气象综合探测技术研讨会分会场.中国浙江杭州,2009.156-161
[6]G. Billet, V. Giovangigli, G. de Gassowski. Impact of volume viscosity on a shock-Hydrogen-bubble interaction. Combustion Theory and Modelling,2008,12 (2): 221-248
[7]戴阳,林兆祥,张文艳等.激光雷达大气湍流测量方法研究.强激光与粒子束,2006,18(11)：1769-1773
[8]张守川,吴毅,侯再红等.激光雷达测量大气湍流廓线.强激光与粒子束,2009,21(12)：1795-1798
[9]陈栋,李红刚,倪志波等.海洋大气湍流对激光通信系统性能的影响分析.大气与环境光学学报,2009,4(3)：178-182
[10]胡月宏,强希文,冯建伟等.基于气象参数戈壁沙漠地区近地面大气湍流建模.强激光与粒子束,2010,22(12)：2799-2802
[11]杨迪.大气湍流闪烁效应对激光通信系统影响及补偿技术研究：[硕士学位论文].长春：长春理工大学,2009
[12]朱文越,马晓珊,饶瑞中.大气光学湍流对光电探测器性能的影响.红外与激光工程,2006,35(3)：354-358
[13]张晓芳,俞信,阎吉祥.大气湍流对光学系统图像分辨力的影响.光学技术,2005,31(2)：263-265
[14]孙昭晨,梁书秀,沈永明等.三维海洋紊流模型对杭州湾附近潮流场数值模拟.大连理工大学学报,2000,40(5)：609-612
[15]魏皓,武建平,张平.海洋湍流模式应用研究.青岛海洋大学学报(自然科学版),2001,31(1)：7-13
[16]邱辽原.潜艇粘性流场的数值模拟及其阻力预报的方法研究：[博士学位论文].武汉：华中科技大学,2006
[17]C. Foias, D. D. Holm, E. S. Titi. The Navier-Stokes-alpha model of fluid turbulence. Physica D:Nonlinear Phenomena,2001,152-153:505-519
[18]D. J. Webb. An ocean model code for array processor computers. Computers & Geosciences,1996,22 (5):569-578
[19]G. N. Ivey, K. B. Winters, J. R. Koseff. Density Stratification, Turbulence, but How Much Mixing? Annual Review of Fluid Mechanics,2008,40 (1):169-184
[20]A. H. H. Renner, K. J. Heywood, S. E. Thorpe. Validation of three global ocean models in the Weddell Sea. Ocean Modelling,2009,30 (1):1-15
[21]M. P. Strand. Imaging model for underwater range-gated imaging systems. Proc.SPIE 1537,1991.151-160
[22]J. S. Jaffe. Monte Carlo modeling of underwater-image formation:validity of the linear and small-angle approximations. Applied Optics,1995,34 (24):5413-5421
[23]G. L. Mellor, T. Yamada. A hierarchy of turbulence closure models for planetary boundary layers. Journal of the Atmospheric Sciences,1974,31 (7):1791-1806
[24]A. Rosati, K. Miyakoda. A general circulation model for upper ocean simulation. J Phys Oceanogr,1988,18 (11):1601-1626
[25]B. E. Launder, D. B. Spalding. Lectures in mathematical models of turbulence. London, England:Academic Press,1972
[26]G. L. Mellor, T. Yamada. Development of a turbulence closure model for geophysical fluid problems. Reviews of geophysics and space physics,1982,20 (4):851-875
[27]H. Burchard. Applied Turbulence Modelling in Marine Waters. New York:Springer-Verlag Berlin Heidelberg,2002.1-5
[28]H. Burchard, O. Petersen. Models of turbulence in the marine environment --a comparative study of two-equation turbulence models. Journal of Marine Systems, 1999,21 (1-4):29-53
[29]H. Burchard, K. Bolding, M. R. Villarreal, et al. GOTM, a general ocean turbulence model:Theory, implementation and test cases. Tech. Rep. EUR 18745 EN. European Commission:Space Applications Institute,1999.103-106
[30]R. J. Adrian. Twenty years of particle image velocimetry. Experiments in Fluids,2005, 39(2):159-169
[31]M. R. Dhanak, K. Holappa. An Autonomous Ocean Turbulence Measurement Platform. Journal of Atmospheric and Oceanic Technology,1999,16 (11):1506-1518
[32]S. A. Thorpe, T. R. Osborn, J. F. E. Jackson, et al. Measurements of Turbulence in the Upper-Ocean Mixing Layer Using Autosub. Journal of Physical Oceanography,2003, 33 (1):122-145
[33]朱红钧,林元华,谢龙汉.FLUENT流体分析及仿真实用教程.北京：人民邮电出版社,2010.1-131
[34]B. Ruth. Superposition of Two Dynamic Speckle Patterns. Journal of Modern Optics, 1987,34(2):257-273
