摘要
导弹在助推段及飞行中段的红外辐射主要来自其羽焰,而其飞行的背景主要是云层。为了能有效地从云层背景中识别出导弹,必须研究导弹羽焰及云层背景的红外辐射特性。云层的红外辐射特性主要决定于云层中水滴粒子系和冰晶粒子系对太阳光的多次散射。本课题受航天支撑技术基金资助,旨在研究导弹羽焰及云层背景的红外辐射特性,以便为导弹预警的实时场景仿真提供红外辐射模型。
论文的研究工作主要包括两部分:一、为了识别来袭导弹,研究了导弹羽焰真实温度及发射率的计算方法,提出了两种新的多光谱数据处理方法:基于亮温模型的逼近法和基于亮温模型的连续测量法。二、为了区分云层背景,计算了零距离时云层中水滴粒子系及冰晶粒子系的多次散射及云层发射率、透过率。为了计算远距离时云层的辐射亮度,提出了一种辐射传输方程的快速计算方法,即累积因子法。
论文主要完成了以下几方面的研究工作:
(1)提出了基于亮温模型的逼近法。目前大多数多光谱数据处理方法需要事先假设发射率与波长之间的函数关系,本文根据亮度温度与真实温度及波长的关系,当波长趋近于0时,亮度温度就是真实温度。由测量得到的各通道的亮度温度与对应的波长进行非线性最小二乘拟合,可以得到波长趋于0时的亮度温度,即为真实温度。对应大气的两个窗口3~5μm和8~12μm,分别在高温段(1500~300K)、中温段(500~1500K)和低温段(160~500K)进行了仿真试验。然后用实测数据对该算法进行了验证,并考察了基于亮温模型的逼近法对随机噪声的承受能力。仿真结果证明:基于亮温模型的逼近法可以识别出常见工程材料的真实温度,而且在低温段比在高温段有更高的计算精度。该方法对随机噪声的承受能力很弱。但可以把其计算结果作为其他多光谱数据处理方法的初值,避免初值估计的盲目性。
(2)提出了基于亮温模型的连续测量法。在很窄的波段范围内及很短的一个连续测量周期内,假设光谱发射率在所选定的波长处与温度有近似的线性关系,通过处理两个不同时刻多光谱测温仪的测量数据,可以求得多个波长下的法向光谱发射率。仿真实验结果证明:基于亮温模型的连续测量法承受随机噪声的能力很强,无论有无噪声,该算法的计算结果都令人满意。利用该算法对实测数据进行处理,结果证明该算法的计算精度很高,能较好地解决目标真实温度的测量问题。
(3)提出了基于超椭球方程计算任意形状粒子的等效半径的方法。球形粒子的散射计算要用Mie理论,而非球形粒子的散射计算要用T矩阵方法。T矩阵方法中首先要计算非球形粒子的等效半径,目前计算非球形粒子的等效半径的方法大都属于曲面积分方法,计算比较繁琐。本文利用空间超椭球方程的体积及表面积计算公式则可以很方便地计算出非球形粒子的体积等效半径和表面积等效半径,这样就可以对T矩阵方法进行改进,以提高计算速度。用FORTRAN语言编写了改进的T矩阵计算程序,并计算了零距离时卷云中非球形冰晶粒子系的散射特性,将计算结果与文献数据进行比对,证明对T矩阵方法的改进是成功的。
论文还分析了粒子系的散射参数随等效半径的变化规律及修正的伽马分布的四个参数对粒子系散射特性的影响。
(4)提出了累积因子法。为了计算远距离时云层的红外辐射特性,需要考虑辐射传输问题,求解辐射传输方程。目前辐射传输方程的求解方法如逐次迭代法、蒙特卡罗法等速度慢,不能用于在线实时仿真。本文提出的累积因子法,首先计算单次散射,然后求出累积因子,即多次散射对单次散射的比率,进而计算多次散射,即可计算出云层的辐射亮度。该算法可以快速有效地求解辐射传输方程,提高多次散射的计算速度。将累积因子法的计算结果与逐次迭代法和LOWTRAN的计算结果进行了比对。表明在相同计算精度下,累积因子法计算速度远比逐次迭代法快,可以用于在线实时仿真。
The infrared radiation of missile during boosting phase and mid-course radiate mainly from its plume, and its background is most likely to be cloud. In order to distinguish attacking missile from cloud background effectively, it’s necessary to study the infrared radiation signature of missile plume and that of cloud background. The infrared signature of cloud depends on the multiple scattering of water droplets or ice crystals within clouds. This project is supported by foundation of spaceflight supporting technology. Its intention is to study the infrared signature of missile plume and that of cloud, to establish radiation models for real time scene simulation in missile early-warning system.
