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Ren Shenhe, Gao Ming, Wang Mingjun, Bao Xiujuan, Li Yan. Scattering properties of non-spherical cluster core-shell structure particle laser[J]. Infrared and Laser Engineering, 2020, 49(9): 20190545. doi: 10.3788/IRLA20190545
Citation: Ren Shenhe, Gao Ming, Wang Mingjun, Bao Xiujuan, Li Yan. Scattering properties of non-spherical cluster core-shell structure particle laser[J]. Infrared and Laser Engineering, 2020, 49(9): 20190545. doi: 10.3788/IRLA20190545

Scattering properties of non-spherical cluster core-shell structure particle laser

doi: 10.3788/IRLA20190545
  • Received Date: 2019-12-04
  • Rev Recd Date: 2020-01-28
  • Available Online: 2020-09-22
  • Publish Date: 2020-09-22
  • On the basis of heterogeneous nucleation theory of ice crystal particles, three types of ice crystal particle models were established with nucleation-shell structures of ellipsoid, hexagonal flat plate and hexagonal prism. The extinction, absorption and scattering efficiency of these three special cluster-shaped core-shell structures were numerically calculated by discrete dipole approximation (DDA) method. Under the same incident wavelength, the effect of effective size on the extinction efficiency, absorption efficiency and scattering efficiency of core-shell ice crystal particles, the influence of the intermediate uniform mixing layer on the scattering intensity of core-shell ice crystal particles, and the variation of Mueller matrix elements with the scattering angle were calculated. The numerical results show that the extinction coefficient, absorption coefficient and scattering coefficient of ice crystallites with three clusters of ellipsoidal, hexagonal and hexagonal prisms show different trends with the increase of effective size. Under the condition of equal size, the scattering intensity with the change of the scattering angle and particle shape have close relations, and compared with the ellipsoid and hexagonal flat two cluster core-shell structure of ice crystal particles, core-shell structure of ice crystal particles hexagonal prisms forward scattering intensity, the largest scattering intensity curve along with the change of the scattering angle oscillation is more obvious. According to the distribution of the Mueller matrix elements with the scattering angle, it can be seen that the scattering direction of the hexagonal prism cluster ice crystal structure is the most obvious, and the forward scattering intensity is the largest. The Mueller matrix elements of the hexagonal plate and hexagonal prism cluster ice crystal structure are relatively spherical and the deviation of the ellipsoid in the backscattered field area is more obvious. The research results of the thesis provide support for further analysis of the scattering characteristics of complex ice crystal particles, and the research and analysis of the scattering characteristics of various complex geometric clusters of ice crystal particles in high-altitude clouds.
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Scattering properties of non-spherical cluster core-shell structure particle laser

doi: 10.3788/IRLA20190545
  • 1. School of Optoelectronic Engineering, Xi'an Technological University Xi’an 710021, China
  • 2. School of Physics and Electronic Engineering, Xianyang Normal University, Xianyang 712000, Shaanxi, China
  • 3. Institute of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China

Abstract: On the basis of heterogeneous nucleation theory of ice crystal particles, three types of ice crystal particle models were established with nucleation-shell structures of ellipsoid, hexagonal flat plate and hexagonal prism. The extinction, absorption and scattering efficiency of these three special cluster-shaped core-shell structures were numerically calculated by discrete dipole approximation (DDA) method. Under the same incident wavelength, the effect of effective size on the extinction efficiency, absorption efficiency and scattering efficiency of core-shell ice crystal particles, the influence of the intermediate uniform mixing layer on the scattering intensity of core-shell ice crystal particles, and the variation of Mueller matrix elements with the scattering angle were calculated. The numerical results show that the extinction coefficient, absorption coefficient and scattering coefficient of ice crystallites with three clusters of ellipsoidal, hexagonal and hexagonal prisms show different trends with the increase of effective size. Under the condition of equal size, the scattering intensity with the change of the scattering angle and particle shape have close relations, and compared with the ellipsoid and hexagonal flat two cluster core-shell structure of ice crystal particles, core-shell structure of ice crystal particles hexagonal prisms forward scattering intensity, the largest scattering intensity curve along with the change of the scattering angle oscillation is more obvious. According to the distribution of the Mueller matrix elements with the scattering angle, it can be seen that the scattering direction of the hexagonal prism cluster ice crystal structure is the most obvious, and the forward scattering intensity is the largest. The Mueller matrix elements of the hexagonal plate and hexagonal prism cluster ice crystal structure are relatively spherical and the deviation of the ellipsoid in the backscattered field area is more obvious. The research results of the thesis provide support for further analysis of the scattering characteristics of complex ice crystal particles, and the research and analysis of the scattering characteristics of various complex geometric clusters of ice crystal particles in high-altitude clouds.

