基于光谱消光法的颗粒粒径分布重建算法的研究
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摘要
随着科学技术的高速发展和新材料的不断涌现，科研和工程领域出现了越来越多与颗粒密切相关的技术问题，其中，对颗粒粒径大小及其分布情况的快速测量已成为实用测量领域一个重要的研究课题。众多粒径测量方法中光谱消光法因其原理简单、方便，能实现纳米级至微米级颗粒系的测量而备受关注，特别是随着在线粒度监测需求的日益迫切，光谱消光法已逐渐显示出较大发展空间和应用潜力。
光谱消光粒径测量方法是通过测量多个波长下的消光值来实现待测颗粒系粒径分布信息的重建。由于消光系数矩阵中核函数的剧烈振荡性，导致这类测量方法的数据处理中都会遇到第一类Fredholm积分方程的求解问题。这是一类典型的不适定问题，对此类问题进行理论求解具有相当大的困难。因此，发展快速有效的重建算法用于颗粒粒径测量一直受到国内外学者广泛的关注和重视。本课题受到国家自然科学基金资助(No.61071036)，研究目的是探索基于光谱消光法的准确快速重建算法，以解决目前该方法中存在的重建过程复杂、重建速度较慢以及重建结果不稳定等问题，以期使光谱消光法更加适合于颗粒粒径的在线测量。
本文首先针对颗粒粒径测量中多波长的最优选取问题进行研究。粒径分布重建过程中，每个波长下的消光值都不同程度包含关于待测颗粒粒径分布的信息。传统的粒径测量通常是在相对较窄光谱区域(如可见光谱区)内随机选取入射波长，这会对重建结果的准确度和抗噪声能力造成一定影响。此外，考虑到许多工业现场对快速性和简便性的高要求，必须选用少量且重要的特征波长用于粒径分布的重建。为此，本文依据不同波长消光系数间的关联程度，提出多光谱区间内分段最优波长的选取方法。在紫外-可见-近红外多光谱区域内分别选取各自区间内与所有波长的消光系数关联程度较高而彼此具有较小关联度的重要波长组合成全波段最优波长组进行颗粒粒径分布的重建。对于测量次数少于待测粒径间隔数而导致信息量不足的情况，该少量最优波长下的消光值包含了绝大部分的待测颗粒粒径信息，因而既保证了测量精度，又节省了整个粒径分布重建的计算时间。多光谱区分段最优波长选取方法为后续粒径分布重建中波长选取提供了理论依据。
光谱消光法粒径测量中，消光系数的计算是个关键问题，在很大程度上影响了粒径分布重建的快速性和准确性。本文针对球形颗粒和非球形颗粒消光系数的严格方法普遍存在理论复杂、计算繁琐、收敛速度较慢、易出现数值困难和解不稳定等问题，开展了基于近似方法的颗粒粒径分布快速重建的研究。提出将精确Mie理论与广义程函近似法相结合用于颗粒消光系数的计算，并在此基础上利用优化算法分别反演球形颗粒和椭球颗粒的粒径分布。采用组合近似方法计算的消光系数代替严格方法获得的消光系数，既可增大近似方法的适用范围，有效保证计算结果的准确性，又简化了颗粒消光系数的计算，从而降低了整个粒径分布重建过程的复杂性，提高了重建速度。组合的近似方法可作为当严格方法出现计算困难和数值不稳时的一种有效替代。
反演算法的合理设计和选用是保证实现准确快速粒径分布重建至关重要的一个环节。本文针对无函数限制模式下粒径分布反演算法尚处于发展阶段的研究现状，开展了反演算法用于准确快速颗粒粒径分布重建的研究。提出基于模式搜索的光谱消光粒径分布反演算法，同时引入Tikhonov平滑泛函构建算法的目标函数。为保证整个粒径分布重建的准确性和快速性，相应设计了关于模式搜索算法初始点的优选策略。在反演过程中，首先将粒径分布重建问题转化为最小化问题，Tikhonov平滑泛函用于该最小化问题的目标函数构建，在此基础上，应用改进模式搜索算法不断调节目标函数值直到满足设定的停止准则。模式搜索算法的突出优势是既不需要像很多传统方法那样计算梯度信息，也不像很多智能算法那样需要进行复杂的种群选择和变异，因而使反演计算更加简便高效。实验结果表明，改进模式搜索算法能够成功用于颗粒粒径分布的重建，具有很好的可靠性和稳定性。在综合考虑重建精度和重建时间的条件下，所提反演算法有一定优势，更适合于准确快速的颗粒粒径现场测量。
在理论分析和数值模拟的基础上，利用核工业北京化工冶金研究院提供的国家标准物质，分别对多光谱区分段最优波长的选取、基于广义程函近似的重建算法以及改进模式搜索反演算法用于颗粒粒径分布的重建进行了实测数据验证，并对实际粒径分布重建结果进行了分析和研究。实验验证了所提方法用于实际颗粒粒径分布重建的可行性和准确性。
With the rapid development of scientific field and the appearance of all kindsof new materials, there are more and more technical problems correlated withparticle issues, and the measurement of particle size distribution (PSD) has becomeone of the most important research fields. Among all the particle size measuringmethods, spectral extinction method is probably the most attractive one due to itstheoretical simplicity and convenience and its realization of measurement on micronor sub-micron particle systems. In particular, with the urgent demand for in situmeasurements of PSD, the spectral extinction method has shown greatdevelopments and potential applications.
In spectral extinction particle sizing method, the PSD can be retrieved by someinversion methods using the extinction values of multiple wavelengths. Owing toserious oscillation of the extinction efficiency, the data processing of this method isrelated to the solution of a Fredholm integral equation of the first kind. It is a wellknown typical ill-posed problem, and there are significant difficulties for solvingthe theoretical solution of this problem. Therefore, the development of rapid andefficient retrieval algorithms for recovering the PSD has received increasedattention and concerns by many researchers. This subject is supported by theNational Natural Science Foundation of China (No.61071036). The objective of thissubject is to investigate accurate and fast retrieval algorithms of PSD based on thespectral extinction method, which can solve the problems along with highcomplexity of whole retrieval process, low retrieval speed, and instability of theretrieval results, thus making the spectral extinction method more suitable foronline particle sizing.
This study is firstly focused on the selection of optimal wavelengths inmultispectral region. In the PSD retrieval process, the extinction values of eachincident wavelength may involve different amount of information about the PSD.The traditional measurement is performed only within a narrow spectral region (i.e.visible spectrum region), which may result in the decrease of accuracy andanti-noise effect of the retrieval results to some degree. Furthermore, consideringboth rapidity and simplicity in many practical industrial occasions, only limitedprincipal wavelengths can be chosen to deal in the data processing. Therefore,according to the degree of correlation for extinction efficiency of differentwavelengths, the method of sectional optimal wavelength selection in multispectralregion is presented. In the ultraviolet-visible-near-infrared spectrum region, theprincipal wavelengths selected in each spectrum region, which own high correlation of extinction efficiency with all other wavelengths and share low correlation ofextinction efficiency each other, constitute the whole optimum wavelengths ofmultispectral range to retrieve the PSD. For the case that the number of wavelengthsis less than particle subintervals which can result in the deficiency of information,the less optimum wavelengths involve most amount of information about the PSD,therefore the measuring accuracy can be effectively ensured and the computationtime of the whole retrieval can be significantly reduced. The method of sectionaloptimal wavelength selection in multispectral region offers the theorical basis forthe retrieval of PSD in succeeding chapters.
In spectral extinction particle sizing method, the calculation of extinctionefficiency is a critical issue which affects the accuracy and rapidity of the wholeretrieval. Aiming at overcoming complexity in theory, intricacy in calculation, lowconvergence speed, and instability for calculating the extinction efficiency ofspherical and spheroidal particles with rigorous methods, the approximate methodfor fast and accuracy retrieval is explored. The combination of Mie theory andgeneralized eikonal approximation (GEA) method is proposed in this paper tocalculate the extinction efficiency. Based on the extinction efficiency calculated bythe combined approximate method, the retrieval of PSD of spherical particles andspheroidal particles are then investigated. The combined approximate method, usedas an alternative to the rigorous Mie theory, not only can extend the applicablerange and guarantee the accuracy of the retrieval results, but also can simplify thecalculation process and improve the speed of the whole retrieval process. Theapproximate method can be used as an effective replacement when the rigoroussolutions suffer computational difficulties and numerical instability.
