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光与散射介质相互作用时,光的偏振状态会改变,可以用Stokes矢量及MM来描述这种现象。Stokes矢量的四个分量的物理意义与偏振椭圆的椭圆度ε和方位角θ有关[27]。偏振光在散射介质中传输过程中发生的偏振状态的改变可以使用4×4的MM来描述[28],以这样一种方式,出射光的Stokes矢量可表示为入射光Stokes矢量和MM的乘积。散射介质的MM可以通过测量辐射得到,这些辐射是由不同偏振状态的偏振光对散射介质及目标进行照明产生的,并随后对辐射的偏振进行分析,这种情况用下列表达式在数学上加以描述:
$$ {{I = }}{{{S}}_{{{PSA}}}}{{{M}}_{{{Sample}}}}{{{S}}_{{{PSG}}}} $$ (1) 式中:I为由辐射强度组成的n×n矩阵;MSample为样品的4×4 MM;SPSG是一个4×n矩阵,其中n列表示照亮样品的不同偏振态的Stokes矢量;SPSA是一个n×4矩阵,它是n行Stokes向量的转置,这些向量代表从偏振分析仪出射的偏振态。通过计算分析仪和照明矩阵(SPSA和SPSG)的伪逆,可以推导出MM,得到:
$$ {{{M}}_{{{Sample}}}}{{ = \tilde S}}_{{{PSA}}}^{{{ - 1}}}{{ I \tilde S}}_{{{PSG}}}^{{{ - 1}}} $$ (2) 上式表明至少需要四组不同照明和分析状态用于测量完整的MM。因此,至少需要16次辐射测量才能完全确定散射介质及目标的MM。
无源线性光学系统(退偏系统)可以等效为四个纯系统(非退偏系统)的非相干叠加[29-32]。穆勒-琼斯矩阵(Muller-Jones Matrix, MJM)可用来描述一个纯系统,所有的完全偏振光入射到这个纯系统后,不会发生退偏,出射光的DoP仍然等于1。并且所有纯系统MJM都满足无源性的条件,即透光率永远不超过1[29]:
$$ \left\{ \begin{array}{l} {{{g}}_{{f}}} \leqslant {\rm{1}} \\ {{{g}}_{{r}}} \leqslant {\rm{1}} \\ {{{g}}_{{f}}} \equiv {{{m}}_{{\rm{00}}}}{{ + }}\sqrt {{{m}}_{{\rm{01}}}^{\rm{2}}{{ + m}}_{{\rm{02}}}^{\rm{2}}{{ + m}}_{{\rm{03}}}^{\rm{2}}} \\ {{{g}}_{{r}}} \equiv {{{m}}_{{\rm{00}}}}{{ + }}\sqrt {{{m}}_{{\rm{10}}}^{\rm{2}}{{ + m}}_{{\rm{20}}}^{\rm{2}}{{ + m}}_{{\rm{30}}}^{\rm{2}}} \end{array} \right. $$ (3) 式中:
${{{g}}_{{f}}}$ 表示纯系统的正向无源条件;${{{g}}_{{r}}}$ 表示纯系统的反向无源条件。任意退偏系统等效为四个纯系统的非相干叠加,因此可以得到,任何退偏系统MM必须满足正向无源条件:$$ {{{m}}_{{\rm{00}}}}{\rm{ + }}\sqrt {{{m}}_{{\rm{01}}}^{\rm{2}}{{ + m}}_{{\rm{02}}}^{\rm{2}}{{ + m}}_{{\rm{03}}}^{\rm{2}}} \leqslant {\rm{1}} $$ (4) 同时还要满足反向无源条件:
$$ {{{m}}_{{\rm{00}}}}{\rm{ + }}\sqrt {{{m}}_{{\rm{10}}}^{\rm{2}}{{ + m}}_{{\rm{20}}}^{\rm{2}}{{ + m}}_{{\rm{30}}}^{\rm{2}}} \leqslant {\rm{1}} $$ (5) 从退偏系统MM中提取出来的协方差为半正定矩阵H(M),能够体现出退偏系统的统计信息。协方差矩阵H(M)与其对应的退偏系统MM之间的关系可以表示为[29]:
$$ \begin{split}& {{H(M)}}{{ = }}\dfrac{{\rm{1}}}{{\rm{4}}}\left( {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{{{m}}_{{\rm{00}}}}{\rm{ + }}{{{m}}_{{\rm{01}}}}{{ + }}{{{m}}_{\rm{1}}}_{\rm{0}}{{ + }}{{{m}}_{{\rm{11}}}}}\\ {{{{m}}_{{\rm{02}}}}{{ + }}{{{m}}_{{\rm{12}}}}{{ - i(}}{{{m}}_{{\rm{03}}}}{{ + }}{{{m}}_{{\rm{13}}}}{{)}}}\\ {{{{m}}_{{\rm{20}}}}{{ + }}{{{m}}_{{\rm{21}}}}{{ + i(}}{{{m}}_{{\rm{30}}}}{{ + }}{{{m}}_{{\rm{31}}}}{{)}}} \end{array}}\\ {{{{m}}_{{\rm{22}}}}{{ + }}{{{m}}_{{\rm{33}}}}{{ - i(}}{{{m}}_{{\rm{23}}}}{{ - }}{{{m}}_{{\rm{32}}}}{{)}}} \end{array}}&{\begin{array}{*{20}{c}} {{{{m}}_{{\rm{02}}}}{\rm{ + }}{{{m}}_{{\rm{12}}}}{\rm{ + i(}}{{{m}}_{{\rm{03}}}}{\rm{ + }}{{{m}}_{{\rm{13}}}}{\rm{)}}}\\ {{{{m}}_{{\rm{00}}}}{\rm{ - }}{{{m}}_{{\rm{01}}}}{\rm{ + }}{{{m}}_{{\rm{10}}}}{\rm{ - }}{{{m}}_{{\rm{11}}}}}\\ {{{{m}}_{{\rm{22}}}}{\rm{ - }}{{{m}}_{{\rm{33}}}}{\rm{ + i(}}{{{m}}_{{\rm{23}}}}{\rm{ + }}{{{m}}_{{\rm{32}}}}{\rm{)}}}\\ {{{{m}}_{{\rm{20}}}}{\rm{ - }}{{{m}}_{{\rm{21}}}}{\rm{ + i(}}{{{m}}_{{\rm{30}}}}{\rm{ - }}{{{m}}_{{\rm{31}}}}{\rm{)}}} \end{array}} \end{array}} \right.\\& \left. {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{{{m}}_{{\rm{20}}}}{\rm{ + }}{{{m}}_{{\rm{21}}}}{\rm{ - i(}}{{{m}}_{{\rm{30}}}}{\rm{ + }}{{{m}}_{{\rm{31}}}}{\rm{)}}}\\ {{{{m}}_{{\rm{22}}}}{\rm{ - }}{{{m}}_{{\rm{33}}}}{\rm{ - i(}}{{{m}}_{{\rm{23}}}}{\rm{ + }}{{{m}}_{{\rm{32}}}}{\rm{)}}}\\ {{{{m}}_{{\rm{00}}}}{\rm{ + }}{{{m}}_{{\rm{01}}}}{\rm{ - }}{{{m}}_{{\rm{10}}}}{\rm{ - }}{{{m}}_{{\rm{11}}}}}\\ {{{{m}}_{{\rm{02}}}}{\rm{ - }}{{{m}}_{{\rm{12}}}}{\rm{ - i(}}{{{m}}_{{\rm{03}}}}{\rm{ - }}{{{m}}_{{\rm{13}}}}{\rm{)}}} \end{array}}&{\begin{array}{*{20}{c}} {{{{m}}_{{\rm{22}}}}{\rm{ + }}{{{m}}_{{\rm{33}}}}{\rm{ + i(}}{{{m}}_{{\rm{23}}}}{\rm{ - }}{{{m}}_{{\rm{32}}}}{\rm{)}}}\\ {{{{m}}_{{\rm{20}}}}{\rm{ - }}{{{m}}_{{\rm{21}}}}{\rm{ - i(}}{{{m}}_{{\rm{30}}}}{\rm{ - }}{{{m}}_{{\rm{31}}}}{\rm{)}}}\\ {{{{m}}_{{\rm{02}}}}{\rm{ - }}{{{m}}_{{\rm{12}}}}{\rm{ + i(}}{{{m}}_{{\rm{03}}}}{\rm{ - }}{{{m}}_{{\rm{13}}}}{\rm{)}}}\\ {{{{m}}_{{\rm{00}}}}{\rm{ - }}{{{m}}_{{\rm{01}}}}{\rm{ - }}{{{m}}_{{\rm{10}}}}{\rm{ + }}{{{m}}_{{\rm{11}}}}} \end{array}} \end{array}} \right) \end{split} $$ (6) 由于MM与其协方差矩阵H(M)之间的一对一关系,所以任何以MM表示的并行分解都可以直接转换成以H(M)表示的对应表达式[29]。MM可分解为四个纯系统MJM,其相对权重由H(M)的特征值大小决定。
H(M)的特征值可以写成如下形式:
$$ {\rm{1}} \geqslant {\lambda _0} \geqslant {\lambda _1} \geqslant {\lambda _2} \geqslant {\lambda _3} \geqslant {\rm{0}} $$ (7) 现在考虑H(M)的四个特征值之间的相对差异,即纯系统相对权重之间的差异。从H(M)的特征值中可以定义三个新的无量纲的不变量。这三个量包含了有关偏振纯度的所有信息,被称为IPPs:
$$ \left\{ {\begin{array}{*{20}{c}} {{P_{\rm{1}}}{\rm{ = }}\dfrac{{{\lambda _0} - {\lambda _1}}}{{{{tr}}{{H}}}}} \\ {{P_{\rm{2}}}{\rm{ = }}\dfrac{{{\lambda _0} + {\lambda _1} - 2{\lambda _2}}}{{{{tr}}{{H}}}}} \\ {{P_{\rm{3}}}{\rm{ = }}\dfrac{{{\lambda _0} + {\lambda _1} + {\lambda _2} - 3{\lambda _3}}}{{{{tr}}{{H}}}}} \end{array}} \right. $$ (8) 式中:trH表示H(M)的迹,在退偏系统等效分解成的四个纯系统中;
${P_1}$ 表示权重最大的两个纯系统的权重之差;${P_2}$ 表示权重最大的两个纯系统权重之和减去权重第三的纯系统的权重的两倍;${P_3}$ 表示权重最大三个纯系统的权重之和减去权重最小的纯系统权重的三倍[32]。IPPs构成纯度空间的可行域如图1所示[32],其是由${P_1}$ 、${P_2}$ 、${P_3}$ 构成的三维数学空间,它们不是完全独立的,而是相互关联的。纯度空间不仅提供了光在相互作用中被退偏的信息,而且还提供了关于它是如何被样品退偏的信息[29]。利用${P_1}$ 、${P_2}$ 、${P_3}$ 的不同,可以揭示不同退偏系统之间的差异,从而用于区分不同类型的退偏系统。图中O点代表完全退偏的系统,IPPs都等于0;C点IPPs都等于1,代表纯系统。系统的退偏能力越弱,分布在纯度空间中的表征点越靠近C点;相反,系统退偏能力越强,表征点就越靠近O点。与IPPs提供完整的退偏信息相比,退偏指数${P_\Delta }$ 提供了样品整体退偏能力,其可从IPPs中计算得到:$$ {P_\Delta }{\rm{ = }}\frac{{\rm{1}}}{{\sqrt {\rm{3}} }}\sqrt {{\rm{2(}}{P_{\rm{1}}}{{\rm{)}}^2}{\rm{ + }}\frac{{\rm{2}}}{{\rm{3}}}{{{\rm{(}}{P_2}{\rm{)}}}^2}{\rm{ + }}\frac{{\rm{1}}}{{\rm{3}}}{{{\rm{(}}{P_3}{\rm{)}}}^2}} $$ (9) 也可从MM中计算得到:
$$ {P_\Delta }{\rm{ = }}\sqrt {\frac{{\left( {\displaystyle\sum\limits_{{{i,j = 0}}}^{\rm{3}} {{{m}}_{{{ij}}}^{\rm{2}}} } \right){\rm{ - 1}}}}{{\rm{3}}}} $$ (10) -
植物组织图像的对比度可以通过二色性或双折射的测量加以提高。二色性与植物结构对光的偏振依赖性吸收有关,其在很多研究中都被成功地用于揭示植物中叶绿体和相关细胞器的组织和浓度[40-41]。双折射也已成功地用于表征双折射大分子。但退偏作为一种偏振特性,通常被忽略。当不同偏振态的光子非相干地到达探测器的同一区域时,就会出现退偏现象。在植物中,退偏主要是由位于组织内的细胞、细胞器和其他元素散射光引起的。迄今为止,最常用的探测植物组织退偏的方法是测量散射光的DoP。由于DoP依赖于植物成分的内在特征,它是对给定标本状态的一种有针对性和信息性的观察。然而,一种更普遍的方法,IPPs在植物学却上很少被使用。
近来,Albert Van Eeckhout开始尝试利用IPPs对植物组织进行成像,标本为植物叶片。实验中对叶片的退偏进行测量,得到对叶片偏振响应进行编码的MM图像。为了从测量的MM图像中获得进一步的物理信息,对MM图像进行分解,得到一组后续的偏振和退偏振度量图像。在实验中,Albert Van Eeckhout课题组使用了退偏指数