[35]R. Theunissen, M. Riethmuller. Particle image velocimetry in lung bifurcation models- Particle Image Velocimetry. Springer Berlin/Heidelberg,2008,112:73-101
[36]S. Groβe, W. Schroder, M. Klaas. Time-resolved PIV measurements of vortical structures in the upper human airways-Particle Image Velocimetry:New Developments and Recent Applications (Topics in Applied Physics Volume 112). Springer Berlin/Heidelberg,2008.35-53
[37]L. Araneo, A. Coghe, F. Cozzi, et al. Natural Gas Burners for Domestic and Industrial Appliances-Particle Image Velocimetry. Springer Berlin/Heidelberg, 2008.245-257
[38]N. G. Deen, J. Westerweel, E. Delnoij. Two-phase PIV in bubbly flows:Status and trends. Chemical Engineering & Technology,2002,25 (1):97-101
[39]钱广强,董治宝,王洪涛等.粒子图像测速(PIV)技术在风沙环境风洞中的应用.中国沙漠,2006,26(6)：890-893
[40]F. Scarano. Overview of PIV in supersonic flows-Particle Image Velocimetry. Springer Berlin/Heidelberg,2008.445-463
[41]F. Felice, F. Pereira. Developments and Applications of PIV in Naval Hydrodynamics-Particle Image Velocimetry. Springer Berlin/Heidelberg,2008.475-503
[42]徐斌.湍流的现代实验研究方法.沿海企业与科技,2009,9(9)：13-15
[43]M. T. Milbocker. Laser Doppler velocimetry stabilized in one dimension. Biomedical Engineering, IEEE Transactions on,1991,38 (9):928-930
[44]S. So, H. Morikita, S. Takagi, et al. Laser Doppler velocimetry measurement of turbulent bubbly channel flow. Experiments in Fluids,2002,33(1):135-142
[45]A. L. Tassin, D. E. Nikitopoulos. Non-intrusive measurements of bubble size and velocity. Experiments in Fluids,1995,19 (2):121-132
[46]X. Liu, W. H. Doub, C. Guo. Evaluation of droplet velocity and size from nasal spray devices using phase Doppler anemometry (PDA). International journal of pharmaceutics,2010,388 (1-2):82-87
[47]A. B. Parthasarathy, E. L. Weber, L. M. Richards, et al. Cerebral Blood Flow Imaging during Neurosurgery with Laser Speckle Contrast Imaging. Biomedical Optics: Optical Society of America,2010. JMA991-3
[48]D. Tarlet, C. Bendicks, C. Roloff, et al. Gas Flow Measurements by 3D Particle Tracking Velocimetry Using Coloured Tracer Particles. Flow, Turbulence and Combustion,2010,88 (3):343-365
[49]D. Broder, M. Sommerfeld. A PIV/PTV system for analysing turbulent bubbly flows. Proceedings of the 10th International Symposium Application of Laser Techniques to Fluid Mechanics Lisbon,2000.10.1-10.11
[50]M. Kreizer, D. Ratner, A. Liberzon. Real-time image processing for particle tracking velocimetry. Experiments in Fluids,2010,48 (1):105-110
[51]N. Damaschke, H. Nobach, T. I. Nonn, et al. Size and velocity measurements with the global phase Doppler technique. In:11th international symposium on application of laser techniques to fluid mechanics, Lisbon,2002.1-11
[52]S. Kruger, G. Grunefeld. Stereoscopic flow-tagging velocimetry. Applied Physics B: Lasers and Optics,1999,69 (5):509-512
[53]C. Elkins, M. Alley. Magnetic resonance velocimetry:applications of magnetic resonance imaging in the measurement of fluid motion. Experiments in Fluids,2007, 43 (6):823-858
[54]R. J. Adrian. Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow:speckle velocimetry vs particle image velocimetry. Appl Opt,1984,23 (11):1690-1691
[55]C. J. D. Pickering, N. A. Halliwell. Laser speckle photography and particle image velocimetry:photographic film noise. Appl Opt,1984,23 (17):2961-2969