This dissertation is composed of two parts. Firstly, in order to distinguish missile form cloud background, algorithm for true temperature of missile plume and its emissivity were studied. Two new data processing algorithms for multiple wavelength pyrometer were put forward. One algorithm is approach method based on brightness temperature (AMBT). The other one is continuous measuring method based on brightness temperature (CMBT). Secondly, in order to distinguish cloud background, the multiple scattering of water droplets and ice crystals in clouds were calculated. Emissivities and transmissivities of clouds were also computed. In order to calculate radiation brightness of cloud at a distance, a new algorithm to speedup the calculation of radiation transfer equation, build-up factor algorithm was proposed.
Finished research works including:
Ⅰ. Put forward a new multi-spectral data processing method, AMBT. In order to avoid guessing the relationship between emissivity and wavelength, according to the relationship among brightness temperature, true temperature and wavelength, it’s known that true temperature is equal to brightness temperature when the wavelength approaching to zero. Thus, the calculated true temperature can be derived through non-linear least squares fitting between brightness temperatures at different channels and the corresponding wavelengths. Simulation experiments were made at high temperature (1500~3000K), intermediate temperature (500~1500K) and at low temperature (160~500K) corresponding to the two atmospheric windows from 3 to 5 micron and from 8 to 12 micron. Actual measured data were used to validate the effectiveness of AMBT. Then stochastic noise was superimposed to evaluate its influence on the precision of AMBT. Simulation results prove that AMBT is more accurate used at low temperature than to be used at high temperature. This method can obtain true temperature of most engineering materials at a distance. Influence of stochastic noise on AMBT is uncertain. So we can use AMBT to estimate the preliminary value for other algorithms avoiding the blindness of estimation.
Ⅱ. Described another new multi-spectral data processing method, CMBT. Supposing linear relation exists between emissivity and temperature at chosen wavelength during narrow waveband and in short measuring period, through processing measured data at two different time, spectral emmissivites at different wavelength can be obtained. Simulation results prove that CMBT can bear high random noise. All the calculation results are satisfied. Actual measured data was processed by CMBT and shows that CMBT is of high precision. This algorithm can be used in practical measurement and get better results.
Ⅲ. Use superellipsoid equation to simulate nonspherical particles with arbitrary shapes and calculate their equivalent radius. Mie theory is used to calculate scattering of global particles, while T-matrix method is used to calculate scattering of nonspherical particles. Equivalent radius is very important in T-matrix method. Till now, most of the algorithms for equivalent radius of nonspherical particles are using integral on curved surface. They are inconvenient and time consuming. Using superellipsoid equation can shorten the calculating time for equal-volume-sphere radius and equal-surface-area-sphere radius. Program of the improved T-matrix method was compiled using FORTRAN language. Scattering parameters of ice crystals in cirrus was calculated. The computation results were compared with that of reference and proved that the improvement for T-matrix method is successful. Relations between scattering parameters and equivalent radius were analyzed. Modified Gamma distribution parameters’influence on the scattering signature of clouds was also researched.
Ⅳ. A new algorithm of calculation of radiation transfer equation, build-up factor algorithm was proposed. In order to calculate infrared signature of clouds at a distance, radiation transfer must be taken into account. Algorithms of calculation of radiation transfer equation, such as successive iterative method and Monte Carlo method, are time-consuming and couldn’t be used online. As build-up factor algorithm, single scattering was calculated firstly. Then a build-up factor was defined to estimate the contribution of multiple scattering. The total scattering of particle system is the sum of single scattering and multiple scattering. Then the radiation brightness of cloud can be calculated. This algorithm can speedup the calculation of radiation transfer equation, calculate multiple scattering quickly. The results of this algorithm were compared with that of successive iterative method and that of LOWTRAN. Results show that to get the same calculating precision, build-up factor algorithm is much faster than successive iterative method and can be used in online simulation.
