A Review of Infrared Spectrum Modeling Based on Convolutional Neural Networks
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摘要: 红外光谱技术存在着数据预处理复杂、预测精度不高,且难以处理大量非线性数据的问题,适于用卷积神经网络进行处理。本文首先分析了卷积神经网络应用在红外光谱上的优点,并对卷积神经网络结构组成进行简单的概述。然后针对卷积神经网络在光谱分析建模中的输入数据维度问题进行详细阐述;针对模型设计中卷积核参数的影响、多任务处理模型以及训练过程中的优化方法进行综述。最后分析了该研究的优点与不足,并展望了未来的发展趋势。Abstract: Convolutional neural networks are used to solve problems such as complex data preprocessing, low prediction accuracy, and difficulty in dealing with a large amount of nonlinear data in infrared spectroscopy. Moreover, owing to their strong feature extraction ability and good nonlinear expression ability, the application of convolutional neural networks in the modeling of infrared spectrum analysis has attracted attention. In this study, the advantages of the application of a convolutional neural network for the infrared spectrum are analyzed, and the structure and composition of the convolutional neural network are briefly summarized. Then, the dimension problem of the input data in the spectral analysis modeling of the convolutional neural network is described in detail. This paper reviews the influence of convolution kernel parameters in the model design, multi-task processing model, and optimization methods in the training process. Finally, the advantages and disadvantages of this research are analyzed, and future development trends are discussed.
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Keywords:
- infrared spectroscopy /
- convolutional neural network /
- dimension /
- modeling
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0. 引言
烟幕材料对电磁波产生衰减的基本原理是电磁波经过物质颗粒时,与颗粒发生了散射和吸收等相互作用,电磁波沿原有方向的传输能量减弱[1-2]。烟幕粒子对红外辐射消光能力的强弱取决于颗粒的成分、复折射率、带电性等自身特性参量[3-5]。建立适用于各种粒子的消光计算模型,可以揭示材料产生遮蔽/干扰效能的内在作用机制,加深对粒子与电磁波相互作用原理的理解。同时,如果能够借助大量的理论模拟和计算,获得材料的形状、尺寸、物理特性等基础参数,并基于最优参数集进行干扰材料设计,将大大加快光电干扰材料的研发进度,节约研发成本。
当前,可用于烟幕粒子消光性能计算的方法主要有两类,一类是适用于球形粒子精确求解的Lorenz-Mie理论[6],该理论是最早发展的光散射模型,能够对球形粒子的消光特性进行精确求解。另一类是适用于球形和非球形粒子精确求解的数值计算方法,此类方法通过在一定边界条件下直接数值求解电磁波传播方程,如Maxwell方程组及Helmholtz方程等,获得粒子的电磁散射特性。按照计算原理,常见的数值散射理论及模型大致可分为[7-8]:①基于场展开方式的散射模型,主要包括T矩阵法、扩展边界条件法、分离变量法和点匹配法等;②基于体积积分方程的散射模型,主要包括矩量法和离散偶极近似法等;③基于微元法的散射模型,主要包括时域有限差分法和有限元法等。每种计算方法都有自己的优点和局限性,目前还没有一种方法能够精确计算所有类型粒子的电磁波散射特性。因此,在实践中通常是对一种方法尽可能地优化近似以提高其计算准确性,同时也可采用多种计算方法相结合的方式,互为补充、互相验证,以获取更加精确的计算结果。