[56]R. D. Keane, R. J. Adrian. Optimization of particle image velcimeters:1.double pulsed systems. Measurement Science & Technology,1990,1 (11):1202-1215
[57]N. Farrugia, S. Kanne, D. A. Greenhalgh. Three-pulse digital particle image velocimetry. Opt Lett,1995,20 (17):1827-1829
[58]R. D. Keane, R. J. Adrian. Optimization of particle image velcimeters:2.multiple pulsed systems. Measurement Science & Technology,1991,2 (10):963-974
[59]M. Sutton, W. Wolters, W. Peters, et al. Determination of displacements using an improved digital correlation method. Image and Vision Computing,1983,1 (3): 133-139
[60]R. D. Keane, R. J. Adrian. Theory of cross-correlation analysis of PIV images. Applied Scientific Research,1992,49 (3):191-215
[61]C. Willert, M. Gharib. Digital particle image velocimetry. Experiments in Fluids,1991, 10(4):181-193
[62]J. Westerweel. Analysis of PIV interrogation with low-pixel resolution. In:Soyoung SC, James DT, editors:SPIE,1993.624-635
[63]R. J. Adrian. Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry. Applied Optics,1986,25 (21):3855-3858
[64]C. Meinhart, S. Wereley, J. Santiago. PIV measurements of a microchannel flow. Experiments in Fluids,1999,27 (5):414-419
[65]R. Lima, S. Wada, S. Tanaka, et al. In vitro blood flow in a rectangular PDMS microchannel:experimental observations using a confocal micro-PIV system. Biomedical Microdevices,2008,10 (2):153-167
[66]M. R. Bown, J. M. Maclnnes, R. W. K. Allen, et al.. Three-dimensional, three-component velocity measurements using stereoscopic micro-PIV and PTV. Measurement Science and Technology,2006,17 (8):2175-2185
[67]S. Coudert, J. Foucaut, J. Kostas, et al. Double large field stereoscopic PIV in a high Reynolds number turbulent boundary layer. Experiments in Fluids,2011,50 (1):1-12
[68]R. C. Chen, L. S. Fan. Particle image velocimetry for characterizing the flow structure in three-dimensional gas-liquid-solid fluidized beds. Chem Eng Sci,1992,47 (13-14):3615-3622
[69]L. Gui, R. Lindken, W. Merzkirch. Phase-separated PIV measurements of the flow around systems of bubbles rising in water. FEDSM'97:ASME Fluids Engineering Division Summer Meeting(June),1997.1-6
[70]A. Tokuhiro, M. Maekawa, K. Iizuka, et al. Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques. Int J Multiph Flow,1998,24 (8): 1383-1406
[71]R. Lindken, W. Merzkirch. Velocity measurements of liquid and gaseous phase for a system of bubbles rising in water. Experiments in Fluids,2000,29 (Suppl):S194-S201
[72]R. Lindken, W. Merzkirch. A novel PIV technique for measurements in multiphase flows and its application to two-phase bubbly flows. Experiments in Fluids,2002,33 (6):814-825
[73]E. Delnoij, J. A. M. Kuipers, W. P. M. van Swaaij, et al. Measurement of gas-liquid two-phase flow in bubble columns using ensemble correlation PIV. Chem Eng Sci, 2000,55 (17):3385-3395
[74]A. Fujiwara, Y. Danmoto, K. Hishida, et al. Bubble deformation and flow structure measured by double shadow images and PIV/LIF. Experiments in Fluids,2004,36 (1):157-165
[75]D. Broder, M. Sommerfeld. Combined PIV/PTV-measurements for the analysis of bubble interactions and coalescence in a turbulent flow. Can J Chem Eng,2003,81 (3-4):756-763
[76]M. J. Sathe, I. H. Thaker, T. E. Strand, et al. Advanced PIV/LIF and shadowgraphy system to visualize flow structure in two-phase bubbly flows. Chem Eng Sci,2010,65 (8):2431-2442