引文
1 杨华,凌永顺,陈昌明,高桂清.美国反导系统红外探测、跟踪和识别技术分析.红外技术,2001,23(4):1-3
2 S.F. Gimelshein, D.A. Levin, J.A. Drakes, et al.Modeling of Ultraviolet Radiation in Steady and Transient High-Altitude Plume Flows.AIAA J. of Thermophysics and Heat Transfer,2002,16(1):58-67
3 L. Ibgui, J.M. Hartmann. An Optimized Line-by-Line Code for Plume Signature Calculations-I : Model and Date. Journal of Quantitative Spectroscopy & Radiative Transfer, 2002, 75:273-295
4 H.P. Tan, Y. Shuai, S.K. Dong. Analysis of Rocket Plume Base Heating by Using Backward Monte-Carlo Method.AIAA J. of Thermophysics and Heat Transfer,2005,19(1):125-127
5 Y. Shuai, S.K. Dong, H.P. Tan. Simulation of the Infrared Radiation Characteristics of High-Temperature Exhaust Plume Including Particles using the Backward Monte Carlo Method.J. of Quantitative Spectroscopy and Radiative Transfer,2005,95(2):231-240
6 帅永,董士奎,谈和平.数值模拟喷焰 2.7 微米红外辐射特性.航空学报,2005,26(4):402-405
7 董士奎,贺志宏,帅永,谈和平.多普勒漂移对超音速燃气流光辐射特性计算的影响.工程热物理学报,2005,26(6):1001-1003
8 张 涵 信 , 黎 作 武 . 超 高 声 速 层 流 尾 迹 的 数 值 模 拟 . 力 学 学报.1992,24(4):389-399
9 闫大鹏,贺安之,苗鹏程等.火箭发动机燃气流流场的光学显示方法研究.航空动力学报. 1993,8(1):1-5
10 戴景民,石义国,康为民等. 烧蚀材料的多光谱真温测量法. 宇航学报,1996, 17(3):25~30
11 孙晓刚, 戴景民, 丛大成, 褚载祥. 多光谱辐射测温的理论研究:发射率模型的自动判别.红外与毫米波学报. 1998,17(3):221~225
12 张海兴,张建奇,杨威. 飞机红外辐射的理论计算.西安电子科技大学学报.1997,24(1):78-81
13 孙晓刚,何瑾,戴景民,褚载祥. 基于神经网络模型的多波长辐射测温的研究. 哈尔滨工业大学学报. 1998,30(6):1~3
14 孙晓刚, 戴景民, 丛大成,褚载祥. 基于神经网络模型的辐射真温测量方法研究. 红外与毫米波学报. 2001,20(2):151~153
15 丛大成, 何瑾, 戴景民, 孙晓刚, 褚载祥. 基于径向基函数网络多光谱辐射测温技术理论研究, 2000,21(5):480~484
16 丛大成, 戴景民, 孙晓刚, 褚载祥. RBF 网络在多光谱测温中的应用研究. 红外与毫米波学报. 2001,20(2):97~101
17 王东明,唐斌.火箭尾喷焰流场的研究.指挥技术学院学报.2001,12(6):104-107
18 王志健,田欣利,胡仲翔.空气超音速火焰喷枪速度场和温度场的数值仿真.兵工学报.2002,23(4):565-568
19 杨栋,王俊德,赵宝昌等.原子发射光谱双谱线法测量固体火箭发动机内燃气温度.光谱学与光谱分析.2002,22(2):307-310
20 郝金波,董士奎,谈和平.固体火箭发动机尾喷焰红外特性数值模拟.红外与毫米波学报,2003,22(4):246-250
21 孙晓刚,戴景民,王雪峰,褚载祥.一种测量固体火箭发动机羽焰温度的数据处理方法研究. 红外与毫米波学报. 2003,22(2):141-144
22 于胜春,汤龙生.固体火箭发动机喷管及羽流流场的数值分析.固体火箭技术.2004,27(2):95-97
23 聂万胜,杨军辉,何浩波等.液体火箭发动机尾喷焰红外辐射特性.国防科技大学学报,2005,27(5):91-94
24 田耀四,蔡国飙,朱定强等.固体火箭发动机喷流流场数值仿真.宇航学报,2006,27(5):876-879
25 李 翔 , 易 新 建 . 固 体 火 箭 发 动 机 羽 焰 温 度 流 场 测 试 研 究 . 航 空 兵器,2006,(6):45-48
26 范 传 新 , 王 鹏 . 固 体 火 箭 发 动 机 羽 焰 测 温 方 法 研 究 . 宇 航 计 测 技术,2006,26(4):18-22
27 范传新.固体火箭羽焰的辐射特性及其温度测量技术评述.固体火箭技术,2004,27(3):238-242
28 C.F. Bohren, D.R. Huffman. Absorption and Scattering of Light by Small Particles.John Willey & Sons,1983
29 Van de Hulst.Light Scattering by Small Particles.Willey,1981
30 O.V. Kalashnikova,I.N. Sokolik.Modeling the Radiative Properties ofNonspherical Soil-derived Mineral Aerosols. Journal of Quantitative Spectroscopy & Radiative Transfer,2004,87:137-166
31 C. Bourrely,P. Chiappetta,B. Torresani.Light Scattering by Particles of Arbitrary Shape: a Fractal Approach.Journal of the Optical Society of America A,1986,3(2):250-255
32 W.M. Wauben,J.F. De Haan,J.W. Hovenier.Influence of Particle Shape on the Polarized Radiation in Planetary Atmospheres . Journal of Quantitative Spectroscopy & Radiative Transfer,1993,50(3):237-246