    • 激光在高空云层冰晶粒子中的传输与散射特性研究最早从经典的Mie理论球形[1]、椭球形冰晶粒子的散射特性研究开始,随后越来越多的学者开展了更为复杂的几何形状冰晶粒子散射特性的研究。通过查阅文献发现:(1)国外冰晶粒子散射特征的研究有从气象学或者大气科学角度开展的,如美国加州大学Kuo-Nan Liou教授和美国德州农工大学Yang Ping教授等人领导的团队所做的工作[2];(2)从物理和数学方法上研究不同粒子形状、不同介电常数、磁导率与不同光束相互作用的散射特征,如Mishchenko, M.I.和Gérard Gouesbet等人所做的工作[3]。目前,学者对规则冰晶粒子如球、椭球、圆柱和椭圆柱的研究已经趋于成熟,但是对任意形状冰晶粒子如各种簇团粒子、含核粒子、多粒子体系的散射特征研究较少。

      事实上,自然界冰晶粒子的结构中,壳形结构冰晶粒子是冰晶粒子一种重要的结构形式,其散射特性研究对了解高空云层的辐射传输特性至关重要。Yang对空心冰球和烟煤包裹冰晶两种壳形结构冰晶粒子的散射特性分析结果表明:壳形结构冰晶粒子的散射特性与内外层介质的折射率以及尺寸大小等有关。Raisanen[4]与Yang的研究不同,他考虑到了可溶性H2SO4/H2O气溶胶涂层对于壳形结构冰晶粒子散射特性的影响,张晋源[5]和陈洪滨[6]两人都考虑到了气温对于冰晶的影响,建立了水包冰的双层壳形结构冰晶粒子模型。分析了入射光波长以及内外层冰−水壳层结构冰晶粒子散射特性的影响情况,参考文献[6]主要比较了纯水、纯冰和冰−水壳层结构3种粒子的散射情况。这些研究都没有考虑到冰晶异质核化生成机制对于核壳结构冰晶粒子散射特性的影响。Sassen和Kenneth[7]通过实验验证了气溶胶粒子引起高空云层异质核化冰晶的形成过程,他们的研究结果表明:非洲北部获取的粉尘粒子对该地区高空的冰云形成过程产生了非常大的影响。

      然而,高空中冰云的形成很大程度上受沙尘等形成的气溶胶粒子的影响[8],甚至改变该地区的环境与气候。目前的研究中涉及到壳层结构冰晶粒子的散射特性,缺乏对异质核化的核壳结构冰晶粒子散射特性的研究,且壳形结构都是理想化的模型,无法体现特殊形状(非球形簇团粒子等)粒子对散射特性的影响。

      文中以空地链路激光通信中冰晶粒子对激光的衰减性为研究背景,簇团核壳结构冰晶粒子为研究对象,研究高空云层中核壳结构冰晶粒子的激光散射特性,建立了3种不同形状(椭球、六角平板和六角棱柱)的簇团型核壳结构冰晶粒子模型,分析了粒子形状、粒子有效尺寸、粒子内部分布结构对散射效率和Mueller矩阵元素的影响情况,为进一步研究更为复杂结构冰晶粒子的散射特性提供理论支持。

    • 1973年,由Purcell和Pennypacke[9]提出了离散偶极子近似(Discrete Dipole Approximation,DDA)方法,后经发展成为了一种能对任意几何形状、非均匀和各向异性粒子光散射进行计算的方法,从而被广泛应用于大气气溶胶、水滴、冰晶等粒子的光学散射特征的研究上。相较于Mie理论应用于多层球的散射计算,DDA法更精确地用于复杂核壳结构粒子的散射计算,特别是针对非球形核壳结构粒子的散射有一定的计算优势。离散偶极子近似的基本思想就是将目标散射体用有限个离散且相互作用的偶极子阵列来替代,以其中任何一个点对局域电场的响应获来取偶极矩,这些点的辐射总和就构成了总的散射场[10]。假设第$j$个偶极子取自于${r_j}\left( {j = 1,2,...,N} \right)$,偶极子的极化率为${\alpha _j}$,若电场设为${E_j}$,偶极矩${P_j}$,则极化强度可表示为:

      式中:${E_j}$为入射场${E_{inc,j}}$${r_j}$处总的散射场;系数${A_{jk}}$是一个$3 \times 3$矩阵,表达式有:

      式中:${r_{jk}} = \left| {{r_j} - {r_k}} \right|$${\hat r_{jk}} = \left( {{r_j} - {r_k}} \right)/{r_{jk}}$$k = {{2{\text{π}} } / \lambda }$$\lambda $为入射光波长;${I_3}$$3 \times 3$的单位矩阵。在离散偶极子近似法的计算中,解出参量${P_k}$后就可求解簇团核壳粒子所有的散射参量。

    • 冰晶粒子的核壳结构会对冰晶粒子的消光、吸收和散射效率产生影响。通过对云层的监测发现,云层底部烟煤粒子、沙尘粒子、水溶性粒子以及海洋性粒子是冰晶异质核化的主要成分[11],尤其是烟煤粒子作为晶核介质时吸收效率最为显著。为研究这四种粒子作为核壳介质时非球形簇团粒子的散射特性,文中以烟煤粒子作为核壳介质,建立了如图1(c)、(d)、(e)所示的椭球形、六角平板和六角棱柱3种特殊核壳结构冰晶粒子模型,分别是由图(a)和图(b)构成的不同粒子形状。

      Figure 1.  Three special core-shell structure ice crystal submodels

      设核壳结构冰晶粒子的内外层折射率分别为${n_1}$${n_2}$,利用参考文献[12]中计算均匀混合光学介质膜的折射率公式,得到簇团核壳结构冰晶粒子中间均匀混合层的折射率计算公式:

      式中:${n_x}$${n_y}$分别为不考虑介质吸收性的核壳结构冰晶粒子的内外层介质折射率,即${n_x} = {\rm{Re}} \left( {{n_1}} \right)$${n_y} = {\rm{Re}} \left( {{n_2}} \right)$;其中有${k_x} = \dfrac{{{n_x}}}{{\left( {{n_x} + {n_y}} \right)}}$${k_y} = \dfrac{{{n_y}}}{{\left( {{n_x} + {n_y}} \right)}}$

      文中设入射波长$\lambda = 1.06\;{\text{μ}} {\rm m}$,烟煤、冰晶两种介质的折射率分别为${n_1} = 1.75 + 0.44i$${n_2} = 1.300\;5 + 1.69 \times {10^{ - 6}}i$,计算可得烟煤−冰晶2种介质的中间混合层折射率为$n = 1.566\;4$

    • 自然界中冰晶粒子形状不一、结构复杂,多数学者研究不规则粒子以椭球、六角平板、六角棱柱形状为主[13-14]。为了解激光在簇团核壳结构冰晶粒子中的散射特性受粒子形状及粒子密度的影响情况,基于Cluster-Cluster Aggregation (CCA)模型[15],建立了如图2所示的6种特殊簇团形核壳结构的冰晶粒子模型。模型主要选取2个粒子和10个粒子组成的簇团形结构,各簇团形冰晶粒子模型是模拟近似椭球形、六角平板和六角棱柱形状的特定形状。在同一形状的结构模型中,单个核壳结构中冰晶粒子的偶极子个数相同,粒子的空间分布也相同。

      Figure 2.  Schematic diagram of 6 kinds of agglomerated nucleation core-shell structure ice crystal grains

      其中,簇团结构中单个冰晶粒子的核壳结构由4部分组成,从外到内分别为真空介质、冰晶、中间混合层和晶核。其中$R$$r$$d$分别表示核壳结构冰晶粒子的粒子半径、晶核半径、中间混合层厚度。如图3所示。

      Figure 3.  Core-shell structure composed of ice crystal grains

      自然界中簇团粒子的空间取向是随机的,对于随机取向的簇团粒子缪勒矩阵元素的统计平均值可以用公式(4)给出[16]