The design or selection of inversion methods is one of the most importantaspects of the whole retrieval which can guarantee to obtain accurate and fastretrieval results. Considering the inversion methods for the retrieval of PSD are stillin stage of development, this paper focuses on the study of inversion method. Thepattern search algorithm combined with the Tikhonov smoothing functional for thedetermination of PSD is proposed. To ensure good rapidity and accuracy of thewhole search process, a competitive strategy about the pattern search algorithm isalso designed. In the inversion process, the PSD retrieval problem is firstformulated as a minimization problem, with the Tikhonov smoothing functionalemployed in modeling the objective function, and then the improved pattern searchalgorithm is applied to adjust the objective function until a given stopping criterionhas been achieved. The pattern search algorithm does not require any gradientinformation like many traditional methods; also it does not require complexselection and mutation of populations like many intelligent optimization algorithms;therefore making the inversion process more convenient and efficient. Experimental results indicate that the proposed algorithm can be successfully applied to retrievethe PSD with high reliability and stability. In condition of fully considering retrievalprecision and retrieval time, the proposed inversion method has certain advantage,which is more suitable for accurate and quick field measurement of particle sizing.
Based on the theoretical analyses and numerical simulations, by using thestandard polystyrene samples offered by Beijing Institute of Nuclear Engineering,the three proposed methods, namely, the method of sectional optimal wavelengthselection in multispectral region, the retrieval algorithm of PSD based on the GEAmethod, the inversion method of improved pattern search algorithm for retrieval ofPSD, are further verified by the practical experimental data, and the retrieval resultsof PSD for standard polystyrene samples are also analyzed and studied. Theexperiments validate the feasibility and accuracy of the above proposed methods inpractical retrieval of PSD.
光谱消光粒径测量方法是通过测量多个波长下的消光值来实现待测颗粒系粒径分布信息的重建。由于消光系数矩阵中核函数的剧烈振荡性，导致这类测量方法的数据处理中都会遇到第一类Fredholm积分方程的求解问题。这是一类典型的不适定问题，对此类问题进行理论求解具有相当大的困难。因此，发展快速有效的重建算法用于颗粒粒径测量一直受到国内外学者广泛的关注和重视。本课题受到国家自然科学基金资助(No.61071036)，研究目的是探索基于光谱消光法的准确快速重建算法，以解决目前该方法中存在的重建过程复杂、重建速度较慢以及重建结果不稳定等问题，以期使光谱消光法更加适合于颗粒粒径的在线测量。
本文首先针对颗粒粒径测量中多波长的最优选取问题进行研究。粒径分布重建过程中，每个波长下的消光值都不同程度包含关于待测颗粒粒径分布的信息。传统的粒径测量通常是在相对较窄光谱区域(如可见光谱区)内随机选取入射波长，这会对重建结果的准确度和抗噪声能力造成一定影响。此外，考虑到许多工业现场对快速性和简便性的高要求，必须选用少量且重要的特征波长用于粒径分布的重建。为此，本文依据不同波长消光系数间的关联程度，提出多光谱区间内分段最优波长的选取方法。在紫外-可见-近红外多光谱区域内分别选取各自区间内与所有波长的消光系数关联程度较高而彼此具有较小关联度的重要波长组合成全波段最优波长组进行颗粒粒径分布的重建。对于测量次数少于待测粒径间隔数而导致信息量不足的情况，该少量最优波长下的消光值包含了绝大部分的待测颗粒粒径信息，因而既保证了测量精度，又节省了整个粒径分布重建的计算时间。多光谱区分段最优波长选取方法为后续粒径分布重建中波长选取提供了理论依据。
光谱消光法粒径测量中，消光系数的计算是个关键问题，在很大程度上影响了粒径分布重建的快速性和准确性。本文针对球形颗粒和非球形颗粒消光系数的严格方法普遍存在理论复杂、计算繁琐、收敛速度较慢、易出现数值困难和解不稳定等问题，开展了基于近似方法的颗粒粒径分布快速重建的研究。提出将精确Mie理论与广义程函近似法相结合用于颗粒消光系数的计算，并在此基础上利用优化算法分别反演球形颗粒和椭球颗粒的粒径分布。采用组合近似方法计算的消光系数代替严格方法获得的消光系数，既可增大近似方法的适用范围，有效保证计算结果的准确性，又简化了颗粒消光系数的计算，从而降低了整个粒径分布重建过程的复杂性，提高了重建速度。组合的近似方法可作为当严格方法出现计算困难和数值不稳时的一种有效替代。
反演算法的合理设计和选用是保证实现准确快速粒径分布重建至关重要的一个环节。本文针对无函数限制模式下粒径分布反演算法尚处于发展阶段的研究现状，开展了反演算法用于准确快速颗粒粒径分布重建的研究。提出基于模式搜索的光谱消光粒径分布反演算法，同时引入Tikhonov平滑泛函构建算法的目标函数。为保证整个粒径分布重建的准确性和快速性，相应设计了关于模式搜索算法初始点的优选策略。在反演过程中，首先将粒径分布重建问题转化为最小化问题，Tikhonov平滑泛函用于该最小化问题的目标函数构建，在此基础上，应用改进模式搜索算法不断调节目标函数值直到满足设定的停止准则。模式搜索算法的突出优势是既不需要像很多传统方法那样计算梯度信息，也不像很多智能算法那样需要进行复杂的种群选择和变异，因而使反演计算更加简便高效。实验结果表明，改进模式搜索算法能够成功用于颗粒粒径分布的重建，具有很好的可靠性和稳定性。在综合考虑重建精度和重建时间的条件下，所提反演算法有一定优势，更适合于准确快速的颗粒粒径现场测量。
在理论分析和数值模拟的基础上，利用核工业北京化工冶金研究院提供的国家标准物质，分别对多光谱区分段最优波长的选取、基于广义程函近似的重建算法以及改进模式搜索反演算法用于颗粒粒径分布的重建进行了实测数据验证，并对实际粒径分布重建结果进行了分析和研究。实验验证了所提方法用于实际颗粒粒径分布重建的可行性和准确性。
With the rapid development of scientific field and the appearance of all kindsof new materials, there are more and more technical problems correlated withparticle issues, and the measurement of particle size distribution (PSD) has becomeone of the most important research fields. Among all the particle size measuringmethods, spectral extinction method is probably the most attractive one due to itstheoretical simplicity and convenience and its realization of measurement on micronor sub-micron particle systems. In particular, with the urgent demand for in situmeasurements of PSD, the spectral extinction method has shown greatdevelopments and potential applications.
In spectral extinction particle sizing method, the PSD can be retrieved by someinversion methods using the extinction values of multiple wavelengths. Owing toserious oscillation of the extinction efficiency, the data processing of this method isrelated to the solution of a Fredholm integral equation of the first kind. It is a wellknown typical ill-posed problem, and there are significant difficulties for solvingthe theoretical solution of this problem. Therefore, the development of rapid andefficient retrieval algorithms for recovering the PSD has received increasedattention and concerns by many researchers. This subject is supported by theNational Natural Science Foundation of China (No.61071036). The objective of thissubject is to investigate accurate and fast retrieval algorithms of PSD based on thespectral extinction method, which can solve the problems along with highcomplexity of whole retrieval process, low retrieval speed, and instability of theretrieval results, thus making the spectral extinction method more suitable foronline particle sizing.
This study is firstly focused on the selection of optimal wavelengths inmultispectral region. In the PSD retrieval process, the extinction values of eachincident wavelength may involve different amount of information about the PSD.The traditional measurement is performed only within a narrow spectral region (i.e.visible spectrum region), which may result in the decrease of accuracy andanti-noise effect of the retrieval results to some degree. Furthermore, consideringboth rapidity and simplicity in many practical industrial occasions, only limitedprincipal wavelengths can be chosen to deal in the data processing. Therefore,according to the degree of correlation for extinction efficiency of differentwavelengths, the method of sectional optimal wavelength selection in multispectralregion is presented. In the ultraviolet-visible-near-infrared spectrum region, theprincipal wavelengths selected in each spectrum region, which own high correlation of extinction efficiency with all other wavelengths and share low correlation ofextinction efficiency each other, constitute the whole optimum wavelengths ofmultispectral range to retrieve the PSD. For the case that the number of wavelengthsis less than particle subintervals which can result in the deficiency of information,the less optimum wavelengths involve most amount of information about the PSD,therefore the measuring accuracy can be effectively ensured and the computationtime of the whole retrieval can be significantly reduced. The method of sectionaloptimal wavelength selection in multispectral region offers the theorical basis forthe retrieval of PSD in succeeding chapters.
In spectral extinction particle sizing method, the calculation of extinctionefficiency is a critical issue which affects the accuracy and rapidity of the wholeretrieval. Aiming at overcoming complexity in theory, intricacy in calculation, lowconvergence speed, and instability for calculating the extinction efficiency ofspherical and spheroidal particles with rigorous methods, the approximate methodfor fast and accuracy retrieval is explored. The combination of Mie theory andgeneralized eikonal approximation (GEA) method is proposed in this paper tocalculate the extinction efficiency. Based on the extinction efficiency calculated bythe combined approximate method, the retrieval of PSD of spherical particles andspheroidal particles are then investigated. The combined approximate method, usedas an alternative to the rigorous Mie theory, not only can extend the applicablerange and guarantee the accuracy of the retrieval results, but also can simplify thecalculation process and improve the speed of the whole retrieval process. Theapproximate method can be used as an effective replacement when the rigoroussolutions suffer computational difficulties and numerical instability.
