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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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