碳基材料烟幕对多波段电磁波有很好的衰减效果,也是目前应用最为广泛的光电干扰材料之一[9-10]。本文采用计算精度较高的矩量法建立旋转体烟幕粒子的消光计算模型,研究基本参数对石墨粒子红外消光性能的影响,对其形状、尺寸等参数进行优化设计,以进一步提升其消光性能。矩量法离散得到的矩阵方程为满阵,存储复杂度和计算复杂度高,是一种比较耗费计算内存和时间的数值方法[11]。旋转体基本囊括了主要的烟幕粒子形状,如球体、柱体、圆片等,旋转体具有轴对称性,计算区域由传统的三维区域转换为由母线和旋转轴构成的二维区域,求解区域和未知量的数目大大减小,可以节约计算内存和计算时间,实现高速的计算。
1. 消光计算模型
1.1 计算方法
旋转体粒子矩量法消光计算模型的基本思想是将粒子表面的未知电流密度积分方程用基函数和权函数离散化成矩阵形式的代数方程,然后计算矩阵元素并求解该矩阵方程,最后得到表面电磁场和各种衰减截面积[12]。该模型是在Mautz和Harrington[13-14]用矩量法研究旋转体散射特性的基础上建立的,此后又经过不断的完善和发展[15-17],现在广泛用于解决旋转体粒子的光学散射问题,本文只简要介绍一下其基本原理。
用来表示散射体表面电磁场的未知电流$\overrightarrow J $和磁流$\overrightarrow M $可利用矩量法展开成如下形式[17]:
$$ \overrightarrow J (t, \varphi ) = \sum\limits_{n = - \infty }^\infty {\sum\limits_{j = 1}^N {I_{nj}^t} \overrightarrow J _{nj}^t(t, \varphi ) + I_{nj}^\varphi \overrightarrow J _{nj}^\varphi (t, \varphi )} $$ (1) $$ \overrightarrow M (t, \varphi ) = \eta \sum\limits_{n = - \infty }^\infty {\sum\limits_{j = 1}^N {M_{nj}^t} \overrightarrow J _{nj}^t(t, \varphi ) + M_{nj}^\varphi \overrightarrow J _{nj}^\varphi (t, \varphi )} $$ (2) 式中:$\overrightarrow J _{nj}^t$、$\overrightarrow J _{nj}^\varphi $、$\overrightarrow M _{nj}^t$、$M_{nj}^\varphi $均为待求电磁流系数;阻抗$\eta = \sqrt {{\mu _0}/{\varepsilon _0}} $,μ0和ε0分别为真空中的磁导率和介电常数;基函数定义为:
$$ \overrightarrow J _{nj}^t(t, \varphi ) = {\hat u_t}{f_j}(t){{\rm{e}}^{{\rm{j}}n\varphi }} $$ (3) $$ \overrightarrow J _{nj}^\varphi (t, \varphi ) = {\hat u_\varphi }{f_j}(t){{\rm{e}}^{{\rm{j}}n\varphi }} $$ (4) 式中:fj(t)为三角分段函数;t是沿旋转曲线方向的弧长;Φ是从x轴方向开始的方位角;${\hat u_t}$和${\hat u_\varphi }$分别是t和Φ的切向量;N为三角展开函数的个数;n表示按第n个方位角展开函数展开的状态。
同样,权函数可定义为:
$$ \overrightarrow W _{ni}^t(t, \varphi ) = {\hat u_t}{f_i}(t){{\rm{e}}^{{\rm{i}}n\varphi }} $$ (5) $$ \overrightarrow W _{ni}^\varphi (t, \varphi ) = {\hat u_t}{f_i}(t){{\rm{e}}^{{\rm{i}}n\varphi }} $$ (6) 于是可得到矩阵方程如下:
$$ \left[ \begin{array}{l} \left[ {Z_n^{tt}} \right]\left[ {Z_n^{t\varphi }} \right]\left[ {X_{n - }^{tt}} \right]\left[ {X_{n - }^{t\varphi }} \right]\\ \left[ {Z_n^{\varphi t}} \right]\left[ {Z_n^{\varphi \varphi }} \right]\left[ {X_{n - }^{\varphi t}} \right]\left[ {X_{n - }^{\varphi \varphi }} \right]\\ \left[ {Z_{nd}^{tt}} \right]\left[ {Z_{nd}^{t\varphi }} \right]\left[ {X_{nd + }^{tt}} \right]\left[ {X_{nd + }^{t\varphi }} \right]\\ \left[ {Z_{nd}^{\varphi t}} \right]\left[ {Z_{nd}^{\varphi \varphi }} \right]\left[ {X_{nd + }^{\varphi t}} \right]\left[ {X_{nd + }^{\varphi \varphi }} \right] \end{array} \right]\left[ \begin{array}{l} \left[ {I_n^t} \right]\\ \left[ {I_n^\varphi } \right]\\ \left[ {M_n^t} \right]\\ \left[ {M_n^\varphi } \right] \end{array} \right] = \left[ \begin{array}{l} \left[ {V_n^t} \right]\\ \left[ {V_n^\varphi } \right]\\ \left[ 0 \right]\\ \left[ 0 \right] \end{array} \right] $$ (7) 各矩阵元素的内积表示形式为:
$$ \eta {(Z_n^{pq})_{ij}} = < \overrightarrow W _{ni}^p, \hat L\left[ {\overrightarrow J _{nj}^q} \right] > $$ (8) $$ \eta {(Z_{n{\rm{d}}}^{pq})_{ij}} = < \overrightarrow W _{ni}^p, {\hat L^{\rm{d}}}\left[ {\overrightarrow J _{nj}^q} \right] > $$ (9) $$ {(X_{n - }^{pq})_{ij}} = < \overrightarrow W _{ni}^p, {\hat K_ - }\left[ {\overrightarrow J _{nj}^q} \right] > $$ (10) $$ {(X_{n{\rm{d}} + }^{pq})_{ij}} = < \overrightarrow W _{ni}^p, \hat K_ + ^{\rm{d}}\left[ {\overrightarrow J _{nj}^q} \right] > $$ (11) $$ \eta {(V_n^t)_i} = < \overrightarrow W _{ni}^t, {\overrightarrow E ^i} > $$ (12) $$ \eta {(V_n^\varphi )_i} = < \overrightarrow W _{ni}^\varphi , {\overrightarrow E ^i} > $$ (13) 式中:p=t, φ,q=t, φ,n=0, 1, …;${\overrightarrow E ^i}$为入射电场;$\hat L$、$\hat K$为积分算子;“d”表示在介质空间中,无“d”表示在自由空间中;“+”表示在粒子表面以外,“-”表示在粒子表面以内。
由矩阵方程可求得各系数,于是其散射振幅函数可表示为:
$$ \begin{array}{l} {S_{\alpha \beta }}({{\hat k}^{\rm{s}}}, {{\hat k}^{\rm{i}}}) = - \frac{j}{{4{\rm{ \mathsf{ π} }}}}\sum\limits_{n, j} {\{ {{(R_n^{t\alpha })}_j}{{(I_n^{t\beta })}_j} + {{(R_n^{\varphi \alpha })}_j}{{(I_n^{\varphi \beta })}_j}} \\ \quad \quad \;\quad \;\;\;\;\; - (R_n^{t\alpha })_j^{{\rm{mag}}}{(M_n^{t\beta })_j} - (R_n^{\varphi \alpha })_j^{{\rm{mag}}}{(M_n^{\varphi \beta })_j}\} \end{array} $$ (14) 其中:
$$ {{(R_{n}^{p\alpha })}_{j}}=k\iint\limits_{s}{{{\text{e}}^{-\text{j}{{\overrightarrow{k}}^{\text{s}}}\cdot \overrightarrow{r}}}{{{\hat{u}}}_{\alpha }}\cdot \overrightarrow{j}_{nj}^{p}\text{d}s} $$ (15) $$ (R_{n}^{p\alpha })_{j}^{\text{mag}}=k\iint\limits_{s}{{{\text{e}}^{^{-\text{j}{{\overrightarrow{k}}^{\text{s}}}\cdot \overrightarrow{r}}}}({{{\hat{k}}}^{\text{s}}}\times {{{\hat{u}}}_{\alpha }})\cdot \overrightarrow{j}_{nj}^{p}\text{d}s} $$ (16) 式中:α、β表示极化系数,α≠β;${{\hat{k}}^{\text{s}}}$、${{\hat{k}}^{\text{i}}}$分别为散射方向和入射方向的单位矢量;波数k=2π/λ,λ为入射波长;$\overrightarrow r $为坐标原点至粒子表面的矢量。