The design or selection of inversion methods is one of the most importantaspects of the whole retrieval which can guarantee to obtain accurate and fastretrieval results. Considering the inversion methods for the retrieval of PSD are stillin stage of development, this paper focuses on the study of inversion method. Thepattern search algorithm combined with the Tikhonov smoothing functional for thedetermination of PSD is proposed. To ensure good rapidity and accuracy of thewhole search process, a competitive strategy about the pattern search algorithm isalso designed. In the inversion process, the PSD retrieval problem is firstformulated as a minimization problem, with the Tikhonov smoothing functionalemployed in modeling the objective function, and then the improved pattern searchalgorithm is applied to adjust the objective function until a given stopping criterionhas been achieved. The pattern search algorithm does not require any gradientinformation like many traditional methods; also it does not require complexselection and mutation of populations like many intelligent optimization algorithms;therefore making the inversion process more convenient and efficient. Experimental results indicate that the proposed algorithm can be successfully applied to retrievethe PSD with high reliability and stability. In condition of fully considering retrievalprecision and retrieval time, the proposed inversion method has certain advantage,which is more suitable for accurate and quick field measurement of particle sizing.
Based on the theoretical analyses and numerical simulations, by using thestandard polystyrene samples offered by Beijing Institute of Nuclear Engineering,the three proposed methods, namely, the method of sectional optimal wavelengthselection in multispectral region, the retrieval algorithm of PSD based on the GEAmethod, the inversion method of improved pattern search algorithm for retrieval ofPSD, are further verified by the practical experimental data, and the retrieval resultsof PSD for standard polystyrene samples are also analyzed and studied. Theexperiments validate the feasibility and accuracy of the above proposed methods inpractical retrieval of PSD.
引文
[1]蔡小舒,苏明旭,沈建琪等.颗粒粒径测量技术及应用[M].北京：化学工业出版社,2010:1-19.
[2] Frontini G L, Elicabe G E. A Novel Methodology to Estimate the Particle SizeDistribution of Latex Using Relative Measurements of Elastic Light Scatteringand Turbidimetry[J]. Journal of Chemometrics,2000,14:51-61.
[3] Burr D W, Daun K J, Thomson K A, et al. Optimization of MeasurementAngles for Soot Aggregate Sizing by Elastic Light Scattering, ThroughDesign-of-Experiment Theory[J]. Journal of Quantitative Spectroscopy andRadiative Transfer,2012,113:355-365.
[4] Jagodnicka A K, Stacewicz T, Karasinski G, et al. Particle Size DistributionRetrieval from Multiwavelength Lidar Signals for Droplet Aerosol[J]. AppliedOptics,2009,48(4): B8-B16.
[5]沈建琪.光散射法测粒技术延伸测量下限的研究[D].上海：上海理工大学博士学位论文,1999:1-4.
[6] Cao Z, Xu L J, Ding J. Integral Inversion to Fraunhofer Diffraction forParticle Sizing[J]. Applied Optics,2009,48(25):4842-4850.
[7]徐峰,蔡小舒,苏明旭等.光谱消光法测量高压湿蒸汽的研究[J].动力工程,2009,29(3):254-260.
[8] Zhang X D, Twardowski M, Lewis M. Retrieving Composition and Sizes ofOceanic Particle Subpopulations from the Volume Scattering Function[J].Applied Optics,2011,50(9):1240-1259.
[9] Moulin F, Devel M, Picaud S. Optical Properties of Soot Nanoparticles[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2008,109:1791-1801.
[10]葛宝臻,马云峰,魏耀林.求解粒子群粒度分布的改进Projection算法[J].光学精密工程,2012,20(1):197-203.
[11]李亦军.基于Mie散射的微粒浓度和粒度测试的理论与实验研究[D].太原：中北大学博士学位论文,2005:1-5.
[12]胡松青,李琳,郭祀远等.现代颗粒粒度测量技术[J].现代化工,2002,22(1):58-61.
[13]王乃宁.颗粒粒径的光学测量技术及应用[M].北京：原子能出版社,2000:4-29.
[14]曾凡,胡永平.矿物加工颗粒学[M].北京：中国矿业大学出版社,1995:4-14.
[15] Yu A B, Standish N. A Study of Particle Size Distribution[J]. PowderTechnology,1990,62:101-118.
[16]李文凯,吴玉新,黄志民等.激光粒度分析和筛分法测粒径分布的比较[J].中国粉体技术,2007,13(5):10-14.
[17]钱效林,郝小勇,王荣杰.粒径测试技术及粒径分布对陶瓷生产的影响[J].佛山陶瓷,2002,3:4-6.
[18]邹涛,周素红,陈萦等.微纳粉体粒度测试方法简述[J].过程工程学报,2004,4(增刊1):9-14.
[19] Cheng W P, Yu R F, Hesieh Y J, et al. Prove the Relationship between ParticleSize and Turbidity Fluctuations by Image Analysis[C]. IADIS EuropeanConference Data Mining,2008:170-172.
[20]谭正立.炭素粉末颗粒粒度的测量方法及原理[J].炭素技术,1995,(1):36-39.
[21]吴和平,张宏,宋尚军等.玻璃微纤维直径分布测量新方法—重力沉降法实验初探[J].保温材料与节能技术,2002,(5):20-23.
[22]杨粉荣,文洪杰,钟勤.几种粒度测定方法的比较[J].物理测试,2005,23(5):36-39.
[23]谭立新,余志明,蔡一湘.激光粒度法测试结果与库尔特法、沉降法的比较[J].中国粉体技术,2009,15(3):60-63.
[24]沙菲.几种常用的粉体粒度测试方法[J].理化检验—物理分册,2012,48(6):374-377.
[25]张振中,白宏刚.颗粒粒径的光散射法测量研究[J].山西科技,2011,26(1):89-91.
[26] Ehrl L, Soos M, Morbidelli M. Sizing Polydisperse Dispersion by FocusedBeam Reflectance and Small Angle Static Light Scattering[J]. Particle andParticle Systems Characterization,2007,23(6):438-447.
[27] Igushi T, Yoshida H. Investigation of Low-Angle Laser Light ScatteringPatterns Using the Modified Twomey Iterative Method for Particle Sizing[J].Review of Scientific Instruments,2011,82:015111.
[28]杨福桂,王安廷,明海等.激光衍射粒径测量中的Chin-Shifrin反演算法[J].光学精密工程,2011,19(2):323-331.
[29] Vargas-Ubera J, Aguilar J F, Gale D M. Reconstruction of Particle-SizeDistributions from Light-Scattering Patterns Using Three InversionMethods[J]. Applied Optics,2007,46(1):124-132.
[30] Gauardani R, Nascimento C, Onimaru R S. Use of Neural Networks in theAnalysis of Particle Size Distribution by Laser Diffraction: Tests withDifferent Particle Systems[J]. Powder Technology,2002,126:42-50.
[31] Wang N N, Wei J M, Hong C Y, et al. Influence of Refractive Index on ParticleSize Analysis Using the Turbidimetric Spectrum Method[J]. Particle andParticle Systems Characterization,1996,13:238-244.
[32] Oshchepkov S L, Sinyuk A F. Optical Sizing of Ultrafine Metallic Particles:Retrieval of Particle Size Distribution from Spectral ExtinctionMeasurements[J]. Journal of Colloid and Interface Science,1998,208:137-146.
[33] Ren K F, Xu F, Cai X S, et al. Development of a Precise and in Situ TurbidityMeasurement System[J]. Chemical Engineering Communications,2010,197:250-259.
[34] Kim I S, Kim Y, Lim H B. Turbidimetric Measurement for On-LineMonitoring of SiO2Particles[J]. Bulletion of the Korean Chemical Society,2004,25(6):801-805.
[35]王刚.用于纳米颗粒粒度测量的模拟探测动态光散射技术研究[D].长春：吉林大学博士学位论文,2006:47-51.
[36] Liu X Y, Shen J, Thomas J C, et al. Multiangle Dynamic Light ScatteringAnalysis Using a Modified Chahine Method[J]. Journal of QuantitativeSpectroscopy and Radiative Transfer,2012,113:489-497.
[37]张明信,魏建维,王晓霞等.固体推进剂燃烧中凝相粒子激光全息测试[J].固体火箭技术,2000,23(1):70-74.
[38]王清华.光散射法颗粒大小与形状分析[D].南京：南京工业大学博士学位论文,2003:4-7.
[39] Meyer S, Berrut S, Goodenough T I, et al. A Comparative Study of Ultrasoundand Laser Light Diffraction Techniques for Particle Size Determination inDairy Beverages[J]. Measurement Science and Technology,2006,17:289-297.
[40]陈宁,果晶晶,宫惠峰.纳米颗粒粒度测量方法进展[J].现代科学仪器,2012,(2):160-163.
[41] Wales M. Particle Size Distribution in Rubber Latex[J]. Journal of PhysicsChemistry.1962,66:1768-1772.
