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PIMI方法通过对入射或出射光的调制,检测光场的远场变化,通过对远场变化的反演获得光量子状态参数图谱,具有较强的分辨能力[14-18]。本文中的PIMI光路原理图如图 1所示。主要由发光二极管(light-emitting diode,LED)白光光源、固定偏振片、人脸、旋转偏振片和输出相机等组成。采集过程中,保持固定偏振片不动,通过多次改变旋转偏振片的角度进行原图采集,对原图通过下述计算获得斯托克斯参量图谱。
光路的穆勒矩阵关系如下:
$ \boldsymbol{S}_{\text {out }}=\boldsymbol{M}_{\mathrm{r}} \cdot \boldsymbol{M}_{\mathrm{s}} \cdot \boldsymbol{M}_{\mathrm{f}} \cdot \boldsymbol{S}_{\mathrm{in}} $
(1) 式中, Sout为系统出射光的斯托克斯矢量;Mr为旋转偏振片的穆勒矩阵;Ms为人脸的穆勒矩阵;Mf为固定偏振片的穆勒矩阵,与光轴方向平行;Sin为入射光源的斯托克斯矢量:
$ \boldsymbol{S}_{\mathrm{in}}=\left[\begin{array}{llll} S_{\mathrm{in}, 0} & S_{\mathrm{in}, 1} & S_{\mathrm{in}, 2} & S_{\mathrm{in}, 3} \end{array}\right]^{\mathrm{T}} $
(2) 式中,斯托克斯参数Sin, 0为入射光的总光强;Sin, 1为水平偏振光强与垂直偏振光强之差;Sin, 2为45°偏振光强与135°偏振光强之差;Sin, 3为左旋圆偏振光强与右旋圆偏振光强之差。
本文作者将人脸抽象成一个波片加反射镜的穆勒矩阵模型Ms,计算过程中入射角i按45°处理,φ和δ分别是线偏振光照射到人脸发生漫反射的过程中产生的消光角和相位差,消光角和相位差与面部皮肤的各向异性及特征直接相关。
$ \begin{gathered} \boldsymbol{M}_{\mathrm{s}}=\boldsymbol{M}_{\mathrm{w}} \boldsymbol{M}_{45^{\circ}}= \\ \frac{p^2}{2}\left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & Q & R & \sin (2 \varphi) \sin \delta \\ 0 & R & Q & -\cos (2 \varphi) \sin \delta \\ 0 & -\sin (2 \varphi) \cos (2 \delta) & \cos (2 \varphi) \sin \delta & \cos \delta \end{array}\right] \end{gathered} $
(3) 式中,Q=cos2(2φ)+sin2(2φ)cosδ,R=cos(2φ)sin(2φ)×(1-cosδ),Mw为波片的穆勒矩阵,M45°为入射角i=45°时反射镜的穆勒矩阵,p为反射系数。
旋转偏振片以固定间隔角度θ旋转,经过n次旋转可以获取n张不同偏振角度的光强图,其穆勒矩阵可以表示为Mr, θ:
$ \begin{gathered} \boldsymbol{M}_{\mathrm{r}, \theta}= \\ \frac{1}{2}\left[\begin{array}{cccc} 1 & \cos (2 \theta) & \sin (2 \theta) & 0 \\ \cos (2 \theta) & \cos ^2(2 \theta) & \sin (2 \theta) \cos (2 \theta) & 0 \\ \sin (2 \theta) & \sin (2 \theta) \cos (2 \theta) & \sin ^2(2 \theta) & 0 \\ 0 & 0 & 0 & 0 \end{array}\right] \end{gathered} $
(4) 系统最终出射光为Sout:
$ \begin{array}{l} {\mathit{\boldsymbol{S}}_{{\rm{out }}}} = \left[ {\begin{array}{*{20}{c}} {{S_0}}\\ {{S_1}}\\ {{S_2}}\\ {{S_3}} \end{array}} \right] = \frac{{{p^2}}}{8}{\left( {\frac{{n - 1}}{{n + 1}}} \right)^2}\left( {{S_{{\rm{in }}, 0}} + {S_{{\rm{in }}, 1}}} \right) \times \\ \left[ {\begin{array}{*{20}{c}} {1 + Q\cos (2\theta ) + R\sin (2\theta )}\\ {\cos (2\theta ) + Q{{\cos }^2}(2\theta ) + R\sin (2\theta )\cos (2\theta )}\\ {\sin (2\theta ) + Q\sin (2\theta )\cos (2\theta ) + R{{\sin }^2}(2\theta )}\\ 0 \end{array}} \right] \end{array} $
(5) 式中,斯托克斯参数S0为出射光的总光强;S1为出射光的水平偏振光强与垂直偏振光强之差;S2为出射光的45°偏振光强与135°偏振光强之差;S3为出射光的左旋圆偏振光强与右旋圆偏振光强之差。
不同检偏角度光路的出射光强为I:
$ \begin{gathered} I=\frac{p^2}{8}\left(\frac{n-1}{n+1}\right)^2\left(S_{\mathrm{in}, 0}+S_{\mathrm{in}, 1}\right) \times \\ {[1+Q \cos (2 \theta)+R \sin (2 \theta)]} \end{gathered} $
