偏振散射光谱术的蒙特卡罗模拟研究
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摘要
偏振散射光谱术,作为一种无损光学检测技术,利用后向偏振散射光谱探测上皮组织细胞核形态学参数,对早期癌症检测具有巨大的潜在应用价值。然而,对这一技术的机理研究目前尚缺乏较好的手段。蒙特卡罗模拟是一种可用于研究光在混浊介质中传输的常用方法,被广泛地用于研究各种生物光学成像技术。但是,由于受计算资源的限制,蒙特卡罗方法在使用上受到很大限制,往往无法用于光谱研究。我们因此引入并行计算方法,实现了可用于模拟偏振散射光谱的并行偏振蒙特卡罗模拟程序,进而在此基础上对偏振散射光谱术进行了初步研究。
首先给出了整个模拟的详细算法,其主要内容为:采用多聚小球悬浮液模型模拟具有混浊特性的生物组织,其光学参数如各向异性因子、散射系数、以及米勒矩阵等采用米氏理论计算获得。光子的偏振特性则采用斯托克斯矢量来描述。通过跟踪光子在模型中迁移引起的参考坐标系及斯托克斯矢量的变化,光在组织中的传输得以模拟。最后对相关物理参量进行统计分析,给出实验可观测的各项光学量。进一步,我们忽略不同波长之间光的相互作用,光子被认为服从独立同分布,因此采用并行计算方法实现了光谱模拟的并行蒙特卡罗程序。随后的并行性能分析表明,我们的并行程序具有良好的可扩展性。模拟结果和实验结果对比,其较好的吻合有效地验证了程序的正确性。
然后利用此并行蒙特卡罗模拟程序,我们研究了组织特性对偏振散射光谱的影响以及偏振散射光谱术中的一些关键问题:偏振门技术,单次与多次光谱特性和双层模型的偏振散射光谱。得到一系列结论:1)光谱振荡频率随着粒子直径的增大而增大,振荡振幅随着粒子尺寸分布方差的增大而减小,甚至消失。2)在偏振门作用下,探测深度随各向异性因子的增大而增大,随入射角的增大而减小。3)同种组织的单次和多次偏振散射光谱具有相似的特征。4)双层模型中,当上层组织较薄或者其各向异性因子较大时,下层组织对测量上层组织偏振散射光谱的影响较大,这种影响可以通过增大入射角来减小,甚至完全消除。
Polarized light scattering spectroscopy, a non-invasive diagnostic technique, can be used to extract morphological information of epithelial cell nuclei. It has a great potential application in precancerous diagnosis. However, so far there lacks perfect theoretical method to study the mechanism of this technique. Monte Carlo simulation can be used to study light transportation in turbid media and has been used to study kinds of biomedical optical techniques. Limited by computing resource, Monte Carlo simulation can be hardly used to study spectroscopy. With the techniques of parallel computing, a Monte Carlo program, which can be used to simulate polarized light scattering spectra of turbid media, was developed in this paper. Based on this program, the mechanism of polarized light scattering spectroscopy was studied.
At first, Monte Carlo algorithm was described in detail.
Biological tissue is modeled as suspension of micro-spheres and its optical properties, such as anisotropic factor, scattering coefficient, Mueller matrix and so on, are calculated by Mie theory. Stokes vector is applied to describe light polarization. Stokes vector and reference coordinate are tracked while simulating. At last, physical quantities are calculated statistically to provide experimental results.
Furthermore, the relation between wavelengths is neglectable, so all photons obey independent identical distribution. A Monte Carlo program for spectroscopy simulation is implemented with parallel computing. Results showed that this program was provided with good parallel efficiency. Comparison of simulated and experimental results validated our program.
At last, based on our parallel Monte Carlo program, some basic issues of polarized light scattering spectroscopy, such as polarization gating, characters of single and multiple scattering spectra and so on, were studied. It's found that, 1) oscillation frequency and amplitude of spectra are much affected by particle diameter and standard deviation. 2) The change of anisotropy factor and incident angle affects the detection depth much. 3) For one-layer model, the characters of single and multiple scattering spectra are much similar. 4) For two-layer model, bottom layer has much effect on detection of top layer's polarized light scattering spectra, as top layer is thin or has large anisotropic factor. This effect can be decreased or even removed by increasing incident angle.