[42] Hodkinson J R. The Optical Measurement of Aerosols[J]. Aerosol ScienceAcademic,1966:287-357.
[43] Kiparssides C. Modelling and Experimental Studies of a Continuous EmulsionPolymerization Reactor[D]. McMaster University, Hmailton, Ontario, Canda,Ph.D Thesis.1978:9-15.
[44] Wyler J S. Moisture Measurement in a Low-Pressure Steam Turbine UsingLaser Light Scattering Probe[J]. Transactions of the ASME: Journal ofEngineering for Power,1978:1-7.
[45] Kourti T. Ploymer Latexes: Production by Homogeneous Concentrations andMethods for Particle Size Distrimination[D]. McMaster University, Hamilton,Ontario, Canada, Ph.D Thesis.1989:13-33.
[46] Perelman A Y. Extinction and Scattering by Soft Spheres[J]. Applied Optics,1991,30(4):475-484.
[47] Ramachandran G, Leith D. Extraction of Aerosol-Size Distribution fromMultispectral Light Extinction Data[J]. Aerosol Science and Technology,1992,17:303-325.
[48] Ferri F, Bassini A, Paganini E. Modified Version of the Chahine Algorithm toInvert Spectral Extinction Data for Particle Sizing[J]. Applied Optics,1995,34(25):5829-5839.
[49] Ligon D A, Chen T W, Gillespie J B. Determination of Aerosol Parametersfrom Light-Scattering Data Using an Inverse Monte Carlo Technique[J].Applied Optics,1996,35(21):4297-4303.
[50] Raphael M, Rohani S. On-Line Estimation of Solids Concentrations and MeanParticle Size Using a Turbidimetry Method[J]. Powder Technology,1996,89:157-163.
[51] Crawley G, Cournil M, Benedetto D D. Size Analysis of Fine ParticleSuspensions by Spectral Turbidimetry: Potential and Limits[J]. PowderTechnology,1997,91:197-208.
[52] Llosent M A. The Effect of Light Absorption of Particle and Medium on theParticle Size Estimation by Turbidimetry[J]. Journal of Optics A: Pure andApplied Optics,1999,1:590-600.
[53] Kandlikar M, Ramachandran G. Inverse Methods for Analysing AerosolSpectrometer Measurements: A Critical Review[J]. Journal of Aerosol Science,1999,30(4):413-437.
[54] Gordon S, Hammond R, Roberts K, et al. In-Process Particle Characterizationby Spectral Extinction[J]. Trans IChemE,2000,78:1147-1152.
[55] Marioth E, Koenig B, Krause H, et al. Fast Particle Size and Droplet SizeMeasurement in Supercritical CO2[J]. Industrial and Engineering ChemistryResearch,2000,39:4853-4857.
[56] Franssens G R. Retrieval of the Aerosol Size Distribution in the ComplexAnomalous Diffraction Approximation[J]. Atmospheric Environment,2001,35:5099-5104.
[57] Li M Z, Wilkinson D. Particle Size Distribution Determination from SpectralExtinction Using Evolutionary Programming[J]. Chemical EngineeringScience,2001,56:3045-3052.
[58] Vega J R, Frontini G L, Gugliotta L M, et al. Particle Size Distribution byCombined Elastic Light Scattering and Turbidity Measurements: A NovelMethod to Estimate the Required Normalization Factor[J]. Particle andParticle Systems Characterization,2003,20:361-369.
[59] Kocifaj M, Horvath H. Retrieval of Size Distribution for Urban AerosolsUsing Multispectral Optical Data[J]. Journal of Physics: Conference Series,2005,6:97-102.
[60] Dubovik O, Sinyuk A, Lapyonok T, et al. Application of Spheroid Models toAccount for Aerosol Particle Nonsphericity in Remote Sensing of DesertDust[J]. Journal of Geophysical Research-Atmospheres,2006,111(11):11208-11210.
[61] Wagner R, Benz S, Mohler O, et al. Influence of Particle Aspect Ratio on theMidinfrared Extinction Spectra of Wavelength-Sized Ice Crystals[J]. Journalof Physics Chemistry,2007,111:13003-13022.
[62] Zasetsky A Y, Earle M E, Cosic B. Retrieval of Aerosol Physical and ChemicalProperties from Mid-Infrared Extinction Spectra[J]. Journal of QuantitativeSpectroscopy and Radiative Transfer,2007,107:294-305.
[63] Herman B R, Gross B, Moshary F, et al. Bayesian Assessment of Uncertaintyin Aerosol Size Distributions and Index of Refraction Retrieved fromMultiwavelength Lidar Measurements[J]. Applied Optics,2008,47(10):1617-1627.
[64] Schmidt K, Wauer J, Rother T, et al. Scattering Database for SpheroidalParticles[J]. Applied Optics,2009,48(11):2154-2164.
[65] Erlick C, Haspel M, Rudich Y. Simultaneous Retrieval of the ComplexRefractive Indices of the Core and Shell of Coated Aerosol Particles fromExtinction Measurements[J]. Applied Optics,2011,50(22):4393-4402.
[66] Devore J G. The Truncated Geometric Approximation and the SizeDistribution of Small Atmospheric Particles[J]. Journal of Atmospheric andOceanic Technology,2011,28:779-786.
[67] Mroczka J, Szczuczynski D. Simultaneous Research on Improved RegularizedSolution of the Inverse Problem in Spectral Extinction Measurements[J].Applied Optics,2012,51(11):1715-1723.
[68]顾冠亮,王乃宁.有关光散射的物理量的数值计算[J].上海机械学院学报,1984,5(4):21-33.
[69]王乃宁.用光学探针测量汽轮机内的蒸汽湿度和水滴直径[J].工程热物理学报,1985,6(1):99-103.
[70]庄锦祥,沈小康,林之融.光学水蒸汽测量仪的校验方法研究[J].厦门大学学报(自然科学版),1986,25(2):159-164.
[71]王乃宁.光学全散射微粒测量方法的改进和发展[J].上海机械学院学报,1987,9(4):7-16.
[72]王乃宁,郑刚,蔡小舒. TSM型全散射式细微颗粒测量仪[J].粉体技术,1996,2(1):40-47.
[73]王少清,任中京,张希明等. Mie散射系数的新算法[J].激光杂志,1997,18(3):9-14.
[74]朱震,王式民,叶茂等.前向光散射粒子消光测量的校正[J].激光杂志,1998,19(6):32-35.
[75]郑刚,李孟超,黄廷磊等.多波长消光测粒技术的一种改进方法[J].光学仪器,2000,20(2):252-256.
[76]王建萍,张以谟,李贺桥. Projection算法在粒子尺寸测量中的实验研究[J].天津大学学报,2000,33(4):460-463.
[77]赵建华,袁宏永,刘申友等.多波长激光全散射法探测火灾烟雾的研究[J].应用激光,2001,21(2):79-81.
[78]余荣斌,何振江,余勇昌.利用散射光信息提高消光法粉尘浓度测量的精度[J].光电工程,2002,29(1):52-54.
[79]任智斌,卢振武,刘玉玲.旋转微椭球体光散射的研究[J].光电子激光,2003,14(11):1196-1199.
[80]徐峰,蔡小舒,苏明旭等.独立模式算法求解颗粒粒径分布的研究[J].中国激光,2004,31(2):223-228.
[81]苏明旭,任宽芳, Grehan G等.光复散射对消光法粒径测量的影响:复散射模型与数值模拟[J].光学学报,2004,24(5):696-699.
[82]严建华,黄群星,马增益等.遗传算法用于颗粒粒度分布重建的研究[J].计量学报,2005,26(1):86-89.
[83]菅立川,齐宏,阮立明等.微粒群算法反演粒径分布的研究[J].节能技术,2007,25:7-9.
[84]齐宏,王希影,刘兵等.反演非球形粒子光学常数的理论建模[J].工程热物理学报,2009,30(5):837-840.
[85]刘涛,左浩毅.遗传算法反演气溶胶粒径分布计算模拟研究[J].光散射学报,2009,21(4):332-334.
[86]赵剑琦.非吸收椭球形粒子尺度分布反演的一种新方法[J].中国科学院研究生院学报,2010,27(3):323-330.
[87]李耀东,张启兴,邓小玖等.基于模拟退火的火灾烟颗粒粒径反演[J].中国激光,2011,38(1):0108005.
[88]赵俊杰,段远源,王晓东等.红外遮光剂颗粒的光学和辐射特性分析[J].热科学与技术,2012,11(4):283-288.
[89] Zege E P, Katsev I L, Prikhach A S, et al. Simple Model of the OpticalCharacteristics of Bubbles and Sediments in Seawater of the Surf Zone[J].Applied Optics,2006,45(25):6577-6585.
[90] Kerker M. The Scattering of Light and Other Electromagnetic Radiation[M].New York: Academic Press,1969:27-44.
[91] Mishchenko M I, Travis L D, Mackowski D W. T-matrix Method and ItsApplications to Electromagnetic Scattering by Particles: A CurrentPerspective[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2010,111(11):1700-1703.
