﻿ 基于Jones矢量的单粒子散射Mueller矩阵的数值计算 Numerical Calculation for Mueller Matrix of a Single Particle Based on Jones Vectors

Optoelectronics
Vol.05 No.02(2015), Article ID:15504,6 pages
10.12677/OE.2015.52005

Numerical Calculation for Mueller Matrix of a Single Particle Based on Jones Vectors

Chaowei Zhou, Qinghua Wang*, Zhenhua Li

School of Science, Nanjing University of Science and Technology, Nanjing Jiangsu

*通讯作者。

Email: *qhwang@mail.njust.edu.cn

Received: Jun. 6th, 2015; accepted: Jun. 22nd, 2015; published: Jun. 25th, 2015

ABSTRACT

The formulae of a single particle’s scattering based on Jones vectors are derived. Then, the scattering Jones vectors of the single particle for the typical polarization states can be calculated. Further, the Stokes parameters can be obtained according to the scattering Jones vectors. The proper linear combination of the typical scattering Stokes parameters will provide the elements of Mueller matrix. The simulations for the single particle show that the subgraphs of the 2D Mueller matrix are symmetrical about the diagonal. The values for m41, m42, m43, m14, m24, m34 are all zeros. Only five subgraphs for the nonzero elements are independent and the others can be gained by rotation.

Keywords:Jones Vector, Stokes Parameters, Mueller Matrix, Scattering

Email: *qhwang@mail.njust.edu.cn

1. 引言

2. 偏振态的描述与转换矩阵

2.1. 基于Jones矢量的粒子散射模型

1941年Jones用在X，Y轴上互为正交的两个振动分量的合成来表示偏振光电矢量 [8] ：

(1)

(2)

(3)

(4)

(5)

(4)式中的旋转角(方位角)为：

(6)

(6)式中

Figure 1. Schematic of particle scattering

Figure 2. Schematic of rotating coordinate system

2.2. Stokes参量与Mueller矩阵

(7)

(8)

(8)式中S和S'分别为入射光和出射光的Stokes参量，M为系统的Mueller矩阵。Mueller矩阵含有16个元素,也可看成有4个列向量组成，如(9)式：

(9)

(10)

3. 二维Mueller矩阵的数值模拟

Figure 3. Simulation diagram of two-dimensional Mueller matrix (distance h from scattering particles to detecting plane is 1 cm)

Figure 4. Simulation diagram of two-dimensional Mueller matrix (Distance h from scattering particles to detecting plane is 5 cm)

Figure 5. Curve: value of m11 element with radial length

4. 结论

Jones矢量和Stokes参量是两种表示光的偏振态的有效手段。本文推导了基于Jones矢量的单粒子散射模型，从而能够方便的获取水平直线偏振光、垂直直线偏振光、45˚直线偏振光、右旋偏振光经过单粒子散射后的Jones矢量。再根据Stokes参量定义，将单粒子散射后的Jones矢量换算成Stokes参量，最后通过不同Stokes参量的线性组合得到Mueller矩阵的各个列向量。本文提出的计算步骤，计算机上容易实现。通过数值模拟清晰的展示了单粒子对称系统中16个子图的特点，为分析随机介质的二维Mueller矩阵提供了一种简单有效的数值模拟手段。

Numerical Calculation for Mueller Matrix of a Single Particle Based on Jones Vectors. 光电子,02,26-32. doi: 10.12677/OE.2015.52005

1. 1. Ossikovski, R. and De Martino, A. (2015) Mueller matrix of a depolarizing homogeneous medium and its relation to the Mueller matrix logarithm. Journal of the Optical Society of America A, 32, 343-348.

2. 2. Hielscher, A.H., Eick, A.A., Mourant, J.R., et al. (1997) Diffuse backscattering Mueller matrices of highly scattering media. Optics Express, 1, 441-453.

3. 3. Espinosa-Luna, R. (2002) Scattering by rough surfaces in a conical configuration: Experimental Mueller matrix. Optics Letters, 27, 1510-1512.

4. 4. Ramella-Roman, J.C., Prahl, S.A. and Jacques, S.L. (2005) Three Monte Carlo programs of polarized light transport into scattering media: Part I. Optics Express, 13, 4420-4438.

5. 5. Ramella-Roman, J.C., Prahl, S.A. and Jacques, S.L. (2005) Three Monte Carlo programs of polarized light transport into scattering media: Part II. Optics Express, 13, 10392-10405.

6. 6. Wang, X., Wang, L.V., Sun, C.W., et al. (2003) Polarized light propagation through scattering media: Time-resolved Monte Carlo simulations and experiments. Journal of Biomedical Optics, 8, 608-617.

7. 7. 王清华, 李振华, 来建成, 贺安之 (2007) 随机介质背散射二维Mueller矩阵的数值模拟与分析. 光学与光电技术, 5, 1-4.

8. 8. Jones, R.C. (1941) A new calculus for the treatment of optical systems. Journal of the Optical Society of America, 31, 500-503.

9. 9. 阿查姆, R.M.A., 巴夏拉, N.M., (梁民基, 尹树百, 张福初, 等, 译) (1986) 椭圆偏振测量术和偏振光(中译版). 科学出版社, 北京, 51.

10. 10. McMaster, W.H. (1954) Polarization and the Stokes parameters. American Journal of Physics, 22, 351-362.

11. 11. Cameron, B.D. (1998) Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium. Optics Letters, 23, 485-487.