首先给出了整个模拟的详细算法,其主要内容为:采用多聚小球悬浮液模型模拟具有混浊特性的生物组织,其光学参数如各向异性因子、散射系数、以及米勒矩阵等采用米氏理论计算获得。光子的偏振特性则采用斯托克斯矢量来描述。通过跟踪光子在模型中迁移引起的参考坐标系及斯托克斯矢量的变化,光在组织中的传输得以模拟。最后对相关物理参量进行统计分析,给出实验可观测的各项光学量。进一步,我们忽略不同波长之间光的相互作用,光子被认为服从独立同分布,因此采用并行计算方法实现了光谱模拟的并行蒙特卡罗程序。随后的并行性能分析表明,我们的并行程序具有良好的可扩展性。模拟结果和实验结果对比,其较好的吻合有效地验证了程序的正确性。
然后利用此并行蒙特卡罗模拟程序,我们研究了组织特性对偏振散射光谱的影响以及偏振散射光谱术中的一些关键问题:偏振门技术,单次与多次光谱特性和双层模型的偏振散射光谱。得到一系列结论:1)光谱振荡频率随着粒子直径的增大而增大,振荡振幅随着粒子尺寸分布方差的增大而减小,甚至消失。2)在偏振门作用下,探测深度随各向异性因子的增大而增大,随入射角的增大而减小。3)同种组织的单次和多次偏振散射光谱具有相似的特征。4)双层模型中,当上层组织较薄或者其各向异性因子较大时,下层组织对测量上层组织偏振散射光谱的影响较大,这种影响可以通过增大入射角来减小,甚至完全消除。
Polarized light scattering spectroscopy, a non-invasive diagnostic technique, can be used to extract morphological information of epithelial cell nuclei. It has a great potential application in precancerous diagnosis. However, so far there lacks perfect theoretical method to study the mechanism of this technique. Monte Carlo simulation can be used to study light transportation in turbid media and has been used to study kinds of biomedical optical techniques. Limited by computing resource, Monte Carlo simulation can be hardly used to study spectroscopy. With the techniques of parallel computing, a Monte Carlo program, which can be used to simulate polarized light scattering spectra of turbid media, was developed in this paper. Based on this program, the mechanism of polarized light scattering spectroscopy was studied.
At first, Monte Carlo algorithm was described in detail.
Biological tissue is modeled as suspension of micro-spheres and its optical properties, such as anisotropic factor, scattering coefficient, Mueller matrix and so on, are calculated by Mie theory. Stokes vector is applied to describe light polarization. Stokes vector and reference coordinate are tracked while simulating. At last, physical quantities are calculated statistically to provide experimental results.
Furthermore, the relation between wavelengths is neglectable, so all photons obey independent identical distribution. A Monte Carlo program for spectroscopy simulation is implemented with parallel computing. Results showed that this program was provided with good parallel efficiency. Comparison of simulated and experimental results validated our program.
At last, based on our parallel Monte Carlo program, some basic issues of polarized light scattering spectroscopy, such as polarization gating, characters of single and multiple scattering spectra and so on, were studied. It's found that, 1) oscillation frequency and amplitude of spectra are much affected by particle diameter and standard deviation. 2) The change of anisotropy factor and incident angle affects the detection depth much. 3) For one-layer model, the characters of single and multiple scattering spectra are much similar. 4) For two-layer model, bottom layer has much effect on detection of top layer's polarized light scattering spectra, as top layer is thin or has large anisotropic factor. This effect can be decreased or even removed by increasing incident angle.