33 O. Dubovik, B.N. Holben, T.Lapyonok, et al. Non-spherical Aerosol Retrieval Method Employing Light Scattering by Spheroids. Geophysical Research Letters, 2001, 29(10):54-1-54-4
34 Michael I. Mishchenko, Gorden Videen, Victor A. Babenko, et al. T-matrix Theory of Electromagnetic Scattering by Particles and Its applications: a Comprehensive Reference Database. Journal of Quantitative Spectorscopy & Radiative Transfer, 2004, 88:357-406
35 Victor P. Tishkovets, Michael I. Mishchenko. Coherent Backscattering of Light by a Layer of Discrete Random Medium. Journal of Quantitative Spectroscopy & Radiative Transfer. 2004, 86:161-180
36 M.I. Mishchenko, J.W. Fhovenier, L.D. Travis . Light Scattering by Nonspherical Particles.Academic Press,New York,2000
37 M.I. Mishchenko, J.W. Hovenier, L.D. Travis. Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications. Academic Press, San Diego, 2000: 417-449
38 Michael I. Mishchenko, Larry D. Travis, Andrew A. Lacis. Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering. Cambridge University Press, 2006
39 Michael I. Mishchenko, Larry D. Travis, Andrew A. Lacis. Scattering, Absorption, and Emission of Light by Small Particles. Cambridge University Press, 2006
40 Stephan Borrmann, Beiping Luo, Michael Mishchenko. Application of the T-matrix Mehtod to the Measurement of Aspherical (Ellipsoidal) Particles with Forward Scattering Optical Particles Counters. J. Aerosol Sci. 2000, 31(7):789-799
41 Michael I. Mishchenko, Janna M. Dlugach, Edgard G. Yanovitskij, et al. Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: an Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces. Journal of Quantitative Spectroscopy & Radiative Transfer, 1999, 63:409-432
42 Michael I. Mishchenko, Larry D. Travis, Daniel W. Mackowski. T-matrix Computatuons of Light Scattering by Nonspherical Particles: a Review. Journal of Quantitative Spectroscopy & Radiative Transfer, 1996,55(5):535-575
43 Michael I. Mishchenko, Daniel W. Mackowski. Electromagnetic Scattering by Randomly Oriented Bispheres: Comparison of Theory and Experiment and Benchmark Calculations. Journal of Quantitative Spectroscopy & Radiative Transfer, 1996, 55(5):683-694
44 Li Liu, Michael I. Mishchenko, Brian Cairns, et al. Modeling Single-scattering Properties of Small Cirrus Particles by Use of a Size-shape Distribution of Ice Spheroids and Cylinders. Journal of Quantitative Spectroscopy & Radiative Transfer, 2006, 101:488-497
45 Bo-Cai Gao, Ping Yang, Wei Han, et al. An algorithm Using Visible and 1.38-μm Channels to Retrieve Cirrus Cloud Reflectances from Aircraft and Satellite Data. IEEE Transactions on Geoscience and Remote Sensing, 2002,40(8):1659-1668
46 Ping Yang, George W. Kattawar, Kuo-Nan Liou, et al. Comparison of Cartesian Grid Configuratuons for Application of the Finite-difference Time-domain Method to Electromagnetic Scattering by Dielectric Particles. Applied Optics. 2004, 43(23):4611-4624
47 C. Li, G.W. Kattawar, P. Yang. A New Algorithm to Achieve Rapid Field Convergence in the Frequency domain when Using FDTD. J. of Electomagn. Waves and Appl. 2004, 18(6):797-807