[92] Bohren C F and Huffman D R. Absorption and Scattering of Light by Smallparticles[M]. John Wiley&Sons Inc.,1998:1-46.
[93] Ye M, Wang S M, Lu Y, et al. Inversion of Particle-Size Distribution fromAngular Light-Scattering Data with Genetic Algorithms[J]. Applied Optics,1999,38(12):2677-2685.
[94] Wiscombe W J. Improved Mie Scattering Algorithms[J]. Applied Optics,1980,19(9):1505-1509.
[95] Yadav M K, Sharma S K. On the Validity of Rayleigh-Gans-Debye TypeApproximations in Red Blood Cell Size Determination[J]. Journal of ModernOptics,2008,55(6):921-929.
[96] Ackerman S A, Stephens G L. The Absorption of Solar Radiation by CloudDroplets: An Application of Anomalous Diffraction Theory[J]. Journal of theAtmospheric Sciences,1987,44(12):1574-1588.
[97] Franssens G, Maziere M D, Fonteyn D. Determination of the Aerosol SizeDistribution by Analytic Inversion of the Extinction Spectrum in the ComplexAnomalous Diffraction Approximation[J]. Applied Optics,2000,39(24):4214-4231.
[98]徐峰,蔡小舒,沈嘉祺.米氏理论的近似及在粒度测量中的应用[J].光学学报,2003,23(12):1464-1469.
[99] Felidj N, Aubard J, Levi G. Discrete Dipole Approximation forUltraviolet-Visible Extinction Spectra Simultation of Silver and GoldColloids[J]. Journal of Chemical Physics1999,111(3):1195-1208.
[100]石广玉.大气辐射学[M].北京：科学出版社,2007:29-41.
[101] Voshchinnikov N V, Farafonov V G. Optical Properties of SpheroidalParticles[J]. Astrophysics and Space Science,1993,204:19-86.
[102] Wriedt T. Light Scattering Theories and Computer Codes[J]. Journal ofQuantitative Spectroscopy and Radiative Transfer,2009,110:833-843.
[103] Mishchenko M I, Travis L D, Lacis A A. Scattering, Absorption and Emissionof Light by Small Particles[M]. UK: Cambridge University Press,2006:191-223.
[104]王燕民,陈琪星,潘志东.激光粒度测量的综合反演及参数选择[J].光学精密工程,2009,17(9):2120-2127.
[105] Su M X, Xu F, Cai X S, et al. Optimization of Regularization Parameter ofInversion in Particle Sizing Using Light Extinction Method[J]. ChinaParticuology,2007,5:295-299.
[106] Zuo H Y, Liu Q J, Wang J Y, et al. Technique to Improve the Accuracy of theRetrieval of Aerosol Size-Distribution[J]. Optics Letters,2010,35(9):1380-1382.
[107]苏明旭,王夕华,黄有贵等. LM优化算法在消光法测粒技术中的应用[J].仪器仪表学报,2005,26(8):63-65.
[108]张启兴.火灾烟雾颗粒散射矩阵模拟测量与粒径折射率反演研究[D].合肥：中国科学技术大学博士学位论文,2011:71-76.
[109] Xu F, Cai X S, Ren K F, et al. Application of Genetic Algorithm in ParticleSize Analysis by Multispectral Extinction Measurements[J]. ChinaParticuology,2004,2(6):235-240.
[110]刘铁英,范利民,郑刚.用双Rosin-Rammler函数求颗粒尺寸分布[J].上海理工大学学报,1998,20(2):135-138.
[111] Pahlow M, Muller D, Tesche M, et al. Retrieval of Aerosol Properties fromCombined Multiwavelength Lidar and Sunphotometer Measurements[J].Applied Optics,2006,45(28):7429-7442.
[112] Sun Z G, Sevick-Muraca E M. Inversion Algorithms for Particle Sizing withPhoto Migration Measurement[J]. AIChE Journal,2001,47(7):1487-1498.
[113]李绍新.动态光散射测量粒径分布的格雷码编码遗传算法反演运算[J].计算物理,2008,25(3):323-329.
[114] Barkey B, Kim H, Paulson S E. Genetic Algorithm Retrieval of RealRefractive Index from Aerosol Distributions That Are Not Lognormal[J].Aerosol Science and Technology,2010,44:1089-1095.
[115] Ma L, Hanson R K. Measurement of Aerosol Size Distribution Functions byWavelength-Multiplexed Laser Extinction[J]. Applied Physics B,2005,81:567-576.
[116] Yang P, Feng Q, Hong G, et al. Modeling of the Scattering and RadiativeProperties of Nonspherical Dust-Like Aerosols[J]. Aerosol Science,2007,38:995-1014.
[117] Wielaard D J, Mishchenko M I, Macke A, et al. Improved T-matrixComputations for Large, Nonabsorbing and Weakly Absorbing NonsphericalParticles and Comparison with Geometrical-Optics Approximation[J]. AppliedOptics,1997,36(18):4305-4313.
[118] Jalava J P, Taavitsainen V M, Haario H, et al. Determination of Particle andCrystal Size Distribution from Turbidity Spectrum of TiO2Pigments by Meansof T-matrix[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,1998,60(3):399-409.
[119] Sharma S K and Somerford D J. Light Scattering by Optically Soft Particles:Theory and Applications[M]. Springer-Praxis,2006:17-88.
[120] Chen T W. High Energy Light Scattering in the Generalized EikonalApproximation[J]. Applied Optics,1989,28(19):4096-4102.
[121] Yang L M. The GEA Method for Light Scattering by Dielectric Spheroids andEllipsoids with Fixed and Random Orientations[D]. New Mexico StateUniversity, Las Cruces, New Mexico, Ph.D Thesis.1999:5-11.
[122] Fournier G R, Evans B T N. Approximation to Extinction Efficiency forRandomly Oriented Spheroids[J]. Applied Optics,1991,30(15):2042-2048.
[123] Veihelmann B, Konert M, van der Zande W J. Size Distribution of MineralAerosol: Using Light-Scattering Models in Laser Particle Sizing[J]. AppliedOptics,2006,45(23):6022-6029.
[124] Schulz F M, Stamnes K, Stamnes J J. Scattering of Electromagnetic Waves bySpheroidal Particles: A Novel Approach Exploiting the T Matrix Computed inSpheroidal Coordinates[J]. Applied Optics,1998,37(33):7875-7896.
[125] Tabtabai H A, Alex A P. Using Genetic Algorithms to Solve OptimizationProblems in Construction[J]. Engineering Construction and ArchitecturalManagement,1999,6(2):121-132.
[126] Clementi L A, Vega J R, Gugliotta L M. Particle Size Distribution ofMultimodal Polymer Dispersions by Multiangle Dynamic Light ScatteringSolution of the Inverse Problem on the Basis of a Genetic Algorithm[J].Particle and Particle Systems Characterization,2010,27:146-157.
[127] Riefler N, Wriedt T. Intercomparison of Inversion Algorithms forParticle-Sizing Using Mie Scattering[J]. Particle and Particle SystemsCharacterization,2008,25:216-230.
[128] Mroczka J, Szczuczynski D. Inversion Problems Formulated in Terms ofFirst-Kind Fredholm Integral Equations in Indirect Measurements[J].Metrology and Measurement Systems,2009,3:333-357.
[129]邵阳,王清华.平滑Chahine迭代算法在光散射法粒度分布反演中应用[J].南京晓庄学院学报,2008,6:15-18.
[130]彭真明.地震反演中的非线性优化方法及应用研究[D].成都：成都理工学院博士学位论文,2001:11-40.
[131] Mera N S, Elliott L, Ingham D B. A Multi-Population Genetic AlgorithmApproach for Solving Ill-Posed Problems[J]. Inversion Problem inEngineering,2009,17(4):437-449.
[132] Ma L, Kranendonk L, Cai W W, et al. Application of Simulated Annealing forSimultaneous Retrieval of Particle Size Distribution and Refractive Index[J].Aerosol Science,2009,40:588-596.
[133]刘晓东,王英立,戴景民.基于SPSO算法的粒子群粒径分布反演[J].激光与红外,2008,38(8):813-817.
[134] Berdnik V V, Loiko V A. Retrieval of Size and Refractive Index of SphericalParticles by Multiangle Light Scattering: Neural Network MethodApplication[J]. Applied Optics,2009,48(32):6178-6187.
[135]郑小平,陈增强.模式搜索算法在毒气泄漏中的源强反算[J].中国安全科学学报,2010,20(5):29-34.
[136]黄天云.约束优化模式搜索法研究进展[J].计算机学报,2008,31(7):1200-1215.
[137] Audet C, Dennis J E. Pattern Search Algorithms for Mixed VariableProgramming[J]. SIAM Journal of Optimization,2000,11(3):573-594.
[138] Torczon V. On the Convergence of Pattern Search Algorithms[J]. SIAMJournal of Optimization,1997,7(1):1-25.