引文
[1] Gurjar R S, Backman V, Perelman L T et al. Imaging human epithelial properties with polarized light scattering spectroscopy. Nature Medicine, 2001, 7(11): 1245~1248
[2]高上凯.医学成像系统.(第1版).北京:清华大学出版社, 2000. 1～8
[3] Benaron D A. The future of cancer imaging. Cancer and Metastasis Reviews, 2002, 21: 45~78
[4] Zevallos M E, Gayen S K, Das B B et al. Picosecond Electronic Time-Gated Imaging of Bones in Tissues. IEEE Journal of Selected Topics in Quantum Electronics, 1999, 5(4): 916~922
[5] Gayen S K, Alrubaiee M, Savage H E et al. Parotid Gland Tissues Investigated by Picosecond Time-Gated and Optical Spectroscopic Imaging Techniques. IEEE Journal of Selected Topics in Quantum Electronics, 2001, 7(6): 906~911
[6] Chen K, Perelman L T, Zhang Q G et al. Optical computed tomography in a turbid medium using early arriving photons. Journal of Biomedical Optics, 2000, 5(2): 144~154
[7]俞晓峰,丁志华,陈宇恒等.光纤型光学相干层析成像系统的研制.光学学报, 2006, 26(2): 235～238
[8] Xie T Q, Zeidel M L, Pan Y T. Detection of tumorigenesis in urinary bladder with optical coherence tomography: optical characterization of morphological changes. Optics Express, 2002, 10(24): 1431~1443
[9]杨桂娟,梅妍,白亚乡.全息术及其应用.应用光学, 2006, 27(2): 96～100
[10] Sappey A D. Optical imaging through turbid media with a degenerate four wave mixing correlation time gate. Applied Optics, 1994, 33(36): 8346~8354
[11] Dilworth D S, Leith E N, Lopez J L. Three-dimensional confocal imaging of objectsembedded within thick diffusing media. Applied Optics, 1991, 30(14): 1796~1803
[12] Sheppard C J R, Connolly T J, Lee J et al. Confocal imaging of a stratified medium. Applied Optics, 1994, 33(4): 631~640
[13] Ghosh N, Patel H S, Gupta P K. Depolarization of light in tissue phantoms-effect of a distribution in the size of scatterers. Optics Express, 2003, 11(18): 2198~2205
[14] Wang X, Wang L V. Propagation of polarized light in birefringent turbid media: A Monte Carlo study. Journal of Biomedical Optics, 2002, 7(3): 279~290
[15] Demos S G, Radousky H B, Alfano R R. Deep subsurface imaging in tissues using spectral and polarization filtering. Optics Express, 2000, 7(1): 23~28
[16] Ni X, Alfano R R. Time-resolved backscattering of circularly and linearly polarized light in a turbid medium. Optics Letters, 2004, 29(23): 2773~2775
[17] Jacques S L, Roman J R, Lee K. Imaging Superficial Tissues with Polarized Light. Lasers in Surgery and Medicine, 2000, 26: 119~129
[18] Jacques S L, Ramella-Roman J C, Lee K. Imaging skin pathology with polarized light. Journal of Biomedical Optics, 2002, 7(3): 329~340
[19] Kartazayeva S A, Ni X, Alfano R R. Backscattering target detection in a turbid medium by use of circularly and linearly polarized light. Optics letters, 2005, 30(10): 1168~1170
[20] Backman V, Gurjar R, Badizadegan K et al. Polarized Light Scattering Spectroscopy for Quantitative Measurement of Epithelial Cellular Structures In Situ. IEEE Journal of Selected Topics in Quantum Electronics, 1999, 5(4): 1019~1026
[21] Kim Y L, Liu Y, Wali R K et al. Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and Its Alteration in Early Precancer. IEEE Journal of Selected Topics in Quantum Electronics, 2003, 9(2): 243~256
[22] Backman V, Wallace M B, Perelman L T et al. Detection of preinvasive cancer cells. Nature, 2000, 406(brief communications): 35~36
[23] Sokolov K, Drezek R, Gossage K et al. Reflectance spectroscopy with polarized light: is it sensitive to cellular and nuclear morphology. Optics Express, 1999, 5(13): 302~317
[24] Johnson T M, Mourant J R. Polarized wavelength-dependent measurements of turbid media. Optics Express, 1999, 4(6): 200~216