(6) 式中,n为旋转次数。
对(6)式利用ABC三角函数(I=A+Bcos(2θ)+Csin(2θ))的傅里叶数字级数算法,结合矢量光场光子状态表征,可以得到相机中对应每一个像素的斯托克斯参量,最终根据像素坐标得出斯托克斯参量图谱。
基于偏振参数非直观光学成像的鼻唇沟量化表征
Quantitative characterization of nasolabial sulcus using polarization parametric indirect macroscopic imaging
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摘要: 鼻唇沟特征的异常变化是脑卒中面诊的重要依据。为了量化表征鼻唇沟特征, 解决传统中医面诊时难以发现精细特征变化和信息交流困难的问题, 采用了偏振参数非直观光学成像(PIMI)方法, 利用非直观成像的斯托克斯S1参量图谱, 取得了不同年龄的健康人员和脑卒中患者病中、预后的鼻唇沟对称性量化表征数据。结果表明, 健康人员鼻唇沟S1图谱特征具有较好的对称性, 鼻肌横部区与上唇提肌区的左右峰值均较为接近; 脑卒中患者患病期鼻唇沟的S1图谱明显不对称, 左右峰值大多相差20以上, 预后状态鼻唇沟S1图谱特征更接近健康人群。该方法有望应用于脑卒中疾病的病情评估及疗效评价, 促进中医数字化的发展。Abstract: Abnormal changes of the nasolabial sulcus characteristics are important symptoms of stroke, usually as the basis for the stroke facial diagnosis by traditional Chinese medicine with naked-eye observation. In order to quantify the characteristics of nasolabial sulcus and to solve the problem that it is difficult to find fine feature changes and difficult to communicate information in traditional Chinese medicine facial diagnosis, the polarization parametric indirect macroscopic imaging(PIMI) method was adopted by using the Stokes S1 parametric image. The nasolabial sulcus characteristics of healthy people, stroke patients, and prognostic people were obtained. The results show that the nasolabial sulcus S1 data of healthy people has good symmetry, while it is obviously asymmetrical for the stroke patients, and the difference between the left and right peaks is more than 20. It becomes more symmetrical when the stroke patient gets better. This method is expected to be applied to the digital diagnosis of stroke diseases and the evaluation of the treatment process, promoting the development of digital Chinese medicine.
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图 5 原始图像和PIMI S1图像的数据分析曲线对比
a, c—面部原始图像及其鼻唇沟区域数据量化结果 b, d—面部PIMI S1图像及其鼻唇沟区域数据量化结果
Figure 5. Comparison of analysis curves between the original images and the PIMI S1 images
a, c—original images of the face and quantitative results of data in the nasolabial sulcus region b, d—PIMI S1 images of the face and quantitative results of data in the nasolabial sulcus region
图 6 a—健康年轻女性鼻唇沟区域的PIMI S1图像及其PIMI S1数据量化结果 b—健康年轻男性鼻唇沟区域的PIMI S1图像及其PIMI S1数据量化结果
Figure 6. a—PIMI S1 image and quantitative results of PIMI S1 data in the nasolabial sulcus region of a healthy young woman b—PIMI S1 image and quantitative results of PIMI S1 data in the nasolabial sulcus region of a healthy young man
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