      式中:$\left\langle {{S_{{{ij}}}}} \right\rangle$为簇团粒子某缪勒矩阵元素的统计平均值;${S_{ij}}\left( {\beta ,\varTheta ,\varPhi } \right)$为系统坐标中某特定取向簇团粒子缪勒矩阵元素值,$\beta ,\varTheta ,\varPhi$为空间方位角。理论上讲,方位角的取值应该尽可能地取尽所有的值,但是受计算条件限制,文中的计算方案均取了1 000个方位角,即方位角${{{n}}_\beta },{{{n}}_\varTheta },{{{n}}_\varPhi }$分别取10,10,10,选取方位角的个数满足计算要求[17]

    • 由公式(1)解出参量${P_k}$后,就可计算出偶极子的电偶极矩${P_j}$,相应就可计算出核壳结构粒子的消光截面${C_{\rm ext}}$、散射截面${C_{\rm sca}}$和吸收截面${C_{\rm abs}}$[18-19]

      吸收截面${C_{\rm abs}}$计算公式为:

      散射截面${C_{\rm sca}}$计算公式为:

      消光截面${C_{\rm ext}}$计算公式:

      由此可得相应的吸收效率因子、散射效率因子、消光效率因子的计算公式。

      式中:$\hat n$为单位散射矢量;*为取复数的共轭;${a_{\rm eff}}$为粒子的等效半径;$\rm{d}\varOmega$为立体角微分量。为研究DDA计算中散射光强随入射光强的变化情况,得到入射光强和散射光强[20]的计算公式为:

      式中:${S_{11}}$为一个散射矩阵元素;$x = k{a_{\rm eff}}$$k = 2{\text{π}} /\lambda$$\lambda $为入射波长,${a_{\rm eff}}$为有效半径:

      式中:$V$为目标散射体的体积。散射振幅矩阵元素为:

      散射特性可用入射参数(${I_i},{Q_i},{U_i},{V_i}$)和散射参数(${I_s},{Q_s},{U_s},{V_s}$)的Mueller散射矩阵来描述,计算公式如下:

      式中:4×4矩阵为散射矩阵,Muller散射矩阵中各元素${S_{ij}}$由公式(12)给出。

      粒子的Muller散射矩阵由16个元素组成,它们体现了散射体所有的散射特性和极化特性,对于随机取向具有某种对称性的粒子,缪勒矩阵中有8个元素不为零,有${S_{21}} = {S_{12}},{S_{43}} = - {S_{34}}$,因此只有6个矩阵元是独立的,分别由振幅散射矩阵的4个元素的模和它们之间的相位差决定,另外${S_{22}}$${S_{11}}$${S_{44}}$${S_{33}}$的变化趋势相似,所以散射矩阵只有4个独立的矩阵元[21]。散射特性用入射参数(${I_i},{Q_i},{U_i},{V_i}$)和散射参数(${I_s},{Q_s},{U_s},{V_s}$)的Mueller散射矩阵来描述。

      矩阵元素${S_{11}}$反映总的入射场强度在散射发生前后的变化情况;${{{S_{12}}} / {{S_{11}}}}$表示平行和垂直于散射平面的线性极化程度;${{{S_{33}}} / {{S_{11}}}}$描述线性极化入射光($\pm {45^{\rm o}}$)相对于线性极化的散射光($\pm {45^{\rm o}}$)的变化情况;${{{S_{34}}} / {{S_{11}}}}$描述圆极化入射光($\pm {90^{\rm o}}$)相对于圆极化的散射光($\pm {90^{\rm o}}$)的变化情况。

    • 根据图2建立的6种簇团形核壳结构冰晶粒子模型,数值计算了同一入射波长下,有效尺寸对核壳结构冰晶粒子消光、吸收和散射效率的影响、中间均匀混合层对核壳结构冰晶粒子散射强度的影响以及冰晶粒子形状对Mueller矩阵元素的影响。

    • 取入射波长$\lambda = 1.06\;\;{\text{μ}} {\rm m}$,单个椭球形核壳结构冰晶粒子尺寸、晶核以及中间混合层厚度满$a:b:r:d = 8:4:2:1$,单个六角平板和六角棱柱的尺寸与晶核比$L:r:d = 10:5:2$图4给出了粒子有效尺寸${a_{\rm eff}} = {\lambda / {100}}\;{\text{μ}} {\rm m}$增加到${a_{\rm eff}} = \lambda \;{\text{μ}} {\rm m}$时,3种形状冰晶粒子的消光效率因子、吸收效率因子和散射效率因子的变化情况。