48 P. Yang,K.N. Liou,M.I. Mishchenko,et al.Efficient Finite-Difference Time-domain Scheme for Light Scattering by Dielectric Particles: Application to Aerosols.Applied Optics,2000,39:3727-3737
49 Ping Yang, K.N. Liou, Michael I. Mishchenko, et al. Efficient Finite-difference Time-domain Scheme for Light Scattering by Dielectric Particles:Application to Aerosols. Applied Optics, 2000, 39(21):3727-3737
50 R. Scott Brock, Xinhua Hu, Ping Yang, et al. Evaluation of a Parallel FDTD Code and Application to Modeling of Light Scattering by Deformed Red Blood Cells. Optics Express, 2005, 13(14):5279-5292
51 Ping Yang, K.N. Liou. An Efficient Algorithm for Truncating Spatical Domain in Modeling Light Scattering by Finite-difference Technique. Journal of Computational Physics, 1998, 140:346-369
52 Ping Yang, K.N. Liou. Finite-diference Time Domain Method for Light Scattering by Small Ice Crystals in Three-Dimensional Space. J. Opt. Am. A. 1996,13(10):2072-2085
53 Yu You, George W. Kattawar, Ping Yang, et al. Sensitivity of Depolarized Lidar Signals to Cloud and Aerosol Particle Properties. Jouranl of Quantitative Spectroscopy & Radiative Transfer, 2006, 100:470-482
54 P. Yang, Y.X. Hu, J. Zhao, et al. The Enhancement of Lidar Backscattering by Horizontally Oriented Ice Crystal Plates in Cirrus Clouds, IEEE, 2000:3608-3610
55 Yu Xie, Ping Yang, Bo-Cai Gao, et al. Effect of Ice Crystal Shape and Effective Size on Snow Bidirectional Reflectance. Journal of Quantitative Spectroscopy & Radiative Transfer, 2006, 100:457-469
56 Ping Yang, K.N. Liou, W.P. Arnott. Extinction Efficiency and Single-Scattering Albedo for Laboratory and Natural Cirrus Clouds. Journal of Geophysical Research, 1997,102(D18):21,825021,835
57 Ping Yang, Bo-Cai Gao, Bryan A. Baum, et al. Radiative Properties of Cirrus Clouds in the Infrared (8-13 m) Spectral Region. Journal of Quantitative Spectroscopy & Radiative Transfer, 2001,70:473-504
58 G. Guo, P. Yang, Y.X. Hu, et al. Manifestations of Interference Fluctuations of Phase Functions and Backscattering Cross Sections for Ice Crystals with Specific Orientations. Journal of Opttics A: Pure and Applied Optics. 2003,5:520-527
59 Ping Yang, K.N. Liou. Light Scattering by Hexagonal Ice Crystals: Comparison of Finite-difference Time Domain and Geometric Optics Models. J. Optical Society of America, 1995, 12(1):162-176
60 Anthony J. Baran, Ping Yang, Stephan Havemann. Calculation of the Single-scattering Properties of Randomly Oriented Hexagonal Ice Columns: a Comparison of the T-matrix and the Finite-difference Time-domain Methods. Applied Optics, 2001,40(24):4376-4386
61 A.E. Dessler, P. Yang. The Distribution of Tropical Thin Cirrus Clouds Inferred from Terra MODIS Data. American Meteorological Society. 2003, 16:1241-1247
62 S.C. Ou, K.N. Liou, P. Yang, et al. Airborne Retrieval of Cirrus Cloud Optical and Microphysical Properties Using Airborne Remote Earth Sensing System 5.1-5.3 and 3.7-μm Channel Data. Journal of Geophysical research, 1998, 103(D18):23,231-23,242