[77]M. Raffel, C. E. Willert, J. Kompenhans. Particle image velocimetry:a practical guide. Springer-Verlag Berlin Heidelberg,1998.1-11
[78]C. F. Boliren, D. R. Huffman. Absorption and scattering of light by small particles. J New York:Wiley & Sons,1983.165-183
[79]C. Matzle. MATLAB Functions for Mie Scattering and Absorption. Report Number 2002-8:Institute of Applied Physics, University of Bern,2002.1-20
[80]G. E. Davis. Scattering of Light by an Air Bubble in Water. J Opt Soc Am,1955,45 (7):572-581
[81]H. C. van de Hulst. Light scattering by small particles. New York:John Wiley & Sons, 1957.203-209
[82]P. L. Marston. Critical angle scattering by a bubble:physical-optics approximation and observations. J Opt Soc Am,1979,69 (9):1205-1211
[83]P. L. Marston, D. L. Kingsbury. Scattering by a bubble in water near the critical angle: interference effects. J Opt Soc Am,1981,71 (2):192-196
[84]L. Wu, H. Yang, X. Li, et al. Scattering by large bubbles:Comparisons between geometrical-optics theory and Debye series. Journal of Quantitative Spectroscopy and Radiative Transfer,2007,108 (1):54-64
[85]H. Yu, J. Shen, Y. Wei. Geometrical optics approximation of light scattering by large air bubbles. Particuology,2008,6 (5):340-346
[86]K. Arai. Phase function of relatively large aerosol particles containing bubbles by means of a ray tracing. Advances in Space Research,2002,29 (11):1813-1818
[87]W. Li. Computation of the scattering intensity distribution for natural light scattered by an air bubble in water. Journal of Optics A:Pure and Applied Optics,2006,8 (1): 93-99
[88]J. Shen, H. Wang, B. Wang, et al. Stability in Debye series calculation for light scattering by absorbing particles and bubbles. Journal of Quantitative Spectroscopy and Radiative Transfer,2010,111 (5):772-781
[89]S. Asano, G. Yamamoto. Light Scattering by a Spheroidal Particle. Appl Opt,1975,14 (1):29-49
[90]S. Asano. Light scattering properties of spheroidal particles. Appl Opt,1979,18 (5):712-723
[91]S. Asano, M. Sato. Light scattering by randomly oriented spheroidal particles. Appl Opt,1980,19(6):962-974
[92]P. C. Waterman. Symmetry, Unitarity, and Geometry in Electromagnetic Scattering. Physical Review D,1971,3 (4):825-839
[93]P. Barber, C. Yeh. Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies. Appl Opt,1975,14 (12):2864-2872
[94]M. I. Mishchenko, L. D. Travis, D. W. Mackowski. T-matrix computations of light scattering by nonspherical particles:A review. J Quant Spectrosc Radiat Transfer, 1996,55 (5):535-575
[95]M. I. Mishchenko, Travis, L.D. Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers. J Quant Spectrosc Radiat Transfer,1998,60:309-324
[96]M. I. Mishchenko, L. D. Travis, A. A. Lacis. Scattering, Absorption, and Emission of Light by Small Particles.3rd revised electronic edition ed. Cambridge:Cambridge University Press,2002.115-186
[97]J. C. Ravey, P. Mazeron. Light scattering in the physical optics approximation; application to large spheroids. Journal of Optics,1982,13 (5):273-282
[98]K. Muinonen, K. Lumme, J. Peltoniemi, et al. Light scattering by randomly oriented crystals. Appl Opt,1989,28 (15):3051-3060
[99]A. Macke, M. I. Mishchenko, K. Muinonen, et al. Scattering of light by large nonspherical particles:ray-tracing approximation versus T-matrix method. Opt Lett, 1995,20(19):1934-1936