[25] Bohren C F, Huffman D R. Absorption and Scattering of Light by Small Particles. New York: Wiley, 1983. 82~129
[26]徐钟济.蒙特卡罗方法. (第1版).上海:上海科学技术出版社, 1985. 1～7
[27] Colasanti A, Guida G, Kisslinger A et al. Multiple processor version of a Monte Carlo code for photon transport in turbid media. Computer Physics Communications, 2000, 132: 84~93
[28] Prahl S A, Keijzer M, Jacques S L et al. A Monte Carlo Model of Light Propagation in Tissue. in: Müller G J, Sliney D H. Dosimetry of Laser Radiation in Medicine and Biology. Bellingham, WA: SPIE, 1989. 102~111
[29] Wang L, Jacques S L, Zheng L. MCML-Monte Carlo modeling of light transport in multi-layered tissues. Computer Methods and Programs in Biomedicine, 1995, 47: 131~146
[30] Hasegawa Y, Yamada Y, Tamura M et al. Monte Carlo simulation of light transmission through living tissues. Applied Optics, 1991, 30(31): 4515~4520
[31] Lu Q, Gan X S, Gu M et al. Monte Carlo modeling of optical coherence tomography imaging through turbid media. Applied Optics, 2004, 43(8): 1628~1637
[32]鲁强,曾绍群,骆清铭等.混浊介质多光子激发荧光显微成像的蒙特卡罗模拟.光学学报, 2001, 21(9): 1073～1078
[33]鲁强,曾绍群,骆清铭等.混浊介质多光子激发显微成像的快速模型.光学学报, 2001, 21(12): 1509～1512
[34] Bartel S, Hielscher A H. Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media. Applied Optics, 2000, 39(10):1580~1588
[35] Cameron B D, Rakovic M J, Mehrubeoglu M et al. Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium. Optics Letters, 1998, 23(7): 485~487
[36] Wang X, Wang L V. Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments. Journal of Biomedical Optics, 2003, 8(4): 608~617
[37] Wang S, Xu L, Li H et al. Monte Carlo Simulation of the Diffusely Scattered Polarized Light in Turbid Media. in: Chance B, Chen M, Chiou A E T et al. Optics in Health Care and Biomedical Optics: Diagnostics and Treatment II. Bellingham, WA: SPIE, 2005. 823~832
[38] Deng Y, Lu Q, Luo Q et al. Monte Carlo simulation of polarization backscattering spectroscopy. in: Tuchin V V. Optical Technologies in Biophysics and Medicine. Bellingham, WA: SPIE, 2004. 259~264
[39] Wang X, Yao G, Wang L V. Monte Carlo model and single-scattering approximation of the propagation of polarized light in turbid media containing glucose. Applied Optics, 2002, 41(4): 792~801
[40] Ramella-Roman J C, Prahl S A, Jacques S L. Three Monte Carlo programs of polarized light transport into scattering media: part I. Optics Express, 2005, 13(12): 4420~4438
[41] Liu Y, Kim Y L, Li X et al. Investigation of depth selectivity of polarization gating for tissue characterization. Optics Express, 2005, 13(2): 601~611
[42] Phillips K G., Xu M, Gayen S K et al. Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media. Optics Express, 2005, 13(20): 7954~7969
[43] Chang S K, Arifler D, Drezek R et al. Analytical model to describe fluorescence spectra of normal and preneoplastic epithelial tissue: comparison with Monte Carlo simulations and clinical measurements. Journal of Biomedical Optics, 2004, 9(3): 511~522
[44] Lu Q, Luo Q. On Phase Function of Monte Carlo Simulation of Light Transport inTurbid Media. in: Luo Q, Tuchin V V, Gu M et al. Photonics and Imaging in Biology and Medicine. Bellingham, WA: SPIE, 2003. 122~130
[45] Born M, Wolf E.光学原理. (第5版).杨葭荪.北京:科学出版社, 1978. 58～71
[46] Hwang K.高等计算机系统结构并行性可扩展性可编程性. (第1版).王鼎兴,沈美明,郑纬民等.北京:清华大学出版社, 1995. 41～116
[47]李晓梅,莫则尧,胡庆丰等.可扩展并行算法的设计与分析. (第1版).北京:国防工业出版社, 2000. 40～45
[48]梁峰,鲁强,曾绍群.一种基于MPI的并行体绘制算法.计算机工程, 2005, 31(13): 171～173
[49]王雷章,张爱武,刘晓萌.三维建模中平面分割并行算法的设计与实现.系统仿真学报, 2006, 18(增刊2): 239～245
[50] Hielscher A H, Eick A A, Mourant J R et al. Diffuse backscattering Mueller matrices of highly scattering media. Optics Express, 1997, 1(13): 441~453