      Figure 4.  Extinction coefficient, absorption coefficient and scattering coefficient of ice crystallites in three clusters of nucleate shell structures are affected by effective size

      比较图4中的椭球、六角平板和六角棱柱3种形状簇团核壳结构冰晶粒子的消光效率、吸收效率和散射效率变化情况,是否考虑中间混合层结构对吸收效率均无明显的影响。不考虑中间混合层时,吸收效率变化不明显是由于晶核体积占总体积比例较小;考虑中间混合层吸收效率变化不明显是由于在求解中间均匀混合层折射率时未考虑折射率的虚部。但是,是否考虑中间混合层结构对簇团核壳冰晶粒子的消光和散射效率影响较大。比较图4(a)、(b),随着有效尺寸增大,粒子的消光效率和散射效率呈现递增变化。并且有效尺寸在${\lambda / 5}\;{\text{μ}} {\rm m}$${{4\lambda } / 5}\;{\text{μ}} {\rm m}$之间时考虑中间混合层的消光和散射效率均大于不考虑中间混合层的情况。比较图4(c)、(d),考虑中间混合层簇团核壳冰晶粒子的散射和消光效率曲线几乎重合,并且有效尺寸为${\lambda / 2}\;{\text{μ}} {\rm m}$时取得极大值,这是由于晶核尺寸较小,六角平板核壳结构冰晶粒子的衰减主要由散射引起。比较图4(e)、(f),六角棱柱簇团核壳结构冰晶粒子的消光和散射效率随有效尺寸的增加均呈现递增趋势,但是两者的差异较小。

    • 入射波长$\lambda = 1.06\;{\text{μ}} {\rm m}$,取粒子有效尺寸${a_{\rm eff}} = {\lambda / 4}\;{\text{μ}} {\rm m}$,单个椭球形核壳结构冰晶粒子尺寸、晶核以及中间混合层厚度满足$a:b:r:d = 8:4:2:1$,单个六角平板和六角棱柱的尺寸与晶核比$L:r:d = 10:5:2$

      图5给出了理想($d = 0\;{\text{μ}} {\rm m}$)和考虑中间混合层两种情况下,椭球形、六角平板和六角棱柱3种形状的簇团形核壳结构冰晶粒子散射强度随散射角度的变换情况。比较图5(a)、(b),考虑中间混合层椭球簇团形核壳结构冰晶粒子的散射强度大于不考虑中间混合层时的散射强度,随着散射角度增大,散射强度呈现递减变化且散射角度在$\theta = {145^ \circ }$附近取极小值。2个和10个椭球簇团形核壳结构冰晶粒子的散射特性曲线变化趋势基本一致,此时可以忽略粒子密度对椭球簇团形核壳结构冰晶粒子的消光、吸收和散射效率的影响。比较图5(c)、(d),2个六角平板簇团形核壳结构冰晶粒子的前、后向散射强度小,且2个六角平板簇团形核壳结构冰晶粒子的散射方向性更明显,后向散射强度更小。这是因为在同一有效尺寸下,10个六角平板簇团形核壳结构冰晶粒子模型的粒子密度大于2个六角平板簇团形核壳结构冰晶粒子模型的粒子密度,导致激光在10个六角平板簇团形冰晶粒子内部的光散射更强。比较图5(e)、( f),随着散射角度的增大,2个六角棱柱和10个六角棱柱簇团形核壳结构冰晶粒子的散射强度在相同散射角度处都出现了两个极小值和一个极大值。

      Figure 5.  Scattering intensity of ice crystallites in three clusters of nucleate shell structures is affected by the intermediate mixed layer

      因此,相同尺寸条件下,椭球簇团形核壳结构冰晶粒子的散射方向性较差,六角棱柱簇团形核壳结构冰晶粒子的散射方向性更明显,并且六角棱柱簇团形核壳结构冰晶粒子的散射强度随散射角度的分布最复杂。