63 Ping Yang, George W. Kattawar, Warren J. Wiscombe. Effect of Particle Asphericity on Single-scattering Parameters: Comparison between Platonic Solids and Spheres. Applied Optics. 2004, 43(22):4427-4435
64 Ping Yang, Zhibo Zhang, Bryan A. Baum, et al. A New Look at Anomalous Diffraction Theory (ADT): Algorithm in cumulative Projected-area Distribution Domain and Modified ADT. Journal of Quantitative Spectroscopy & Radiative Transfer, 2004,89:421-442
65 Guang Chen, Ping Yang, George W. Kattawar, et al. Scattering Phase Functions of Horizontally Oriented Hexagonal Ice Crystals. Journal of Quantitative Spectroscopy & Radiative Transfer, 2006, 100:91-102
66 Qiang Fu, Ping Yang, W.B. Sun. An Accurate Parameterization of the Infrared Radiative Properties of Cirrus Clouds of Climate Models. Journal of Climate, 1998,11:2223-2237
67 L. Mannozzi, F. Di Giuseppe, R. Rizzi. Cirrus loud Optical Properties in Far Infrared. Phys. Chem. Earth (B) 1999, 23(3):269-273
68 R.J. Bantges, J.E. Russell, J.D. Haigh. Cirrus Cloud Top-of-Atmosphere Radiance Spectra in the Thermal Infrared. Journal of Quantitative Spectroscopy & Radiative Transfer, 1999, 63:487-498
69 Jacob C. Jonsson, Geofrey B. Smith, Gunnar A. Niklasson. Experimental and Monte Carlo Analysis of Isotropic Multiple Mie Scattering. Optics communications, 2004,240:9-17
70 Natalia V. Kustova, Anatoli G. Borovoi, Ulrich G. Oppel. Extinction-to-Backscatter Ratio Calculated for Ice Crystal Particles. 13th InternationalWorkshop on Lidar Multiple Scattering Experiments, edited by Anatoli G. Borovoi, Proc. of SPIE, 2005, 5829:163-173
71 Laurent C. Labonnote, Gerard Brogniez, Marie Doutriaux Boucher, et al. Modeling of Light Scattering in Cirrus clouds with Inhomogeneous Hexagonal Monocrystals. Comparison with in-Situ and ADEOS-POLDER Measurements. Geophysical Research Letters, 2000, 27(1):113-116
72 丁继烈,许丽生. 非球形轴对称粒子光散射的散射矩阵元素展开系数的数值计算. 成都气象学院学报. 1999,14(3):219-225
73 饶 瑞 中 . 随 机 取 向 椭 球 粒 子 的 吸 收 特 性 . 强 激 光 与 粒 子 束 . 1998,10(3):371-374
74 薛力芳,魏合理,饶瑞中. 卷云在红外波段的散射特性. 激光与红外,2004,34(4):287-291
75 韩 一 平 . 冰 水 混 合 云 对 可 见 光 的 吸 收 和 散 射 特 性 . 物 理 学 报 ,2006,55(2):682-687
76 李毅.非球形微粒及其形成烟幕的消光机理研究.南京理工大学博士学位论文.2001:12-28
77 关丽,田贵才. 小粒子 Mie 散射理论及应用(Ⅰ). 通化师范学院学报,2001,22(2):30-33
78 田贵才,关丽. 小粒子 Mie 散射理论及应用(Ⅱ). 通化师范学院学报,2001,22(5):46-48
79 孙国正,孙强,任智斌. 基于 Mie 散射理论的微球体颗粒半径分析. 红外与激光光程. 2005, 34(4):495-498
80 任智斌,卢振武,朱海东,孙强. 微球体光散射的研究. 红外与激光工程. 2004,33(4):401-404
81 M. Kochfaj, J. Lukac. Using the Multiple Scattering Theory for Calculation of the Radiation Fluxes from Experimental Aerosol Data. Journal of Quantitative Spectroscopy & Radiative Transfer, 1998, 60(6):933-942
82 A. da Silva, C. Andraud, E. Charron, et al. Multiple Light Scattering in Multilayered Media: Theory, Experiments. Physca B, 2003, 338:74-78
83 R. Vaillon. Derivation of an Equivalent Mueller Matrix Associated to an Absorbing, Emitting and Multiply Scattering Plane Medium. Journal of Quantitative Spectroscopy & Radiative Transfer, 2002, 73:147-157
84 Jaroslav Holoubek. Light Scattering and Reflectance of OpticallyHeterogeneous Polymers in Multiple Scattering Regime. Polymer Communication. 1998, 40:277-280
