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漫反射光谱技术对生物组织快速和无创测量具有非常重要的意义，但缺乏精确的关于漫反射的解析解限制了该技术有效的应用. 本文根据光子迁移理论和二阶相似关系推导了半经验公式，然后利用Monte Carlo方法研究了二阶参量γ对半经验公式的影响. 研究表明，当小孔径收集漫反射光时，反射率与γ成二次函数关系. 与其他含有高阶参量γ的解析模型相比，本文提出的半经验解析模型具有简单的数学形式，这为生物组织光学参量测量和漫反射光谱应用提供了新的理论和技术支持.
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关键词:
- 光学漫反射模型 /
- 高阶光学参量 /
- Monte Carlo 方法
Optical diffuse spectroscopy is crucial in non-invasive measurements and quick analysis of biological tissues. However, the lack of exact analytical solution limits its application. In this paper, a semi-empirical formula for diffuse reflectance is elaborated on the basis of the photon migration theory and the second-order similarity relation, and the influence of second-order parameter γ on the semi-empirical formula is studied by use of Monte Carlo method. Results show that the diffuse reflectance changes with γ nonlinearly when a small aperture detector is used to collected diffuse light. Finally, the proposed semi-empirical formula is mathematically simple compared with the other theoretical mode used at present, and offers a new theoretical and technical support in the measurement of the tissue optical parameters and the application of diffuse reflectance spectroscopy.[1] Barman I, Dingari N C, Rajaram N, Tunnell J W, Dasari R R, Feld M S 2011 Biomed. Opt. Express 2 593
[2] Lai J C, Li Z H, He A Z 2003 Chin. Phys. Lett. 20 2158
[3] He A Z, Lai J C, Li Z H 2005 Chin. Phys. Lett. 22 332
[4] Hayashi T, Kashio Y, Okada E 2003 Appl. Opt. 42 2888
[5] George Z, Aikaterini D 2011 Biomed. Opt. Express 2 3284
[6] Gamm U A, Kanick S C, Sterenborg H J C M, Robinson D J, Amelink A 2012 Opt. Lett. 37 1838
[7] Bolt R A, Bosch J J T 1993 Appl. Opt. 32 4641
[8] Mourant J R, Boyer J, Hielscher A H, Bigio I J 1996 Opt. Lett. 21 546
[9] Bevilacqua F, Depeursinge C 1999 J. Opt. Soc. Am. A 16 2935
[10] LiuY, Zhang X J, Hu Y Z 2004 Acta Optica Sinica 24 877 (in Chinese)[刘迎, 张小娟, 胡佑周 2004 光学学报 24 877]
[11] Tian H J, Liu Y, Wang L J 2006 Opt. Lett. 31 933
[12] Tian H J, Niu P J 2013 Acta Phys. Sin. 62 034201 (in Chinese)[田会娟 2013 62 034201]
[13] Liu Y, Wang L J, Guo Y F, Zhang X J, Gao Z H, Tian H J 2007 Acta Phys. Sin. 56 2119 (in Chinese)[刘迎, 王利军, 郭云峰, 张小娟, 高宗慧, 田会娟 2007 56 2119]
[14] Tian H J, Liu Y, Wang L J, Zhang Z B, Xiao L F 2009 Acta Phys. Sin. 58 243 (in Chinese)[田会娟, 刘迎, 王利军, 张智卜, 肖立峰 2009 58 243]
[15] Liu Y, Liu X J, Qi B B, Tian H J 2011 Acta Phys. Sin. 60 074204 (in Chinese)[刘迎, 刘小君, 齐贝贝, 田会娟 2011 60 074204]
[16] George Z, Aikaterini D 2006 Opt. Express 14 8661
[17] Wu J, Partovi F, Feld M S, Rava R P 1993 Appl. Opt. 32 1115
[18] Bevilacqua F, Piguet D, Marquet P, Gross J D, Tromberg B J, Depeursinge C 1999 A ppl. Opt. 38 4939
[19] Wang L H, Jacques S L, Zheng L Q 1995 Comput. Meth. Prog. Biol. 47 131
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[1] Barman I, Dingari N C, Rajaram N, Tunnell J W, Dasari R R, Feld M S 2011 Biomed. Opt. Express 2 593
[2] Lai J C, Li Z H, He A Z 2003 Chin. Phys. Lett. 20 2158
[3] He A Z, Lai J C, Li Z H 2005 Chin. Phys. Lett. 22 332
[4] Hayashi T, Kashio Y, Okada E 2003 Appl. Opt. 42 2888
[5] George Z, Aikaterini D 2011 Biomed. Opt. Express 2 3284
[6] Gamm U A, Kanick S C, Sterenborg H J C M, Robinson D J, Amelink A 2012 Opt. Lett. 37 1838
[7] Bolt R A, Bosch J J T 1993 Appl. Opt. 32 4641
[8] Mourant J R, Boyer J, Hielscher A H, Bigio I J 1996 Opt. Lett. 21 546
[9] Bevilacqua F, Depeursinge C 1999 J. Opt. Soc. Am. A 16 2935
[10] LiuY, Zhang X J, Hu Y Z 2004 Acta Optica Sinica 24 877 (in Chinese)[刘迎, 张小娟, 胡佑周 2004 光学学报 24 877]
[11] Tian H J, Liu Y, Wang L J 2006 Opt. Lett. 31 933
[12] Tian H J, Niu P J 2013 Acta Phys. Sin. 62 034201 (in Chinese)[田会娟 2013 62 034201]
[13] Liu Y, Wang L J, Guo Y F, Zhang X J, Gao Z H, Tian H J 2007 Acta Phys. Sin. 56 2119 (in Chinese)[刘迎, 王利军, 郭云峰, 张小娟, 高宗慧, 田会娟 2007 56 2119]
[14] Tian H J, Liu Y, Wang L J, Zhang Z B, Xiao L F 2009 Acta Phys. Sin. 58 243 (in Chinese)[田会娟, 刘迎, 王利军, 张智卜, 肖立峰 2009 58 243]
[15] Liu Y, Liu X J, Qi B B, Tian H J 2011 Acta Phys. Sin. 60 074204 (in Chinese)[刘迎, 刘小君, 齐贝贝, 田会娟 2011 60 074204]
[16] George Z, Aikaterini D 2006 Opt. Express 14 8661
[17] Wu J, Partovi F, Feld M S, Rava R P 1993 Appl. Opt. 32 1115
[18] Bevilacqua F, Piguet D, Marquet P, Gross J D, Tromberg B J, Depeursinge C 1999 A ppl. Opt. 38 4939
[19] Wang L H, Jacques S L, Zheng L Q 1995 Comput. Meth. Prog. Biol. 47 131
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