[100]J. C. Ravey, P. Mazeron. Light scattering by large spheroids in the Physical Optics Approximation:numerical comparison with other approximate and exact results. Journal of Optics,1983,14 (1):29-41
[101]P. Latimer. Light scattering by ellipsoids. Journal of Colloid and Interface Science, 1975,53 (1):102-109
[102]P. Latimer, P. Barber. Scattering by ellipsoids of revolution a comparison of theoretical methods. Journal of Colloid and Interface Science,1978,63 (2):310-316
[103]C. F. Bohren, G. Koh. Forward-scattering corrected extinction by nonspherical particles. Appl Opt,1985,24 (7):1023-1029
[104]M. V. Berry, C. Upstill, E. Wolf. IV Catastrophe Optics:Morphologies of Caustics and Their Diffraction Patterns. Progress in Optics:Elsevier,1980.257-346
[105]J. A. Lock. Ray scattering by an arbitrarily oriented spheroid. Ⅰ. Diffraction and specular reflection. Appl Opt,1996,35 (3):500-514
[106]J. A. Lock. Ray scattering by an arbitrarily oriented spheroid. Ⅱ. Transmission and cross-polarization effects. Appl Opt,1996,35 (3):515-531
[107]B. T. Draine, P. J. Flatau. Discrete-dipole approximation for scattering calculations. J Opt Soc Am A,1994,11 (4):1491-1499
[108]M. A. Yurkin, V. P. Maltsev, A. G. Hoekstra. The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength. J Quant Spectrosc Radiat Transf,2007,106 (1-3):546-557
[109]M. A. Yurkin, A. G. Hoekstra. The discrete dipole approximation:An overview and recent development. J Quant Spectrosc Radiat Transf,2007,106 (1-3):558-589
[110]F. Xu, K. F. Ren, X. Cai, et al. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. Ⅱ. By a spheroidal particle with end-on incidence. Appl Opt,2006,45 (20):5000-5009
[111]E. A. Hovenac. Calculation of far-field scattering from nonspherical particles using a geometrical optics approach. Appl Opt,1991,30 (33):4739-4746
[112]G. Gouesbet, B. Maheu, G. Grehanan. Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation. J Opt Soc Am A,1988,5 (9):1427-1443
[113]J. A. Lock, G. Gouesbet. Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz-Mie theory. Ⅰ. On-axis beams. J Opt Soc Am A,1994,11 (9):2503-2515
[114]J. A. Lock, G. Gouesbet. Generalized Lorenz-Mie theory and applications. Journal of Quantitative Spectroscopy and Radiative Transfer,2009,110 (11):800-807
[115]J. P. Chevaillier, J. Fabre, P. Hamelin. Forward scattered light intensities by a sphere located anywhere in a Gaussian beam. Appl Opt,1986,25 (7):1222-1225
[116]J. P. Chevaillier, J. Fabre, G. Grehan, et al. Comparison of diffraction theory and generalized Lorenz-Mie theory for a sphere located on the axis of a laser beam. Appl Opt,1990,29(9):1293-1298
[117]F. Xu, K. F. Ren, X. Cai. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle. Appl Opt,2006,45 (20): 4990-4999
[118]P. Laven. A computer program for scattering of light from a sphere using Mie theory & the Debye series. Switzerland:Geneva,2012.1-5
[119]M. Morkovin. Flow around circular cylinder-a kaleidoscope of challenging fluid phenomena. In:Hansen, A.G. (Ed), ASME Symposium on Fully Separated Flows. Philadelphia, ASME, New York,1964.102-118
[120]M. Raffel, C. Willert, S. Wereley, et al. Image Evaluation Methods for PIV-Particle Image Velocimetry. Springer-Verlag Berlin Heidelberg,2007.123-176