[2]高上凯.医学成像系统.(第1版).北京:清华大学出版社, 2000. 1～8
[3] Benaron D A. The future of cancer imaging. Cancer and Metastasis Reviews, 2002, 21: 45~78
[4] Zevallos M E, Gayen S K, Das B B et al. Picosecond Electronic Time-Gated Imaging of Bones in Tissues. IEEE Journal of Selected Topics in Quantum Electronics, 1999, 5(4): 916~922
[5] Gayen S K, Alrubaiee M, Savage H E et al. Parotid Gland Tissues Investigated by Picosecond Time-Gated and Optical Spectroscopic Imaging Techniques. IEEE Journal of Selected Topics in Quantum Electronics, 2001, 7(6): 906~911
[6] Chen K, Perelman L T, Zhang Q G et al. Optical computed tomography in a turbid medium using early arriving photons. Journal of Biomedical Optics, 2000, 5(2): 144~154
[7]俞晓峰,丁志华,陈宇恒等.光纤型光学相干层析成像系统的研制.光学学报, 2006, 26(2): 235～238
[8] Xie T Q, Zeidel M L, Pan Y T. Detection of tumorigenesis in urinary bladder with optical coherence tomography: optical characterization of morphological changes. Optics Express, 2002, 10(24): 1431~1443
[9]杨桂娟,梅妍,白亚乡.全息术及其应用.应用光学, 2006, 27(2): 96～100
[10] Sappey A D. Optical imaging through turbid media with a degenerate four wave mixing correlation time gate. Applied Optics, 1994, 33(36): 8346~8354
[11] Dilworth D S, Leith E N, Lopez J L. Three-dimensional confocal imaging of objectsembedded within thick diffusing media. Applied Optics, 1991, 30(14): 1796~1803
[12] Sheppard C J R, Connolly T J, Lee J et al. Confocal imaging of a stratified medium. Applied Optics, 1994, 33(4): 631~640
[13] Ghosh N, Patel H S, Gupta P K. Depolarization of light in tissue phantoms-effect of a distribution in the size of scatterers. Optics Express, 2003, 11(18): 2198~2205
[14] Wang X, Wang L V. Propagation of polarized light in birefringent turbid media: A Monte Carlo study. Journal of Biomedical Optics, 2002, 7(3): 279~290
[15] Demos S G, Radousky H B, Alfano R R. Deep subsurface imaging in tissues using spectral and polarization filtering. Optics Express, 2000, 7(1): 23~28
[16] Ni X, Alfano R R. Time-resolved backscattering of circularly and linearly polarized light in a turbid medium. Optics Letters, 2004, 29(23): 2773~2775
[17] Jacques S L, Roman J R, Lee K. Imaging Superficial Tissues with Polarized Light. Lasers in Surgery and Medicine, 2000, 26: 119~129
[18] Jacques S L, Ramella-Roman J C, Lee K. Imaging skin pathology with polarized light. Journal of Biomedical Optics, 2002, 7(3): 329~340
[19] Kartazayeva S A, Ni X, Alfano R R. Backscattering target detection in a turbid medium by use of circularly and linearly polarized light. Optics letters, 2005, 30(10): 1168~1170
[20] Backman V, Gurjar R, Badizadegan K et al. Polarized Light Scattering Spectroscopy for Quantitative Measurement of Epithelial Cellular Structures In Situ. IEEE Journal of Selected Topics in Quantum Electronics, 1999, 5(4): 1019~1026
[21] Kim Y L, Liu Y, Wali R K et al. Simultaneous Measurement of Angular and Spectral Properties of Light Scattering for Characterization of Tissue Microarchitecture and Its Alteration in Early Precancer. IEEE Journal of Selected Topics in Quantum Electronics, 2003, 9(2): 243~256
[22] Backman V, Wallace M B, Perelman L T et al. Detection of preinvasive cancer cells. Nature, 2000, 406(brief communications): 35~36
[23] Sokolov K, Drezek R, Gossage K et al. Reflectance spectroscopy with polarized light: is it sensitive to cellular and nuclear morphology. Optics Express, 1999, 5(13): 302~317
[24] Johnson T M, Mourant J R. Polarized wavelength-dependent measurements of turbid media. Optics Express, 1999, 4(6): 200~216
[25] Bohren C F, Huffman D R. Absorption and Scattering of Light by Small Particles. New York: Wiley, 1983. 82~129