${P_\Delta }$ 和IPPs观测数据,${P_\Delta }$ 和IPPs能够根据其对照明光退偏能力的不同对微观结构进行分类。其中,${P_\Delta }$ 表示散射介质总体的退偏能力,而IPPs可以区分散射介质中不同的退偏成分。图3(b)~(d)为${P_\Delta }$ ,${P_1}$ ,以及${P_2}$ -${P_1}$ 对应的图像。图3(e)显示了植物线性延迟的图像,图3(f)显示其伪彩色图像,它给出了叶片成像区域结构的双折射信息。在图3(b)~(e)中可以看到菊粉的细长形状,菊粉是一种针状结晶的多糖,针状晶体倾向于聚集在一起形成裂片,这种裂片存在于一些植物的实质细胞中。在图3(b)~(e)中,针状晶体的边缘可以清晰的区分出来,整个结构与背景形成了高度对比。在${P_1}$ 图像(图3(c))中,针状晶体红色方形区域的${P_1}$ 平均值为0.11,而与背景相对应的绿色方形区域的${P_1}$ 平均值为0.29,${P_1}$ 的值分别在0.11和0.29附近很好地聚为两组,这表明了${P_1}$ 能够区分不同类型的物质,而这在非偏振光图像下(图3(a))是不可能的。图3(d)中${P_2}$ -${P_1}$ 的观察结果显示,针状晶体的同一部分的值约为0.13,而背景单元格的同一部分的值为0.02。对于不同的退偏物体,${P_1}$ 和${P_2}$ -${P_1}$ 针状晶体的能见度比${P_\Delta }$ 高。因此,使用IPPs观察退偏物体比使用${P_\Delta }$ 和传统的光强效果更好。图 3 植物叶子的偏振分析。(a) 强度;(b)
${P_\Delta }$ ;(c)${P_1}$ ;(d)${P_2}$ -${P_1}$ ;(e) δ 线性延迟;(f) 线性延迟的伪彩色图像Figure 3. Polarization analysis of leaf. (a) Intensity; (b)
${P_\Delta }$ ; (c)${P_1}$ ; (d)${P_2}$ –${P_1}$ ; (e) Linear retardance δ and (f) Pseudo-colored image of linear retardanceAlbert Van Eeckhout团队同样利用IPPs对动物组织进行观测。实验选取了兔腿上的肌肉作为实验样品,使用MM成像时对比度太差,以至于无法对不同生物结构进行分辨,接着他们利用IPPs对生物组织进行成像。IPPs在成像的过程中则具有较好的分辨能力,会导致某些生物结构的对比度增大。并且IPPs与传统方法相比,不需要进行偏振分解,其中的
${P_1}$ 、${P_2}$ 、${P_3}$ 易于获得。紧接着为了进一步的增加不同结构之间的对比度,Albert Van Eeckhout团队利用伪彩色的方法对实验样品的成像结果进行进一步处理,结果如图4所示。通过伪彩色来编码由IPPs提供的偏振信息的方法不是唯一的,其主要目的是尽可能使生物样本目标结构对比度更大,所以需要给
${P_1}$ 、${P_2}$ 、${P_3}$ 设置不同的权重,即α1、α2和α3的取值不同会使得具有不同偏振属性的结构成像的清晰度不同。图4中给出了两种不同的组合,首先,为了得到图4(a)中的图像,使用公式(11)对成像图片进行伪彩色处理,选取α1=3、α2=1和α3=1,这种组合增加了${P_1}$ 通道的权重,从而放大了骨孔和营养通道的对比度。视觉效果如图4(a)所示,其中营养通道形成了很高的对比度(见图4(a)绿色箭头)。图 4 不同基和权重下的伪彩色图片。(a) 公式(11)中α1 = 3、α2 = 1和α3 = 1; (b) 公式(12)中α1 = 2、α2 = 2和α3 = 1
Figure 4. Pseudo-colored image of different bases and weights. (a) α1 = 3, α2 = 1 and α3 = 1 of Eq. (11); (b) α1 = 2, α2 = 2 and α3 = 1 of Eq. (12)
此时,修改公式(11)中的权重,甚至进一步修改伪彩色编码关系本身,以增加目标结构区域的对比度,即可以调整伪颜色编码的基,突出目标结构区域。例如,修改了公式(11)中的基,变成了公式(12):
$$ {C_{{\rm{pix}}}}(x,y) = {\alpha 1}{P_1}(x,y) + {\alpha 2}{P_2}(x,y) + {\alpha 3}{P_3}(x,y) $$ (11) $$\begin{split}{C_{{\rm{pix}}}}(x,y) =& {\alpha 1}{P_3}(x,y) + {\alpha 2}\left[ {{P_2}(x,y) - {P_1}(x,y)} \right] +\\& {\alpha 3}\left[ {{P_3}(x,y) - {P_2}(x,y)} \right] \end{split} $$ (12) 公式(12)使用了一组非正交的伪色基。公式(12)中α1、α2和α3范围也是0~1,不过与公式(11)中考虑伪彩色空间中的点不同,公式(12)选择的非正交轴更接近于一个四面体,四面体中点的色差更大。设置权重α1 = 2、α2 = 2和α3 = 1可最大化斑点状结构和薄肌腱的对比度,得到图4(b)中的图像,薄肌腱现在可以更好地显示(见图4(b)蓝色箭头),斑点状结构清晰可见。实验表明,IPPs在对生物组织进行成像的过程中确实具有独特的优势,并且通过选取伪彩色的基和权重可以对生物组织的目标结构进行突出显示。