85 V.P. Tishkovets. Multiple Scattering of Light by a Layer of Discrete Random Medium: Backscattering. Journal of quantitative Spectroscopy & Radiative Transfer. 2002,72:123-137
86 Brian Stout, Christine Andraud, Sophie Stout, et al. Absorption in Multiple Scattering systems of Coated Spheres: Design Applications. Physica B, 2003, 338:121-125
87 吴 健 . 基 于 扩 展 球 谐 函 数 的 多 次 散 射 理 论 分 析 . 激 光 杂 志 ,2005,26(3):47-48
88 X.G. Sun, W.H Xu, Z.X. Chu. The Theoretical Analysis of Multi-Wavelength Pyrometer: Check and Autosearch for Emissivity General Expression. Journal of Harbin Institute of Technology. 1998,5(3): 36-40
89 盛裴轩,毛节泰,李建国,张霭琛,桑建国,潘乃先. 大气物理学. 北京:北京大学出版社,2003 年 5 月第 1 版. 302-458
90 尹宏. 大气辐射学基础. 北京:气象出版社,1993 年 10 月第 1 版: 180-192
91 J.W. Hovenier, H. Volten, O. Munoz, et al. Laboratory Studies of Scattering Matrices for Randomly Oriented Particles: Potentials, Problems, and Persperctives. Journal of Quantitative Spectroscopy & Radiative Transfer, 2003, 79:741-755
92 谈和平,夏新林,刘林华,阮立明. 红外辐射特性与传输的数值计算—计算热辐射学. 哈尔滨工业大学出版社,2006 年 10 月第 1 版:105-134
93 S. Wolf, N.V. Voshchinnikov. Mie Scattering by Ensembles of Particles with very Large Size Parameters. Computer Physics Communications, 2004, 162:113-123
94 袁易君,任德明,胡孝勇. Mie 理论递推公式计算散射相位函数. 光散射学报,2006,17(4):366-371
95 刘 建 斌 , 吴 健 . 大 气 中 球 形 粒 子 的 散 射 特 性 研 究 . 应 用 光 学 ,2005,26(2):31-33
96 Melanie Kohler, Ingrid Mann. Light-Scattering Models Applied to Circumstellar Dust Properties. Journal of Quantitative Spectroscopy & Radiative Transfer, 2004,89:453-460
97 廖国男著,周诗健译. 大气辐射导论. 北京:气象出版社,1985 年 3 月第 1 版,246-325
98 姬丰,郑刚,屠其军,李孟超,庄松林. 基于 MATLAB 的光散射物理量的数值计算方法. 光学仪器,2003,25(1):29-32
99 任智斌,卢振武,刘玉玲等. Mie 理论归一化散射光强的研究. 光电子·激光,2003,14(1):83-85
100 郑 刚 , 蔡 小 舒 , 王 乃 宁 . Mie 散 射 的 数 值 计 算 . 应 用 激 光 ,1992,12(5):220-222
101 王少清,任中京,张希明等. Mie 散射系数的新算法. 激光杂志,1997,18(3):9-12
102 王少清,任中京,张希明等. Mie 散射系数计算方法的研究. 应用光学,1997,18(2):4-9
103 程玉宝,杨希伟. Mie 散射因子的计算方法及其应用. 光电子技术应用,2005,20(5):12-14
104 C.M. Sorensen, D.J. Fischbach. Patterns in Mie Scattering. Optics Communications, 2000, 173:145-153
105 Delphine Cabaret, Stephanie Rossano, Christian Brouder. Mie Scattering of a Partially Coherent Beam. Optics Communications, 1998, 150:239-250
106 向劲松,谢利利,赵友全. Mie 散射的改进算法. 化工冶金增刊,1999,20:624-628
107 R. Lai, A.J. Sievers. Mie Computational Test of the Extinction Cross-section Sum Rules and Optical Moments for Larger dielectric Spheres and Shells. Optics communications, 1995, 116:72-76
108 Ruo-Jian Zhu, Jia Wang, Guo-Fan Jin. Mie Scattering Calculation by FDTD Employing a Modified Debye Model for Gold Material. Optik, 2005,116:419-422
109 I. Gurvich, N. shiloah, M. Kleiman. Calculations of the Mie Scattering Coefficients for Multilayered Particles with Large Size Parameter. Journal of Quantitative Spectroscopy & Radiative Transfer, 2001, 70:433-440
110 I. Wayan Sudiarta, Petr Chylek. Mie Scattering Efficiency of a Large Spherical Particle Embedded in an Absorbing Medium. Journal of Quantitative Spectroscopy & Radiative Transfer, 2001, 70:709-714
111 王志良,任伟. 电磁散射理论. 成都:四川科学技术出版社,1994 年 1月第 1 版:219-220