散射体的微分散射截面积可表示为:
$$ \sigma _d^{\alpha \beta }({\hat k^{\rm{s}}}, {\hat k^{\rm{i}}}) = \frac{{{{\left| {{S_{\alpha \beta }}({{\hat k}^{\rm{s}}}, {{\hat k}^{\rm{i}}})} \right|}^2}}}{{{k^2}}} $$ (17) 散射截面积为:
$$ \begin{array}{l} \sigma _{\rm{s}}^{\alpha \beta }({\theta _i}) = \int\limits_{4{\rm{ \mathsf{ π} }}} {\sigma _{\rm{d}}^{\alpha \beta }({{\hat k}^{\rm{s}}}, {{\hat k}^{\rm{i}}}){\rm{d}}{\Omega _{\rm{s}}}} \\ \quad \quad \quad = \frac{1}{{{k^2}}}{\int\limits_0^{2{\rm{ \mathsf{ π} }}} {\int\limits_0^{\rm{ \mathsf{ π} }} {\left| {{S_{\alpha \beta }}({{\hat k}^{\rm{s}}}({\theta _{\rm{s}}}, {\varphi _{\rm{s}}}), {{\hat k}^{\rm{i}}}({\theta _{\rm{i}}})} \right|} } ^2}\sin {\theta _{\rm{s}}}{\rm{d}}{\theta _{\rm{s}}}{\rm{d}}{\varphi _{\rm{s}}} \end{array} $$ (18) 式中:θi为入射角;θs为散射角;φs为方位角。
当散射方向为入射方向的反方向时为后向散射,此时,θi+θs=π可由式(18)计算得到后向散射截面积σb。
由前向散射原理,消光截面积为:
$$ \sigma _{\rm{e}}^{\alpha \beta }({\theta _{\rm{i}}}) = \frac{{4{\rm{ \mathsf{ π} }}}}{{{k^2}}}{\mathop{\rm Im}\nolimits} [{S_{\alpha \beta }}( - {\hat k^{\rm{i}}}, {\hat k^{\rm{i}}})] $$ (19) 吸收截面积为消光截面积与散射截面积之差:
$$ \sigma _{\rm{a}}^{\alpha \beta }({\theta _{\rm{i}}}) = \sigma _{\rm{e}}^{\alpha \beta }({\theta _{\rm{i}}}) - \sigma _{\rm{s}}^{\alpha \beta }({\theta _{\rm{i}}}) $$ (20) 对于随机取向的粒子,其各种衰减截面积的平均值都可用下式求得:
$$ {\sigma _{{\rm{random}}}} = \frac{1}{{\rm{ \mathsf{ π} }}}\int_0^{\rm{ \mathsf{ π} }} {\sigma ({\theta _{\rm{i}}}){\rm{d}}{\theta _{\rm{i}}}} $$ (21) 消光效率因子Qext、散射效率因子Qsca、吸收效率因子Qabs和后向散射效率因子Qbac可由相应的截面积除以粒子在电磁波传播方向的投影面积得到,即:
$$ {Q_{{\rm{ext}}}} = {\sigma _{\rm{e}}}/{S_{\rm{R}}} $$ (22) $$ {Q_{{\rm{sca}}}} = {\sigma _{\rm{s}}}/{S_{\rm{R}}} $$ (23) $$ {Q_{{\rm{abs}}}} = {\sigma _{\rm{a}}}/{S_{\rm{R}}} $$ (24) $$ {Q_{{\rm{bac}}}} = {\sigma _{\rm{b}}}/{S_{\rm{R}}} $$ (25) 式中:SR为旋转体粒子在电磁波传播方向的投影面积。
效率因子均为无量纲的量,消光效率因子、散射效率因子和吸收效率因子之间有如下关系:
$$ {Q_{{\rm{ext}}}} = {Q_{{\rm{sca}}}} + {Q_{{\rm{abs}}}} $$ (26) 质量消光系数是单位质量粒子的消光截面,对于单一尺寸的粒子,质量消光系数α为:
$$ \alpha = {\sigma _{\rm{e}}}/m $$ (27) 式中:m为旋转体烟幕粒子的质量。
对于粒子尺度不均的多分散体系,质量消光系数α可用以下公式求得:
$$ \alpha = \int\limits_r {\frac{{\sigma (r)N(r)}}{{m(r)}}{\rm{d}}r} $$ (28) 式中:r为粒子的尺寸;σ(r)为粒子消光截面积;N(r)为粒子数量分布函数;m(r)为粒子质量。
1.2 模型参数
基本粒子共设计了圆片及其等效球体和等效柱体3种形状(如图 1所示),基本涵盖了常见的烟幕粒子类型,如薄片、鳞片等可近似为圆片,纤维、棒体可近似为柱体,其余长径比接近1的如圆珠、立方体、八面体等可近似为球体。圆片的长径比(厚度与直径比)设为1:10,柱体的长径比设为10:1,设圆片的半径为r,可推导得等效球体的半径$R = \sqrt[3]{{3/20}}r$,等效柱体的半径$L = \sqrt[3]{{1/100}}r$。
利用建立的旋转体消光计算模型对3种形状粒子进行消光性能计算,计算参数设置为:
① 半径r:0.25~10 μm;
② 同形状所有粒子为单分散体系(尺寸均一),三角展开函数个数N取值为60~120,方位角展开函数个数n球体取值1,其他形状取20~40;
③ 入射波长中波红外取λ=4 μm,长波红外取λ=10 μm;
④ 石墨粒子密度取值为2.25 g/cm3;
⑤ 复折射率的值取自文献[18]。
对于非球形粒子,入射角随机取向进行角度平均,并且存在电磁极化,其消光性能计算结果取垂直极化和平行极化的平均值。
2. 消光计算结果
2.1 粒子形状
图 2是计算得到的不同尺寸的3种形状粒子对4 μm和10 μm红外的消光效率因子Qext、散射效率因子Qsca、吸收效率因子Qabs和后向散射因子Qbac。对4 μm红外而言,当圆片半径<0.75 μm、球体半径<0.46 μm、柱体半径<0.43 μm时,3种粒子的Qabs>Qsca,即吸收衰减在红外消光效应中占主导。对10 μm红外而言,当圆片半径<1.5 μm、球体半径<0.53 μm、柱体半径<0.32 μm时,3种粒子的Qabs>Qsca,同样是吸收衰减占主导。因此,对两个波长的红外来说,3种粒子在尺寸较小时都以吸收消光为主,尺寸变大后都以散射消光为主。另外,计算结果表明3种形状粒子对红外的后向散射效应都相对较弱。
图 3为不同尺寸的粒子对4 μm和10 μm红外的消光系数计算结果,3种粒子的消光系数都是先随半径增大而增大,到达峰值后变为随着半径增大而减小,说明粒子对特定波长电磁波的衰减应该有相应的最佳尺寸,此时消光系数达到最大值。对比3种形状粒子的消光系数可以发现,对4 μm红外而言:在所有尺寸下,等效球体的消光性能最差;半径大于0.5 μm时,圆片的消光性能最佳;半径小于0.5 μm时,等效柱体表现出最好的消光性能;3种形状粒子对4 μm红外消光性能最大时对应的尺寸分别为圆片半径0.75 μm,球体半径0.53 μm,柱体半径0.08 μm。对10 μm红外而言,消光性能基本类似:等效球体在所有尺寸下都表现出最差的消光性能;半径大于1.5 μm时,圆片的消光性能最佳;圆片半径小于1.5 μm时,等效柱体表现出最好的消光性能;3种粒子对10 μm红外消光性能最大时对应的尺寸分别为圆片半径2.0 μm,球体半径1.6 μm,柱体半径0.19 μm。
总体来看,无论是对中波还是长波红外,球体的消光系数在三者中都是最小的,对10 μm红外,几乎所有尺寸的消光系数都小于0.5 m2/g,消光效率很低。实际上烟幕材料制备加工过程中,球体是较为容易获取的,但从材料消光效率的角度来看,应尽可能避免将烟幕粒子设计成球形。非球形的圆片和柱体粒子对中波和长波红外都表现出了良好的消光能力,特别是圆片形粒子半径处于0.25~2.0 μm之间时,对4 μm红外的消光系数均大于2.0 m2/g,半径处于1.4~2.4 μm之间时,对10 μm红外的消光系数均大于2.0 m2/g。因此,调控设计半径在1.4~2.0 μm的区间时,粒子对中波和长波红外的消光系数均可超过2.0 m2/g。柱体粒子虽然在中波和长波红外也表现出了较好的消光能力,尤其在尺寸较小的时候甚至优于圆片,但柱体粒子加工的技术难度大、成本高,且半径大于1 μm后其消光能力将显著下降,因此综合考虑平均消光能力和制造加工成本,圆片状结构将是石墨类红外消光粒子的最优选择。
2.2 圆片厚度
图 4是不同厚度的圆片粒子对4 μm和10 μm红外的消光系数计算结果,计算参数N取值为100,n取值为20。随着厚度的减小,5种半径粒子的消光系数均显著升高。半径2.0~5.0 μm的4种粒子在片层厚度100 nm时,对两个波长红外的消光系数均可达到4.0 m2/g以上,厚度为50 nm时可进一步提升到6.0 m2/g以上,在厚度小于50 nm的纳米尺度,消光系数会随着厚度的变薄而迅速增加。这一结果表明,圆片粒子对红外的消光系数和消光能力会随着厚度的减小而迅速提升。