[139] Gunes F, Tokan F. Amplitude-Only Pattern Synthesis of Nonuniform LinearArrays Using a Generalized Pattern Search Optimization[J]. InternationalJournal of RF and Microwave Computer-Aided Engineering,2011,21(3):251-262.
[140] Arias M L, Frontini G L. Particle Size Distribution Retrieval from ElasticLight Scattering Measurements by a Modified Regularization Method[J].Particle and Particle Systems Characterization,2006,23:374-380.
[141] Doicu A, Trautmann T, Schreier F. Numerical Regularization for AtmosphericInverse Problems[M]. Springer-Praxis,2010:163-220.
[142] Samarskii A A, Vabishchevich P N. Numerical Methods for Solving InverseProblems of Mathematical Physics[M]. Berlin: Walter de Gruyter GmbH&Co.,2007:240-257.
[2] Frontini G L, Elicabe G E. A Novel Methodology to Estimate the Particle SizeDistribution of Latex Using Relative Measurements of Elastic Light Scatteringand Turbidimetry[J]. Journal of Chemometrics,2000,14:51-61.
[3] Burr D W, Daun K J, Thomson K A, et al. Optimization of MeasurementAngles for Soot Aggregate Sizing by Elastic Light Scattering, ThroughDesign-of-Experiment Theory[J]. Journal of Quantitative Spectroscopy andRadiative Transfer,2012,113:355-365.
[4] Jagodnicka A K, Stacewicz T, Karasinski G, et al. Particle Size DistributionRetrieval from Multiwavelength Lidar Signals for Droplet Aerosol[J]. AppliedOptics,2009,48(4): B8-B16.
[5]沈建琪.光散射法测粒技术延伸测量下限的研究[D].上海：上海理工大学博士学位论文,1999:1-4.
[6] Cao Z, Xu L J, Ding J. Integral Inversion to Fraunhofer Diffraction forParticle Sizing[J]. Applied Optics,2009,48(25):4842-4850.
[7]徐峰,蔡小舒,苏明旭等.光谱消光法测量高压湿蒸汽的研究[J].动力工程,2009,29(3):254-260.
[8] Zhang X D, Twardowski M, Lewis M. Retrieving Composition and Sizes ofOceanic Particle Subpopulations from the Volume Scattering Function[J].Applied Optics,2011,50(9):1240-1259.
[9] Moulin F, Devel M, Picaud S. Optical Properties of Soot Nanoparticles[J].Journal of Quantitative Spectroscopy and Radiative Transfer,2008,109:1791-1801.
[10]葛宝臻,马云峰,魏耀林.求解粒子群粒度分布的改进Projection算法[J].光学精密工程,2012,20(1):197-203.
[11]李亦军.基于Mie散射的微粒浓度和粒度测试的理论与实验研究[D].太原：中北大学博士学位论文,2005:1-5.
[12]胡松青,李琳,郭祀远等.现代颗粒粒度测量技术[J].现代化工,2002,22(1):58-61.
[13]王乃宁.颗粒粒径的光学测量技术及应用[M].北京：原子能出版社,2000:4-29.
[14]曾凡,胡永平.矿物加工颗粒学[M].北京：中国矿业大学出版社,1995:4-14.
[15] Yu A B, Standish N. A Study of Particle Size Distribution[J]. PowderTechnology,1990,62:101-118.
[16]李文凯,吴玉新,黄志民等.激光粒度分析和筛分法测粒径分布的比较[J].中国粉体技术,2007,13(5):10-14.
[17]钱效林,郝小勇,王荣杰.粒径测试技术及粒径分布对陶瓷生产的影响[J].佛山陶瓷,2002,3:4-6.
[18]邹涛,周素红,陈萦等.微纳粉体粒度测试方法简述[J].过程工程学报,2004,4(增刊1):9-14.
[19] Cheng W P, Yu R F, Hesieh Y J, et al. Prove the Relationship between ParticleSize and Turbidity Fluctuations by Image Analysis[C]. IADIS EuropeanConference Data Mining,2008:170-172.
[20]谭正立.炭素粉末颗粒粒度的测量方法及原理[J].炭素技术,1995,(1):36-39.
[21]吴和平,张宏,宋尚军等.玻璃微纤维直径分布测量新方法—重力沉降法实验初探[J].保温材料与节能技术,2002,(5):20-23.
[22]杨粉荣,文洪杰,钟勤.几种粒度测定方法的比较[J].物理测试,2005,23(5):36-39.
[23]谭立新,余志明,蔡一湘.激光粒度法测试结果与库尔特法、沉降法的比较[J].中国粉体技术,2009,15(3):60-63.
[24]沙菲.几种常用的粉体粒度测试方法[J].理化检验—物理分册,2012,48(6):374-377.
[25]张振中,白宏刚.颗粒粒径的光散射法测量研究[J].山西科技,2011,26(1):89-91.
[26] Ehrl L, Soos M, Morbidelli M. Sizing Polydisperse Dispersion by FocusedBeam Reflectance and Small Angle Static Light Scattering[J]. Particle andParticle Systems Characterization,2007,23(6):438-447.
[27] Igushi T, Yoshida H. Investigation of Low-Angle Laser Light ScatteringPatterns Using the Modified Twomey Iterative Method for Particle Sizing[J].Review of Scientific Instruments,2011,82:015111.
[28]杨福桂,王安廷,明海等.激光衍射粒径测量中的Chin-Shifrin反演算法[J].光学精密工程,2011,19(2):323-331.
[29] Vargas-Ubera J, Aguilar J F, Gale D M. Reconstruction of Particle-SizeDistributions from Light-Scattering Patterns Using Three InversionMethods[J]. Applied Optics,2007,46(1):124-132.
[30] Gauardani R, Nascimento C, Onimaru R S. Use of Neural Networks in theAnalysis of Particle Size Distribution by Laser Diffraction: Tests withDifferent Particle Systems[J]. Powder Technology,2002,126:42-50.
[31] Wang N N, Wei J M, Hong C Y, et al. Influence of Refractive Index on ParticleSize Analysis Using the Turbidimetric Spectrum Method[J]. Particle andParticle Systems Characterization,1996,13:238-244.
[32] Oshchepkov S L, Sinyuk A F. Optical Sizing of Ultrafine Metallic Particles:Retrieval of Particle Size Distribution from Spectral ExtinctionMeasurements[J]. Journal of Colloid and Interface Science,1998,208:137-146.
[33] Ren K F, Xu F, Cai X S, et al. Development of a Precise and in Situ TurbidityMeasurement System[J]. Chemical Engineering Communications,2010,197:250-259.
[34] Kim I S, Kim Y, Lim H B. Turbidimetric Measurement for On-LineMonitoring of SiO2Particles[J]. Bulletion of the Korean Chemical Society,2004,25(6):801-805.
[35]王刚.用于纳米颗粒粒度测量的模拟探测动态光散射技术研究[D].长春：吉林大学博士学位论文,2006:47-51.
[36] Liu X Y, Shen J, Thomas J C, et al. Multiangle Dynamic Light ScatteringAnalysis Using a Modified Chahine Method[J]. Journal of QuantitativeSpectroscopy and Radiative Transfer,2012,113:489-497.
[37]张明信,魏建维,王晓霞等.固体推进剂燃烧中凝相粒子激光全息测试[J].固体火箭技术,2000,23(1):70-74.
[38]王清华.光散射法颗粒大小与形状分析[D].南京：南京工业大学博士学位论文,2003:4-7.
[39] Meyer S, Berrut S, Goodenough T I, et al. A Comparative Study of Ultrasoundand Laser Light Diffraction Techniques for Particle Size Determination inDairy Beverages[J]. Measurement Science and Technology,2006,17:289-297.
[40]陈宁,果晶晶,宫惠峰.纳米颗粒粒度测量方法进展[J].现代科学仪器,2012,(2):160-163.
[41] Wales M. Particle Size Distribution in Rubber Latex[J]. Journal of PhysicsChemistry.1962,66:1768-1772.
[42] Hodkinson J R. The Optical Measurement of Aerosols[J]. Aerosol ScienceAcademic,1966:287-357.
[43] Kiparssides C. Modelling and Experimental Studies of a Continuous EmulsionPolymerization Reactor[D]. McMaster University, Hmailton, Ontario, Canda,Ph.D Thesis.1978:9-15.
[44] Wyler J S. Moisture Measurement in a Low-Pressure Steam Turbine UsingLaser Light Scattering Probe[J]. Transactions of the ASME: Journal ofEngineering for Power,1978:1-7.
[45] Kourti T. Ploymer Latexes: Production by Homogeneous Concentrations andMethods for Particle Size Distrimination[D]. McMaster University, Hamilton,Ontario, Canada, Ph.D Thesis.1989:13-33.
[46] Perelman A Y. Extinction and Scattering by Soft Spheres[J]. Applied Optics,1991,30(4):475-484.