112 R. Schuh, T. Wriedt. Computer Programs for Light Scattering by Particles with Inclusions. Jouranl of Quantitative Spectroscopy & Radiative Transfer, 2001,70:715-723
113 Michael I. Mishchenko, Larry D. Travis. Capabilities and Limitations of a Current Fortran Implemetation fo the T-Matrix Method for Randomly Oriented, Rotationally Symmetric Scatterers. Journal of Quantitative Spectroscopy & Radiative Transfer. 1998,60(3):309-324
114 J.W. Hovenier, K. Lumme, M.I. Mishchenko, et al. Computations of Scattering Matrices of Four Types of Non-spherical Particles Using Diverse Methods. Journal of Quantitative Spectroscopy & Radiative Transfer. 1996, 55(6):695-705
115 Arturo Quirantes, Angel Delgado. Cross Section Calculations of Randomly Oriented Bispheres in the Small Particle Regime. Journal of Quantitative Spectroscopy & Radiative Transfer, 2003,78:179-186
116 Arturo Quirantes, Angel Delgado. Experimental Size Determination of Spheroidal Particles via the T-Matrix Method. Journal of Quantitative Spectroscopy & Radiative Transfer. 1998,60(3):463-474
117 Michael I. Mishchenko. Calculation of the Amplitude Matrix for a Nonspherical Particle in a Fixed Orientation. Applied Optics, 2000, 39(6):1026~1031
118 Jean-Claude Auger, Brian Stout. A Recursive Centered T-Matrix Algorithm to Solve the Multiple Scattering Equation: Numerical Validation. Journal of Quantitative Spectroscopy & Radiative Transfer, 2003,79-80:533-547
119 S. Havemann, A.J. Baran. Extension of T-Matrix to Scattering of Electromagnetic Plane Waves by Non-Axisymmetric Dielectric Particles: Application to Hexagonal Ice Cylinders. Journal of Quantitative Spectroscopy & Radiative Transfer, 2001,70:139-158
120 Arturo Quirantes. A T-Matrix Method and Computer Code for Randomly Oriented, Axially Symmetric Coated Scatterers. Journal of Quantitative Spectroscopy & Radiative Transfer, 2005,92:373-381
121 徐飞,顾松山,陈玉林. 用 T 矩阵方法计算超椭球粒子的电磁散射特性. 南京气象学院学报.2005,28(6):815-820
122 王宝瑞,忻翎艳,张培昌,蒋修武. 锥球状粒子对偏振雷达电磁波的散射和衰减特性. 南京气象学院学报,1996,19(4):387-392
123 S. Havemann, A.J. Baran. Extension of T-Matrix to Scattering of Electromagnetic Plane Waves by Non-Axisymmetric Dielectric Particles: Application to Hexagona Ice Cylinders. Journal of Quantitative Spectroscopy & Radiative Transfer, 2001, 70:139-158
124 M.I. Mishchenko. Light Scattering by Randomly Oriented Axially Symmetric Particlws. J. Opt. Soc. Am. A. 1991(8):871-882
125 Nofel Lagrosas, Hiroaki Kuze, Nobuo Takeuchi, et al. Correlation Study between Suspended Particulate Matter and Protable Automated Lidar Data. Journal of Aerosol Science. 2005,36:439-454
126 邹进上,刘长盛,刘文保. 大气物理基础.北京:气象出版社,1982 年 6月第 1 版.135-163
127 R.J. Thornburg, J.G. Devore, J. Thompson. Review of the CLDSIM Cloud Radiance Simulator. PL-TR-93-2232.
128 Yali Luo, Steven K. Krueger, Gerald G. Mace, Kuan-Man Xu. Cirrus Cloud Properties from a Cloud-Resolving Model Simulation Compared to Cloud Radar Observations.
129 Ping Yang, Martin G. Mlynczak, Heli Wei, et al. Spectral Signature of Ice Clouds in the Far-Infrared Region: Single-Scattering Calculations and Radiative Sensitivity Study. MS#2002JD003291