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目前,糖尿病已成为第三大严重危害人类健康的疾病,也是全世界非常关注的问题之一。同时,糖尿病导致的并发症有很多,会危害人的心、脑、肾、血管、神经、皮肤等。糖尿病患者在治疗时血糖的增高或降低,也可能直接导致患者死亡。因此,糖尿病患者需要一种无创血糖监测仪来提高监测频率,更好地指导治疗。尽管其中一些技术已经达到了相当高的精度,到目前为止,没有一种技术被批准用于临床。偏振光为监测葡萄糖浓度(Glucose Concentration,GC)提供了一种可行的方法,其通过GC引起的偏振变化进行浓度的监测。Chou[42]和Pu[43]使用高灵敏度的偏光技术识别与生理GC相关的偏振面的旋转。Ablitt[44]等人利用MC模拟研究了含有手性球状粒子的混浊介质对偏振光散射的影响。Wang[45]开发了一种MC方法,利用单散射模型或双散射模型提取含葡萄糖双折射混浊溶液的MM元素。Phan和Lo[46]使用由偏振扫描发生器和高精度Stokes偏振仪组成的Stokes-MM偏振测量系统,分别检测有散射效应和无散射效应水溶液中的低浓度葡萄糖样品,但由于信噪比较小,检测葡萄糖引起的偏振面小角度的旋转是相当困难的。
近年来,笔者课题组提出利用IPPs对GC进行监测[47],并利用MC算法搭建了实验平台。结果表明,IPPs中的
${P_1}$ 相比较于传统的偏振指标对GC变化更加敏感更具有优势,可以用于指示和监测溶液中的GC。在前向散射探测中,粒径越大,优势越明显,结果如图5所示。接着拟合出${P_1}$ 与GC的多项式关系,通过拟合出的多项式对GC进行反演,误差低于5%。然而,在后向散射探测中,IPPs不能明显的反映出溶液中GC的变化。但是在前向散射的过程中,
${P_1}$ 体现了对GC监测的能力,于是该课题组利用${P_1}$ 频率分布直方图来显示GC的变化。首先,将${P_1}$ 值的区间划分为30等份,分别计算每个区间上的值,然后,将直方图与曲线进行拟合,如图6(e)~(h)所示,其中N为归一化频率。如图6(a)~(b)所示,发现有葡萄糖和没有葡萄糖的两种溶液的${P_1}$ 分布有显著的不同,但在不同GC的溶液中,如图6(b)~(d),${P_1}$ 的空间分布没有明显的区别。从${P_1}$ 的频率分布直方图6(e)~(h)可以看出,随着溶液中GC的增加,最大值点的位置逐渐向左移动,这与正向散射结论一致。
Research progress on theory and applications of index of polarization purities
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摘要: 光信息在散射介质中传播时会发生散射现象,从而导致其强度和偏振信息发生变化。利用出射光的偏振状态可以间接表征散射介质的退偏特性,并对散射介质进行分类和识别。理论上穆勒矩阵( Mueller Matrix, MM)可以描述散射介质的全部偏振属性,对分析散射介质的退偏特性起到至关重要的作用,但是MM参数过多,较为复杂。然而,根据MM推导所得到的偏振纯度指数(Index of Polarization Purities,IPPs)结构简单,并可以更为直接的描述散射介质的退偏特性。IPPs由
${P_1}$ 、${P_2}$ 、${P_3}$ 组成,代表退偏系统等效分解成的四个非退偏纯系统之间的权重差异。以${P_1}$ 、${P_2}$ ,${P_3}$ 为坐标轴可构建出纯度空间,纯度空间中不同的点代表不同的退偏系统,利用纯度空间可以对不同的退偏系统进行分辨。相比较于传统偏振表征指标,IPPs可以表征散射介质及目标更多维度的信息。近年来,IPPs在生物医学和目标检测等诸多方面的研究取得了重要的研究成果。文章主要介绍了IPPs的理论,综述并讨论了其在分析不同分散体系的退偏特性、生物组织成像、医学监测和目标识别等方面的研究进展。