无限介质中近场辐射率的P5近似

刘玲玲; 李晨曦; 万文博; 蒋景英; 贾梦宇; 张丽敏; 高峰; 赵会娟

doi:doi:10.3788/gzxb20164502.0217001

光子学报, 2016, 45 (2): 0217001, 网络出版: 2016-04-01

无限介质中近场辐射率的P5近似

P5 Approximation for Nearfield Radiance in Infinite Medium

论文大纲

刘玲玲 ^1,*李晨曦 ¹万文博 ¹蒋景英 ^1,2贾梦宇 ¹张丽敏 ^1,2高峰 ^1,2赵会娟 ^1,2

作者单位

¹ 天津大学精密仪器与光电子工程学院，天津 300072

² 天津市生物医学检测技术与仪器重点实验室，天津 300072

摘要

针对辐射率的漫射近似、P3近似等正向模型在描述小源探距离及低约化反照率介质下光子传输时存在的局限性，推导了用于小源探距离低反照率无限媒质中各向同性稳态点光源下辐射传输方程在P5近似下的解析解，并将P3近似、P5近似计算的辐射率分别和蒙特卡洛模拟结果进行对比.结果表明:在高约化反照率（0.97）条件下，P5近似和蒙特卡洛模拟结果的最大相对误差为13.17%，而P3为41.57%.在低约化反照率（0.69）条件下，最大相对误差分别为27.78%，286.70%.在其他光学参数下，P5近似与蒙特卡洛模拟的最大相对误差均小于P3.在P5适用的范围内舍弃最大特征根相关项，可以简化解析表达式，提高计算速度，且对P5的计算结果影响甚微.稳态辐射率测量系统仿体验证表明，在高、低约化反照率介质中的小源探距离下，由P5近似计算得到的辐射率和实验测量结果相符.

Abstract

In order to describe photon migration at small source detector separation and in media with low reduced albedo where diffuse approximation and P3 approximation have limitations, the solution of radiance transfer equation in the P5 approximation for the case of an isotropic continuouswave point source in an infinite medium was derived. The P3 and P5 were compared with Monte Carlo simulation to verify the correctness of the derived solution. Under the condition of high reduced albedo (0.97), the maximum relative error between P3 and Monte Carlo simulation is about 41.57% while that between P5 and Monte Carlo simulation is just about 13.17%. In the case of low reduced albedo (0.69), the maximum relative error is about 27.78%, 286.70%, respectively. In the situations of other optical parameters, the maximum relative errors between P5 and Monte Carlo simulation are also no more than that between P3 and Monte Carlo simulation. By abandoning the expressions related to the maximum eigenvalue which has little impact to the result of P5 calculation in the validity condition of P5, a simpler analytical expression can be obtained to accelerate the calculation of P5 approximation. Experiments on a solid phantom with a continuouswave radiance measurement system are conducted and the results show that the radiance calcualted from P5 approximation meets well with that from the experimental measuring at small source detector separation and in media with high or low albedo.

参考文献

[1] ZHU T C, FINLAY J C, HAHN S M. Determination of the distribution of light, optical properties, drug concentration, and tissue oxygenation invivo in human prostate during motexafin lutetiummediated photodynamic therapy［J］. Journal of Photochemistry and Photobiology B: Biology, 2005, 79(3): 231241.

[2] GRABTCHAK S, MONTGOMERY L G, WHELAN W M. Feasibility of interstitial nearinfrared radiance spectroscopy platform for ex vivo canine prostate studies: optical properties extraction, hemoglobin and water concentration, and gold nanoparticles detection［J］. Journal of Biomedical Optics, 2014, 19(5): 057003.

[3] 赵会娟, 贾梦宇, 王微雅, 等. 用于宫颈癌筛查的光电联合检测系统［J］. 光子学报, 2015, 44(10): 0417001.

ZHAO Huijuan, JIA Mengyu, WANG Weiya, et al. A cervical cancer screening system based on an optoelectrical joint measurement［J］. Acta Photonica Sinica, 2015, 44(10): 0417001.

[4] 赵会娟, 王倩, 周晓青, 等. 小鼠荧光层析成像系统级数据提取扩展方法［J］. 光子学报, 2014, 43(10): 1011002.