    • 入射波长$\lambda = 1.06\;{\text{μ}} {\rm m}$,取粒子有效尺寸半径为${a_{\rm eff}} = {\lambda / 4}\;{\text{μ}} {\rm m}$,单个球形核壳结构冰晶粒子的粒子尺寸和中间混合层厚度比满足$R:r:d = 4:2:1$,单个椭球形粒子满足$a:b:r:d = 8:4:2:1$,单个六角平板和六角棱柱核壳结构粒子满足$L:r:d = 10:5:2$。为研究冰晶粒子形状对Mueller矩阵元素的影响,图6分别给出了图2所示的六种特殊簇团形核壳结构冰晶粒子的Mueller矩阵元素${S_{11}}$${{{S_{12}}} / {{S_{11}}}}$${{{S_{33}}} / {{S_{11}}}}$${{{S_{34}}} / {{S_{11}}}}$随散射角度的变化情况。

      Figure 6.  Relationship between the elements of the Mueller matrix and the scattering angle of six special agglomerated nucleation shell structures

      图6可知,6种簇团形核壳结构冰晶粒子的Mueller矩阵元素${S_{11}}$只在前向散射区域(${0^ \circ }$~${60^ \circ }$)有明显变化,对后向散射影响不大;但是Mueller矩阵元素${{{S_{12}}} / {{S_{11}}}}$${{{S_{33}}} / {{S_{11}}}}$${{{S_{34}}} / {{S_{11}}}}$在前向区域变化不显著,在后向散射区域均出现了脉冲式的突变,出现极大值,振荡现象明显。随着粒子形状和粒子密度的变化,Mueller矩阵元素角分布曲线的振荡程度也发生了明显的变化。图6(a)中六角棱柱形簇团核壳结构冰晶粒子的前向散射比例大于椭球形前向散射比例。进一步说明六角棱柱形结构的散射方向性更好。图6(b)中椭球和六角棱柱簇团形核壳结构冰晶粒子的Mueller矩阵元素${{{S_{12}}} / {{S_{11}}}}$在散射角度为$\theta = {120^ \circ }$$\theta = {140^ \circ }$的偏差达到最大值。而六角平板形粒子的Mueller矩阵元素${{{S_{12}}} / {{S_{11}}}}$只在后向散射区域出现偏差。图6(c)中6种簇团形冰晶粒子的Mueller矩阵元素${{{S_{33}}} / {{S_{11}}}}$在后向散射区域(散射角度${100^ \circ } < \theta < {180^ \circ }$范围内)变化明显,特别是椭球和六角平板簇团形核壳结构冰晶粒子Mueller矩阵元素${{{S_{33}}} / {{S_{11}}}}$在后向散射区域的偏差最大,分别出现峰值。图6(d)中6种簇团形核壳结构冰晶粒子的Mueller矩阵元素${{{S_{34}}} / {{S_{11}}}}$散射在整个区域变化不是特别明显,只是分别在后向散射场区域(散射角度${90^ \circ } < \theta < {180^ \circ }$范围内)出现突变。造成上述现象可能与簇团粒子的形状,粒子的密度,簇团粒子的有效直径、粒子的取向比等因素有关,造成上述现象的原因下一步作深入研究。

    • 利用离散偶极子近似法数值模拟了激光在多种簇团形核壳结构冰晶粒子中的散射特性,分析了簇团形核壳结构冰晶粒子消光效率、吸收效率和散射效率随有效尺寸的变换关系,比较了同一尺寸下,3种形状的簇团形核壳结构冰晶粒子的散射强度以及Mueller矩阵元素随散射角度的变化情况。研究结果表明,椭球形、六角平板和六角棱柱3种簇团形核壳结构冰晶粒子的消光效率、吸收效率和散射效率随着有效尺寸的增大分别呈现不同的变化趋势;同一尺寸下,散射强度随散射角度的变化情况与粒子形状有密切关系,且相比于椭球形和六角平板两种簇团形核壳结构冰晶粒子,六角棱柱核壳结构冰晶粒子的散射方向性更明显;根据Mueller矩阵元素随散射角度的分布情况,可以确定粒子个数以及空间分布对簇团形核壳结构冰晶粒子散射特性影响较大,尤其是对于复杂形状的簇团形核壳结构冰晶粒子影响要更显著。

      文中的下一步工作是开展任意不规则形状核壳结构冰晶粒子的激光散射特性研究,考虑簇团粒子的随机分布、整体的空间取向、粒子的个数、取向比、粒子间隙等因素对簇团粒子整体散射特性的影响。论文的工作对开展高空云层复杂冰晶粒子的激光传输与散射特性有重要的意义。

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