[47] Ramachandran G, Leith D. Extraction of Aerosol-Size Distribution fromMultispectral Light Extinction Data[J]. Aerosol Science and Technology,1992,17:303-325.
[48] Ferri F, Bassini A, Paganini E. Modified Version of the Chahine Algorithm toInvert Spectral Extinction Data for Particle Sizing[J]. Applied Optics,1995,34(25):5829-5839.
[49] Ligon D A, Chen T W, Gillespie J B. Determination of Aerosol Parametersfrom Light-Scattering Data Using an Inverse Monte Carlo Technique[J].Applied Optics,1996,35(21):4297-4303.
[50] Raphael M, Rohani S. On-Line Estimation of Solids Concentrations and MeanParticle Size Using a Turbidimetry Method[J]. Powder Technology,1996,89:157-163.
[51] Crawley G, Cournil M, Benedetto D D. Size Analysis of Fine ParticleSuspensions by Spectral Turbidimetry: Potential and Limits[J]. PowderTechnology,1997,91:197-208.
[52] Llosent M A. The Effect of Light Absorption of Particle and Medium on theParticle Size Estimation by Turbidimetry[J]. Journal of Optics A: Pure andApplied Optics,1999,1:590-600.
[53] Kandlikar M, Ramachandran G. Inverse Methods for Analysing AerosolSpectrometer Measurements: A Critical Review[J]. Journal of Aerosol Science,1999,30(4):413-437.
[54] Gordon S, Hammond R, Roberts K, et al. In-Process Particle Characterizationby Spectral Extinction[J]. Trans IChemE,2000,78:1147-1152.
[55] Marioth E, Koenig B, Krause H, et al. Fast Particle Size and Droplet SizeMeasurement in Supercritical CO2[J]. Industrial and Engineering ChemistryResearch,2000,39:4853-4857.
[56] Franssens G R. Retrieval of the Aerosol Size Distribution in the ComplexAnomalous Diffraction Approximation[J]. Atmospheric Environment,2001,35:5099-5104.
[57] Li M Z, Wilkinson D. Particle Size Distribution Determination from SpectralExtinction Using Evolutionary Programming[J]. Chemical EngineeringScience,2001,56:3045-3052.
[58] Vega J R, Frontini G L, Gugliotta L M, et al. Particle Size Distribution byCombined Elastic Light Scattering and Turbidity Measurements: A NovelMethod to Estimate the Required Normalization Factor[J]. Particle andParticle Systems Characterization,2003,20:361-369.
[59] Kocifaj M, Horvath H. Retrieval of Size Distribution for Urban AerosolsUsing Multispectral Optical Data[J]. Journal of Physics: Conference Series,2005,6:97-102.
[60] Dubovik O, Sinyuk A, Lapyonok T, et al. Application of Spheroid Models toAccount for Aerosol Particle Nonsphericity in Remote Sensing of DesertDust[J]. Journal of Geophysical Research-Atmospheres,2006,111(11):11208-11210.
[61] Wagner R, Benz S, Mohler O, et al. Influence of Particle Aspect Ratio on theMidinfrared Extinction Spectra of Wavelength-Sized Ice Crystals[J]. Journalof Physics Chemistry,2007,111:13003-13022.
[62] Zasetsky A Y, Earle M E, Cosic B. Retrieval of Aerosol Physical and ChemicalProperties from Mid-Infrared Extinction Spectra[J]. Journal of QuantitativeSpectroscopy and Radiative Transfer,2007,107:294-305.
[63] Herman B R, Gross B, Moshary F, et al. Bayesian Assessment of Uncertaintyin Aerosol Size Distributions and Index of Refraction Retrieved fromMultiwavelength Lidar Measurements[J]. Applied Optics,2008,47(10):1617-1627.
[64] Schmidt K, Wauer J, Rother T, et al. Scattering Database for SpheroidalParticles[J]. Applied Optics,2009,48(11):2154-2164.
[65] Erlick C, Haspel M, Rudich Y. Simultaneous Retrieval of the ComplexRefractive Indices of the Core and Shell of Coated Aerosol Particles fromExtinction Measurements[J]. Applied Optics,2011,50(22):4393-4402.
[66] Devore J G. The Truncated Geometric Approximation and the SizeDistribution of Small Atmospheric Particles[J]. Journal of Atmospheric andOceanic Technology,2011,28:779-786.
[67] Mroczka J, Szczuczynski D. Simultaneous Research on Improved RegularizedSolution of the Inverse Problem in Spectral Extinction Measurements[J].Applied Optics,2012,51(11):1715-1723.
[68]顾冠亮,王乃宁.有关光散射的物理量的数值计算[J].上海机械学院学报,1984,5(4):21-33.
[69]王乃宁.用光学探针测量汽轮机内的蒸汽湿度和水滴直径[J].工程热物理学报,1985,6(1):99-103.
[70]庄锦祥,沈小康,林之融.光学水蒸汽测量仪的校验方法研究[J].厦门大学学报(自然科学版),1986,25(2):159-164.
[71]王乃宁.光学全散射微粒测量方法的改进和发展[J].上海机械学院学报,1987,9(4):7-16.
[72]王乃宁,郑刚,蔡小舒. TSM型全散射式细微颗粒测量仪[J].粉体技术,1996,2(1):40-47.
[73]王少清,任中京,张希明等. Mie散射系数的新算法[J].激光杂志,1997,18(3):9-14.
[74]朱震,王式民,叶茂等.前向光散射粒子消光测量的校正[J].激光杂志,1998,19(6):32-35.
[75]郑刚,李孟超,黄廷磊等.多波长消光测粒技术的一种改进方法[J].光学仪器,2000,20(2):252-256.
[76]王建萍,张以谟,李贺桥. Projection算法在粒子尺寸测量中的实验研究[J].天津大学学报,2000,33(4):460-463.
[77]赵建华,袁宏永,刘申友等.多波长激光全散射法探测火灾烟雾的研究[J].应用激光,2001,21(2):79-81.
[78]余荣斌,何振江,余勇昌.利用散射光信息提高消光法粉尘浓度测量的精度[J].光电工程,2002,29(1):52-54.
[79]任智斌,卢振武,刘玉玲.旋转微椭球体光散射的研究[J].光电子激光,2003,14(11):1196-1199.
[80]徐峰,蔡小舒,苏明旭等.独立模式算法求解颗粒粒径分布的研究[J].中国激光,2004,31(2):223-228.
[81]苏明旭,任宽芳, Grehan G等.光复散射对消光法粒径测量的影响:复散射模型与数值模拟[J].光学学报,2004,24(5):696-699.
[82]严建华,黄群星,马增益等.遗传算法用于颗粒粒度分布重建的研究[J].计量学报,2005,26(1):86-89.
[83]菅立川,齐宏,阮立明等.微粒群算法反演粒径分布的研究[J].节能技术,2007,25:7-9.
[84]齐宏,王希影,刘兵等.反演非球形粒子光学常数的理论建模[J].工程热物理学报,2009,30(5):837-840.
[85]刘涛,左浩毅.遗传算法反演气溶胶粒径分布计算模拟研究[J].光散射学报,2009,21(4):332-334.
[86]赵剑琦.非吸收椭球形粒子尺度分布反演的一种新方法[J].中国科学院研究生院学报,2010,27(3):323-330.
[87]李耀东,张启兴,邓小玖等.基于模拟退火的火灾烟颗粒粒径反演[J].中国激光,2011,38(1):0108005.
[88]赵俊杰,段远源,王晓东等.红外遮光剂颗粒的光学和辐射特性分析[J].热科学与技术,2012,11(4):283-288.
[89] Zege E P, Katsev I L, Prikhach A S, et al. Simple Model of the OpticalCharacteristics of Bubbles and Sediments in Seawater of the Surf Zone[J].Applied Optics,2006,45(25):6577-6585.
[90] Kerker M. The Scattering of Light and Other Electromagnetic Radiation[M].New York: Academic Press,1969:27-44.
[91] Mishchenko M I, Travis L D, Mackowski D W. T-matrix Method and ItsApplications to Electromagnetic Scattering by Particles: A CurrentPerspective[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,2010,111(11):1700-1703.
[92] Bohren C F and Huffman D R. Absorption and Scattering of Light by Smallparticles[M]. John Wiley&Sons Inc.,1998:1-46.
[93] Ye M, Wang S M, Lu Y, et al. Inversion of Particle-Size Distribution fromAngular Light-Scattering Data with Genetic Algorithms[J]. Applied Optics,1999,38(12):2677-2685.
[94] Wiscombe W J. Improved Mie Scattering Algorithms[J]. Applied Optics,1980,19(9):1505-1509.
[95] Yadav M K, Sharma S K. On the Validity of Rayleigh-Gans-Debye TypeApproximations in Red Blood Cell Size Determination[J]. Journal of ModernOptics,2008,55(6):921-929.
[96] Ackerman S A, Stephens G L. The Absorption of Solar Radiation by CloudDroplets: An Application of Anomalous Diffraction Theory[J]. Journal of theAtmospheric Sciences,1987,44(12):1574-1588.