ZHAO Huijuan, WANG Qian, ZHOU Xiaoqing, et al. Fluorescence tomographical system and a novel dataextractionextensionmethod for small animal imaging［J］. Acta Photonica Sinica, 2014, 43(10): 1011002.

[5] CHIN L C L, WHELAN W M, VITKIN I A. Information content of point radiance measurements in turbid media: implications for interstitial optical property quantification［J］. Applied Optics, 2006, 45(9): 21012114.

[6] BARAJAS O, BALLANGRUD A M, MILLER G G, et al. Monte Carlo modeling of angular radiance in tissue phantoms and human prostate: PDT light dosimetry［J］. Physics in Medicine and Biology, 1997, 42(9): 1675–1687.

[7] CHIN L C L, LLOYD B, WHELAN W M, et al. Interstitial point radiance spectroscopy of turbid media［J］. Journal of Applied Physics, 2009, 105(10):102025.

[8] 史振志, 赵会娟, 陈文亮, 等. 近光源下基于稳态空间分辨漫反射测量的光学参数反构［J］. 天津大学学报, 2012, 45(6): 552559.

SHI Zhenzhi, ZHAO Huijuan, CHEN Wenliang, et al. Derivation of optical properties from steadystate spatially resolved diffuse reflectance measurement at small sourcedetector separations［J］. Journal of Tianjin University, 2012, 45(6): 552559.

[9] LIEMERT A, KIENLE A. Analytical Green’s function of the radiative transfer radiance for the in nite medium［J］. Physical Review, 2011, 83(3):036605.

[10] HULL E L, FOSTER T H. Steadystate reflectance spectroscopy in the P3 approximation［J］. Journal of the Optical Society of America A, 2001, 18(3): 584599.

[11] ZHU T C, DIMOFTE A, FINLAY J C, et al. Optical properties of human prostate at 732nm measured invivo during motexafin lutetium mediated photodynamic therapy［J］. Photochem. Photobiol, 2005, 81(1): 96105.

[12] 魏华江, 邢达, 何博华, 等. 良性前列腺增生组织对钛宝石激光的吸收和散射特性［J］. 光谱学与光谱分析, 2008, 28(1): 1013.

WEI Huajiang, XING Da, HE Bohua, et al. Absorption and scattering characteristics of human benign prostatic hyperplasia tissue with Ti :Sapphire laser irradiation in vitro［J］. Spectroscopy and Spectral Analysis, 2008, 28(1): 1013.

[13] GRABTCHAK S, PALMER T J, FOSCHUM F, et al. Experimental spectroangular mapping of light distribution in turbid media［J］. Journal of Biomedical Optics, 2011, 17(6): 067007.

[14] DICKEY D, BARAJAS O, et al. Radiance modelling using the P3 approximation［J］. Physics in Medicine and Biology, 1998, 43(12): 35593570.

[15] LIEMERT A, KIENLE A. Analytical solutions of the simplified spherical harmonics equations［J］. Optics Letters, 2010, 35(20): 35073509.

[16] FARIS G W. PN approximation for frequencydomain measurements in scattering media［J］. Applied Optics, 2005, 44(11): 2058 2071.

[17] CHAI C G, LUO Q M, LIU Q. Analytical solution of P3 approximation to radiative transfer equation for an infinite homogenous media and its validity［J］. Journal of Modern Optics, 2008, 55(21): 3611–3624.

刘玲玲, 李晨曦, 万文博, 蒋景英, 贾梦宇, 张丽敏, 高峰, 赵会娟. 无限介质中近场辐射率的P5近似[J]. 光子学报, 2016, 45(2): 0217001. LIU Lingling, LI Chenxi, WAN Wenbo, JIANG Jingying, JIA Mengyu, ZHANG Limin, GAO Feng, ZHAO Huijuan. P5 Approximation for Nearfield Radiance in Infinite Medium[J]. ACTA PHOTONICA SINICA, 2016, 45(2): 0217001.

无限介质中近场辐射率的P5近似

关于本站 Cookie 的使用提示

全站搜索

无限介质中近场辐射率的P5近似

相关论文

相关资讯

关于本站 Cookie 的使用提示

全站搜索