为进一步研究厚度对圆片消光性能的影响,将圆片粒子的半径固定在2 μm,控制厚度在20~200 nm之间变化,计算不同厚度的圆片对1~10 μm各波长红外的消光系数,计算参数N取值为60,n取值为10,计算结果见图 5。在计算波长范围内,圆片粒子对红外的消光系数都随着厚度的减小而增加,这进一步说明厚度对圆片粒子的红外消光性能具有极为重要的影响。表 1为半径2 μm圆片粒子对1~10 μm红外的平均消光系数,20 nm厚度圆片的平均消光系数达到了13.2 m2/g。但随着厚度的增加,平均消光系数呈现下降趋势,当厚度增加到200 nm时,平均消光系数下降到3.5 m2/g。厚度为20 nm的圆片,对近红外和中红外的消光系数最大,但往远红外延伸时消光系数却出现了下降趋势,对10 μm红外的消光系数已经与40 nm厚度的圆片接近,说明过小的厚度将不利于圆片粒子对远红外的消光能力。因此,在进行圆片粒子设计时应尽可能减小厚度,但为了兼顾中远红外的消光能力,其厚度不能低于某一范围。对于半径2 μm圆片粒子来说,其厚度不应低于20 nm,否则其对远红外的消光能力将大幅降低。
表 1 半径2 μm的圆片粒子对1~10 μm红外的平均消光系数Table 1. 1-10 μm infrared average extinction coefficients of flake with 2 μm radiusThickness/nm 20 40 60 80 100 150 200 Extinction coefficients/(m2/g) 13.2 10.8 8.6 6.3 5.7 4.4 3.5 2.3 薄层圆片半径
圆片粒子的厚度达到纳米级后,其消光性能会有显著的提升,为进一步研究纳米级的圆片半径对其消光性能的影响,固定圆片的厚度为100 nm,通过调整其半径进行圆片红外消光性能计算,计算结果仍然取垂直极化和平行极化的平均值,计算结果如图 6所示。对每个波长的红外而言,圆片粒子都存在一个最佳半径,尺寸在该半径值时圆片粒子对特定波长红外的消光系数最大,圆片对各个波长红外的最大消光系数和对应的最佳半径如表 2所示。每个波长下圆片的最佳半径随着波长的增大而增大,同时最佳直径略小于相对应的波长的一半。另外,最大消光系数随着红外波长的增大反而减小,说明圆片对远红外的消光能力随着波长的增加而逐渐降低。图 6表明,当半径大于1.2 μm时圆片对所有波长红外的消光系数都大于3.0 m2/g,当半径大于1.5 μm时圆片对所有波长红外的消光系数都大于5.0 m2/g,但当半径超过2.1 μm以后,圆片对所有波长红外的消光系数均有随半径增大而变小的趋势。因此,对于100 nm厚度的圆片而言,如果将其半径设计在1.5~2.1 μm之间,则可使其对1~10 μm红外均表现出良好的消光性能。
表 2 厚度为100 nm的圆片粒子对1~10 μm红外的最大消光系数和对应的最佳半径Table 2. Maximum extinction coefficient and corresponding optimum radius of 100 nm thick flakeWavelength/μm 1 2 3 4 5 6 7 8 9 10 Maximum extinction coefficient/ (m2/g) 9.9 8.2 7.8 7.5 7.4 7.3 7.2 7.1 7.1 7.0 Optimum radius/μm 0.15 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.9 2.1 3. 结论
基于矩量法建立了旋转体烟幕粒子的红外消光模型,并对圆片、球体和柱体等基本粒子进行了消光性能计算。计算结果表明,3种基本形状的粒子,在尺寸较小时都以吸收消光为主,在尺寸较大时都以散射消光为主。相对来说,球体粒子的消光能力最差,圆片粒子具有最佳的红外消光能力。当半径在1.4~2.0 μm区间时,圆片对4 μm和10 μm红外的消光系数均可超过2.0 m2/g。通过减小圆片的厚度,可以显著提升圆片粒子对红外的消光能力,但考虑到远红外波段的消光效果,其厚度不能低于20 nm。对于100 nm厚度的圆片而言,当其半径在1.5~2.1 μm之间时,粒子对1~10 μm红外的消光系数均大于5.0 m2/g,可使该尺寸的圆片粒子在整个红外波段范围内都表现出良好的消光性能。石墨是当前较为高效的烟幕干扰材料之一,本计算结果可为进一步提高石墨干扰能力提供指导,也可为其他先进光电干扰材料的设计和研制提供理论基础。
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图 1 LeNet-5网络模型示意图[19]
Figure 1. Schematic diagram of LeNet-5 network model
图 3 光谱数据编码[38]
Figure 3. Spectral data coding
图 4 维卷积核提取原始红外光谱局部特征模式图[46]
Figure 4. One dimensional convolution kernel extraction of original IR local feature pattern
图 5 不同卷积核尺寸的NIR-CNN模型判别结果[49]
Figure 5. The discrimination results of NIR-CNN model with different convolution kernel sizes
图 6 多任务网络的体系结构[41]
Figure 6. The architecture of a multitasking network
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