[97] Franssens G, Maziere M D, Fonteyn D. Determination of the Aerosol SizeDistribution by Analytic Inversion of the Extinction Spectrum in the ComplexAnomalous Diffraction Approximation[J]. Applied Optics,2000,39(24):4214-4231.
[98]徐峰,蔡小舒,沈嘉祺.米氏理论的近似及在粒度测量中的应用[J].光学学报,2003,23(12):1464-1469.
[99] Felidj N, Aubard J, Levi G. Discrete Dipole Approximation forUltraviolet-Visible Extinction Spectra Simultation of Silver and GoldColloids[J]. Journal of Chemical Physics1999,111(3):1195-1208.
[100]石广玉.大气辐射学[M].北京：科学出版社,2007:29-41.
[101] Voshchinnikov N V, Farafonov V G. Optical Properties of SpheroidalParticles[J]. Astrophysics and Space Science,1993,204:19-86.
[102] Wriedt T. Light Scattering Theories and Computer Codes[J]. Journal ofQuantitative Spectroscopy and Radiative Transfer,2009,110:833-843.
[103] Mishchenko M I, Travis L D, Lacis A A. Scattering, Absorption and Emissionof Light by Small Particles[M]. UK: Cambridge University Press,2006:191-223.
[104]王燕民,陈琪星,潘志东.激光粒度测量的综合反演及参数选择[J].光学精密工程,2009,17(9):2120-2127.
[105] Su M X, Xu F, Cai X S, et al. Optimization of Regularization Parameter ofInversion in Particle Sizing Using Light Extinction Method[J]. ChinaParticuology,2007,5:295-299.
[106] Zuo H Y, Liu Q J, Wang J Y, et al. Technique to Improve the Accuracy of theRetrieval of Aerosol Size-Distribution[J]. Optics Letters,2010,35(9):1380-1382.
[107]苏明旭,王夕华,黄有贵等. LM优化算法在消光法测粒技术中的应用[J].仪器仪表学报,2005,26(8):63-65.
[108]张启兴.火灾烟雾颗粒散射矩阵模拟测量与粒径折射率反演研究[D].合肥：中国科学技术大学博士学位论文,2011:71-76.
[109] Xu F, Cai X S, Ren K F, et al. Application of Genetic Algorithm in ParticleSize Analysis by Multispectral Extinction Measurements[J]. ChinaParticuology,2004,2(6):235-240.
[110]刘铁英,范利民,郑刚.用双Rosin-Rammler函数求颗粒尺寸分布[J].上海理工大学学报,1998,20(2):135-138.
[111] Pahlow M, Muller D, Tesche M, et al. Retrieval of Aerosol Properties fromCombined Multiwavelength Lidar and Sunphotometer Measurements[J].Applied Optics,2006,45(28):7429-7442.
[112] Sun Z G, Sevick-Muraca E M. Inversion Algorithms for Particle Sizing withPhoto Migration Measurement[J]. AIChE Journal,2001,47(7):1487-1498.
[113]李绍新.动态光散射测量粒径分布的格雷码编码遗传算法反演运算[J].计算物理,2008,25(3):323-329.
[114] Barkey B, Kim H, Paulson S E. Genetic Algorithm Retrieval of RealRefractive Index from Aerosol Distributions That Are Not Lognormal[J].Aerosol Science and Technology,2010,44:1089-1095.
[115] Ma L, Hanson R K. Measurement of Aerosol Size Distribution Functions byWavelength-Multiplexed Laser Extinction[J]. Applied Physics B,2005,81:567-576.
[116] Yang P, Feng Q, Hong G, et al. Modeling of the Scattering and RadiativeProperties of Nonspherical Dust-Like Aerosols[J]. Aerosol Science,2007,38:995-1014.
[117] Wielaard D J, Mishchenko M I, Macke A, et al. Improved T-matrixComputations for Large, Nonabsorbing and Weakly Absorbing NonsphericalParticles and Comparison with Geometrical-Optics Approximation[J]. AppliedOptics,1997,36(18):4305-4313.
[118] Jalava J P, Taavitsainen V M, Haario H, et al. Determination of Particle andCrystal Size Distribution from Turbidity Spectrum of TiO2Pigments by Meansof T-matrix[J]. Journal of Quantitative Spectroscopy and Radiative Transfer,1998,60(3):399-409.
[119] Sharma S K and Somerford D J. Light Scattering by Optically Soft Particles:Theory and Applications[M]. Springer-Praxis,2006:17-88.
[120] Chen T W. High Energy Light Scattering in the Generalized EikonalApproximation[J]. Applied Optics,1989,28(19):4096-4102.
[121] Yang L M. The GEA Method for Light Scattering by Dielectric Spheroids andEllipsoids with Fixed and Random Orientations[D]. New Mexico StateUniversity, Las Cruces, New Mexico, Ph.D Thesis.1999:5-11.
[122] Fournier G R, Evans B T N. Approximation to Extinction Efficiency forRandomly Oriented Spheroids[J]. Applied Optics,1991,30(15):2042-2048.
[123] Veihelmann B, Konert M, van der Zande W J. Size Distribution of MineralAerosol: Using Light-Scattering Models in Laser Particle Sizing[J]. AppliedOptics,2006,45(23):6022-6029.
[124] Schulz F M, Stamnes K, Stamnes J J. Scattering of Electromagnetic Waves bySpheroidal Particles: A Novel Approach Exploiting the T Matrix Computed inSpheroidal Coordinates[J]. Applied Optics,1998,37(33):7875-7896.
[125] Tabtabai H A, Alex A P. Using Genetic Algorithms to Solve OptimizationProblems in Construction[J]. Engineering Construction and ArchitecturalManagement,1999,6(2):121-132.
[126] Clementi L A, Vega J R, Gugliotta L M. Particle Size Distribution ofMultimodal Polymer Dispersions by Multiangle Dynamic Light ScatteringSolution of the Inverse Problem on the Basis of a Genetic Algorithm[J].Particle and Particle Systems Characterization,2010,27:146-157.
[127] Riefler N, Wriedt T. Intercomparison of Inversion Algorithms forParticle-Sizing Using Mie Scattering[J]. Particle and Particle SystemsCharacterization,2008,25:216-230.
[128] Mroczka J, Szczuczynski D. Inversion Problems Formulated in Terms ofFirst-Kind Fredholm Integral Equations in Indirect Measurements[J].Metrology and Measurement Systems,2009,3:333-357.
[129]邵阳,王清华.平滑Chahine迭代算法在光散射法粒度分布反演中应用[J].南京晓庄学院学报,2008,6:15-18.
[130]彭真明.地震反演中的非线性优化方法及应用研究[D].成都：成都理工学院博士学位论文,2001:11-40.
[131] Mera N S, Elliott L, Ingham D B. A Multi-Population Genetic AlgorithmApproach for Solving Ill-Posed Problems[J]. Inversion Problem inEngineering,2009,17(4):437-449.
[132] Ma L, Kranendonk L, Cai W W, et al. Application of Simulated Annealing forSimultaneous Retrieval of Particle Size Distribution and Refractive Index[J].Aerosol Science,2009,40:588-596.
[133]刘晓东,王英立,戴景民.基于SPSO算法的粒子群粒径分布反演[J].激光与红外,2008,38(8):813-817.
[134] Berdnik V V, Loiko V A. Retrieval of Size and Refractive Index of SphericalParticles by Multiangle Light Scattering: Neural Network MethodApplication[J]. Applied Optics,2009,48(32):6178-6187.
[135]郑小平,陈增强.模式搜索算法在毒气泄漏中的源强反算[J].中国安全科学学报,2010,20(5):29-34.
[136]黄天云.约束优化模式搜索法研究进展[J].计算机学报,2008,31(7):1200-1215.
[137] Audet C, Dennis J E. Pattern Search Algorithms for Mixed VariableProgramming[J]. SIAM Journal of Optimization,2000,11(3):573-594.
[138] Torczon V. On the Convergence of Pattern Search Algorithms[J]. SIAMJournal of Optimization,1997,7(1):1-25.
[139] Gunes F, Tokan F. Amplitude-Only Pattern Synthesis of Nonuniform LinearArrays Using a Generalized Pattern Search Optimization[J]. InternationalJournal of RF and Microwave Computer-Aided Engineering,2011,21(3):251-262.
[140] Arias M L, Frontini G L. Particle Size Distribution Retrieval from ElasticLight Scattering Measurements by a Modified Regularization Method[J].Particle and Particle Systems Characterization,2006,23:374-380.
[141] Doicu A, Trautmann T, Schreier F. Numerical Regularization for AtmosphericInverse Problems[M]. Springer-Praxis,2010:163-220.
[142] Samarskii A A, Vabishchevich P N. Numerical Methods for Solving InverseProblems of Mathematical Physics[M]. Berlin: Walter de Gruyter GmbH&Co.,2007:240-257.