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Sensitivity of Delta-P1 approximation model to second-order parameter

Wang Rui Wang Yu-Shan

Sensitivity of Delta-P1 approximation model to second-order parameter

Wang Rui, Wang Yu-Shan
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  • The sensitivity of the second-order parameter of the Henyey-Greenstein phase function based on the spatially-resolved diffuse reflectance within the two-point-source approximation to the Delta-P1 approximation model is studied, and the analytical expression of the sensitivity is derived. The results show that the analytic solution of the Delta-P1 approximation model for reflectance contains the second-order parameter of the scattering phase function compared with the diffusion approximation model, and the second-order parameter has significant influence (the extreme value greater than 30%) on the analytic solution for spatially-resolved diffuse reflectance with small source-detector separations ( 1.5 mm) no matter whether the absorption is weak or strong. The research has theoretical significance for obtaining the optical information abour tissue with the second-order parameter .
    • Funds: Project supported by the Natural Science Foundation of the Shihezi University, China (Grant No. ZRKX2009YB11).
    [1]

    Zhang Z X 2008 New Technology and Applications of Biomedical Photonics (Beijing: Science Press) (in Chinese) [张镇西 2008 生物医学光子学新技术及应用(北京: 科学出版社)]

    [2]

    Tuchin V V 2007 Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (Bellingham: SPIE Press)

    [3]

    Xu L Q, Li H, Xie S S 2008 Acta Phys. Sin. 57 6024 (in Chinese) [徐兰青, 李晖, 谢树森 2008 物理学报 57 6024]

    [4]

    Bevilacqua F, Piguet D, Marquet P, Gross J D, Tromberg B J, Depeursinge C 1999 Appl. Opt. 38 4939

    [5]

    Liu Y, Zhang X J, Hu Y Z 2004 Acta Opt. Sin. 24 877 (in Chinese) [刘迎, 张小娟, 胡佑周 2004 光学学报 24 877]

    [6]

    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 物理学报 56 2119]

    [7]

    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 物理学报 58 243]

    [8]

    Venugopalan V, You J S, Tromberg B J 1998 Phys. Rev. E 58 2395

    [9]

    Hayakawa C K, Hill B Y, You J S 2004 Appl. Opt. 43 4577

    [10]

    Wang R, Liu Y 2010 Chin. J. Lasers 37 1147 (in Chinese) [王锐, 刘迎 2010 中国激光 37 1147]

    [11]

    Liu Y, Liu X J, Qi B B, Tian H J 2011 Acta Phys. Sin. 60 74204 [刘迎, 刘小君, 齐贝贝, 田会娟 2011 物理学报 60 74204]

    [12]

    Qi B B, Liu Y, Ja G Y, Liu X J 2011 Acta Phys. Sin. 60 128701 (in Chinese) [齐贝贝, 刘迎, 贾光一, 刘小君 2011 物理学报 60 128701]

    [13]

    Groenhuis R A J, Ferwerda H A, Bosch J J T 1983 Appl. Opt. 22 2456

  • [1]

    Zhang Z X 2008 New Technology and Applications of Biomedical Photonics (Beijing: Science Press) (in Chinese) [张镇西 2008 生物医学光子学新技术及应用(北京: 科学出版社)]

    [2]

    Tuchin V V 2007 Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (Bellingham: SPIE Press)

    [3]

    Xu L Q, Li H, Xie S S 2008 Acta Phys. Sin. 57 6024 (in Chinese) [徐兰青, 李晖, 谢树森 2008 物理学报 57 6024]

    [4]

    Bevilacqua F, Piguet D, Marquet P, Gross J D, Tromberg B J, Depeursinge C 1999 Appl. Opt. 38 4939

    [5]

    Liu Y, Zhang X J, Hu Y Z 2004 Acta Opt. Sin. 24 877 (in Chinese) [刘迎, 张小娟, 胡佑周 2004 光学学报 24 877]

    [6]

    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 物理学报 56 2119]

    [7]

    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 物理学报 58 243]

    [8]

    Venugopalan V, You J S, Tromberg B J 1998 Phys. Rev. E 58 2395

    [9]

    Hayakawa C K, Hill B Y, You J S 2004 Appl. Opt. 43 4577

    [10]

    Wang R, Liu Y 2010 Chin. J. Lasers 37 1147 (in Chinese) [王锐, 刘迎 2010 中国激光 37 1147]

    [11]

    Liu Y, Liu X J, Qi B B, Tian H J 2011 Acta Phys. Sin. 60 74204 [刘迎, 刘小君, 齐贝贝, 田会娟 2011 物理学报 60 74204]

    [12]

    Qi B B, Liu Y, Ja G Y, Liu X J 2011 Acta Phys. Sin. 60 128701 (in Chinese) [齐贝贝, 刘迎, 贾光一, 刘小君 2011 物理学报 60 128701]

    [13]

    Groenhuis R A J, Ferwerda H A, Bosch J J T 1983 Appl. Opt. 22 2456

  • [1] Hu Xiaoliang, Liang Hong, Wang Huili. Lattice Boltzmann method simulations of the immiscible Rayleigh-Taylor instability with high Reynolds numbers. Acta Physica Sinica, 2020, 69(4): 1-10. doi: 10.7498/aps.69.20191504
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  • Received Date:  20 January 2012
  • Accepted Date:  16 March 2012
  • Published Online:  20 September 2012

Sensitivity of Delta-P1 approximation model to second-order parameter

  • 1. Department of Physics, College of Science, Shihezi University, Shihezi 832000, China;
  • 2. College of Water Conservancy & Architectural Engineering, Shihezi University, Shihezi 832000, China
Fund Project:  Project supported by the Natural Science Foundation of the Shihezi University, China (Grant No. ZRKX2009YB11).

Abstract: The sensitivity of the second-order parameter of the Henyey-Greenstein phase function based on the spatially-resolved diffuse reflectance within the two-point-source approximation to the Delta-P1 approximation model is studied, and the analytical expression of the sensitivity is derived. The results show that the analytic solution of the Delta-P1 approximation model for reflectance contains the second-order parameter of the scattering phase function compared with the diffusion approximation model, and the second-order parameter has significant influence (the extreme value greater than 30%) on the analytic solution for spatially-resolved diffuse reflectance with small source-detector separations ( 1.5 mm) no matter whether the absorption is weak or strong. The research has theoretical significance for obtaining the optical information abour tissue with the second-order parameter .

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