Abstract: The optical information will experience the scattering phenomena, when it propagates in the scattering media, which will change the intensity and polarization information of the propagating light. And the depolarization property and the transmission property of the medium can be characterized indirectly, which can be used to classify and recognize the media. In theory, the Mueller Matrix (MM) can describe all polarization properties of the media, which plays a vital role in analyzing the depolarization properties of the medium, but its parameters are too complicated. However, the index of polarization purities (IPPs) obtained from the Mueller matrix can also describe the polarization properties of the media directly. IPPs are composed of${P_1}$ ,${P_2}$ ,${P_3}$ , which represent the weight differences of four non-depolarization pure systems decomposed from the depolarization system equivalently. The${P_1}$ ,${P_2}$ ,${P_3}$ can form a three-dimensional space called purity space, in which different points represent corresponding depolarization systems. And they can be used for recognizing different depolarization systems. Compared to standard polarization indexes, the IPPs can express the more dimensional information of the scatter media, which has obtained many important research achievements in many aspects such as biomedical and target detection. We mainly introduce the IPPs theory, and meanwhile, review and discuss its great role in the analysis of depolarization of the different dispersion system, biological tissue imaging, medical monitoring and target recognition. -
图 2 (a)
${P_1}$ 、${P_2}$ 、${P_3}$ 随大小微粒混合体积比的变化(后向探测);(b)大小微粒混合体积比对散射介质的退偏指数${P_\Delta }$ 的影响(前向探测);(c)粒子标准差为0.01 μm时,${P_1}$ 、${P_2}$ 、${P_3}$ 随粒子均值的变化(后向探测);(d) 粒子标准差为1.05 μm时,${P_1}$ 、${P_2}$ 、${P_3}$ 随粒子均值的变化(后向探测)Figure 2. (a)
${P_1}$ ,${P_2}$ ,${P_3}$ varying with the proportion of small particles in the purity space (backward detection); (b)${P_\Delta }$ of scattering medium as a function of the proportion of small particles (forward detection); (c)${P_1}$ ,${P_2}$ ,${P_3}$ varying with different mean values for standard deviation of 0.01 μm (backward detection); (d)${P_1}$ ,${P_2}$ ,${P_3}$ varying with different mean values for standard deviation of 1.05 μm (backward detection) -
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