[26]徐钟济.蒙特卡罗方法. (第1版).上海:上海科学技术出版社, 1985. 1～7
[27] Colasanti A, Guida G, Kisslinger A et al. Multiple processor version of a Monte Carlo code for photon transport in turbid media. Computer Physics Communications, 2000, 132: 84~93
[28] Prahl S A, Keijzer M, Jacques S L et al. A Monte Carlo Model of Light Propagation in Tissue. in: Müller G J, Sliney D H. Dosimetry of Laser Radiation in Medicine and Biology. Bellingham, WA: SPIE, 1989. 102~111
[29] Wang L, Jacques S L, Zheng L. MCML-Monte Carlo modeling of light transport in multi-layered tissues. Computer Methods and Programs in Biomedicine, 1995, 47: 131~146
[30] Hasegawa Y, Yamada Y, Tamura M et al. Monte Carlo simulation of light transmission through living tissues. Applied Optics, 1991, 30(31): 4515~4520
[31] Lu Q, Gan X S, Gu M et al. Monte Carlo modeling of optical coherence tomography imaging through turbid media. Applied Optics, 2004, 43(8): 1628~1637
[32]鲁强,曾绍群,骆清铭等.混浊介质多光子激发荧光显微成像的蒙特卡罗模拟.光学学报, 2001, 21(9): 1073～1078
[33]鲁强,曾绍群,骆清铭等.混浊介质多光子激发显微成像的快速模型.光学学报, 2001, 21(12): 1509～1512
[34] Bartel S, Hielscher A H. Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media. Applied Optics, 2000, 39(10):1580~1588
[35] Cameron B D, Rakovic M J, Mehrubeoglu M et al. Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium. Optics Letters, 1998, 23(7): 485~487
[36] Wang X, Wang L V. Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments. Journal of Biomedical Optics, 2003, 8(4): 608~617
[37] Wang S, Xu L, Li H et al. Monte Carlo Simulation of the Diffusely Scattered Polarized Light in Turbid Media. in: Chance B, Chen M, Chiou A E T et al. Optics in Health Care and Biomedical Optics: Diagnostics and Treatment II. Bellingham, WA: SPIE, 2005. 823~832
[38] Deng Y, Lu Q, Luo Q et al. Monte Carlo simulation of polarization backscattering spectroscopy. in: Tuchin V V. Optical Technologies in Biophysics and Medicine. Bellingham, WA: SPIE, 2004. 259~264
[39] Wang X, Yao G, Wang L V. Monte Carlo model and single-scattering approximation of the propagation of polarized light in turbid media containing glucose. Applied Optics, 2002, 41(4): 792~801
[40] Ramella-Roman J C, Prahl S A, Jacques S L. Three Monte Carlo programs of polarized light transport into scattering media: part I. Optics Express, 2005, 13(12): 4420~4438
[41] Liu Y, Kim Y L, Li X et al. Investigation of depth selectivity of polarization gating for tissue characterization. Optics Express, 2005, 13(2): 601~611
[42] Phillips K G., Xu M, Gayen S K et al. Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media. Optics Express, 2005, 13(20): 7954~7969
[43] Chang S K, Arifler D, Drezek R et al. Analytical model to describe fluorescence spectra of normal and preneoplastic epithelial tissue: comparison with Monte Carlo simulations and clinical measurements. Journal of Biomedical Optics, 2004, 9(3): 511~522
[44] Lu Q, Luo Q. On Phase Function of Monte Carlo Simulation of Light Transport inTurbid Media. in: Luo Q, Tuchin V V, Gu M et al. Photonics and Imaging in Biology and Medicine. Bellingham, WA: SPIE, 2003. 122~130
[45] Born M, Wolf E.光学原理. (第5版).杨葭荪.北京:科学出版社, 1978. 58～71
[46] Hwang K.高等计算机系统结构并行性可扩展性可编程性. (第1版).王鼎兴,沈美明,郑纬民等.北京:清华大学出版社, 1995. 41～116
[47]李晓梅,莫则尧,胡庆丰等.可扩展并行算法的设计与分析. (第1版).北京:国防工业出版社, 2000. 40～45
[48]梁峰,鲁强,曾绍群.一种基于MPI的并行体绘制算法.计算机工程, 2005, 31(13): 171～173
[49]王雷章,张爱武,刘晓萌.三维建模中平面分割并行算法的设计与实现.系统仿真学报, 2006, 18(增刊2): 239～245
[50] Hielscher A H, Eick A A, Mourant J R et al. Diffuse backscattering Mueller matrices of highly scattering media. Optics Express, 1997, 1(13): 441~453
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