OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 1 — Jan. 4, 2010

Simple and accurate expressions for diffuse reflectance of semi-infinite and two-layer absorbing and scattering media

Dmitry Yudovsky and Laurent Pilon  »View Author Affiliations


Applied Optics, Vol. 48, Issue 35, pp. 6670-6683 (2009)
http://dx.doi.org/10.1364/AO.48.006670


View Full Text Article

Enhanced HTML    Acrobat PDF (1400 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present computationally efficient and accurate semiempirical models of light transfer suitable for real-time diffuse reflectance spectroscopy. The models predict the diffuse reflectance of both (i) semi- infinite homogeneous and (ii) two-layer media exposed to normal and collimated light. The two-layer medium consisted of a plane-parallel slab of finite thickness over a semi-infinite layer with identical index of refraction but different absorption and scattering properties. The model accounted for absorption and anisotropic scattering, as well as for internal reflection at the medium/air interface. All media were assumed to be nonemitting, strongly forward scattering, with indices of refraction between 1.00 and 1.44 and transport single-scattering albedos between 0.50 and 0.99. First, simple analytical expressions for the diffuse reflectance of the semi-infinite and two-layer media considered were derived using the two-flux approximation. Then, parameters appearing in the analytical expression previously derived were instead fitted to match results from more accurate Monte Carlo simulations. A single semiempirical parameter was sufficient to relate the diffuse reflectance to the radiative properties and thickness of the semi- infinite and two-layer media. The present model can be used for a wide range of applications including noninvasive diagnosis of biological tissue.

© 2009 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(160.1190) Materials : Anisotropic optical materials
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(230.4170) Optical devices : Multilayers
(010.5620) Atmospheric and oceanic optics : Radiative transfer

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: August 4, 2009
Revised Manuscript: October 21, 2009
Manuscript Accepted: October 26, 2009
Published: December 1, 2009

Virtual Issues
Vol. 5, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Dmitry Yudovsky and Laurent Pilon, "Simple and accurate expressions for diffuse reflectance of semi-infinite and two-layer absorbing and scattering media," Appl. Opt. 48, 6670-6683 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-48-35-6670


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. M. Kuebler, “How NIR is the future in blood flow monitoring?,” J. Appl. Physiol. 104, 905-906 (2008). [CrossRef]
  2. A. Torricelli, D. Contini, A. Pifferi, L. Spinelli, and R. Cubeddu, “Functional brain imaging by multi-wavelength time-resolved near infrared spectroscopy,” Opto-Electron. Rev. 16, 131-135(2008). [CrossRef]
  3. G. Zonios, A. Dimou, I. Bassukas, D. Galaris, A. Tsolakidis, and E. Kaxiras, “Melanin absorption spectroscopy: new method for noninvasive skin investigation and melanoma detection,” J. Biomed. Opt. 13, 014017 (2008). [CrossRef]
  4. V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE, 2007).
  5. L. Khaodhiar, T. Dinh, K. T. Schomacker, S. V. Panasyuk, J. E. Freeman, R. Lew, T. Vo, A. A. Panasyuk, C. Lima, J. M. Giurini, T. E. Lyons, and A. Veves, “The use of medical hyperspectral technology to evaluate microcirculatory changes in diabetic foot ulcers and to predict clinical outcomes,” Diabetes Care 30, 903-910 (2007). [CrossRef]
  6. R. L. P. van Veen, A. Amelink, M. Menke-Pluymers, C. van der Pol, and H. Sterenborg, “Optical biopsy of breast tissue using differential path-length spectroscopy,” Phys. Med. Biol. 50, 2573-2581 (2005). [CrossRef]
  7. U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121-147 (2003). [CrossRef]
  8. H. Huang, H. Yu, H. Xu, and Y. Ying, “Near infrared spectroscopy for on/in-line monitoring of quality in foods and beverages: a review,” J. Food Eng. 87, 303-313 (2008).
  9. A. A. Gowen, C. P. O'Donnell, P. J. Cullen, G. Downey, and J. M. Frias, “Hyperspectral imaging-an emerging process analytical tool for food quality and safety control,” Trends Food Sci. Technol. 18, 590-598 (2007). [CrossRef]
  10. G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427-1432 (2007).
  11. I. Kim, M. S. Kim, Y. R. Chen, and S. G. Kong, “Detection of skin tumors on chicken carcasses using hyperspectral fluorescence imaging,” Trans. Am. Soc. Agric. Eng. 47, 1785-1792(2004).
  12. N. Yamada and S. Fujimura, “Nondestructive measurement of chlorophyll pigment content in plant leaves from three-color reflectance and transmittance,” Appl. Opt. 30, 3964-3973(1991). [CrossRef]
  13. M. J. D. van Gemert, and W. M. Star, “Relations between the Kubelka-Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287-298 (1987). [CrossRef]
  14. D. Landgrebe, “Hyperspectral image data analysis,” IEEE Signal Processi. Mag. 19, 17-28 (2002). [CrossRef]
  15. E. S. Chalhoub and H. F. Campos Velho, “Simultaneous estimation of radiation phase function and albedo in natural waters,” J. Quant. Spectrosc. Radiat. Transfer 69, 137-149(2001). [CrossRef]
  16. L. L. Richardson, “Remote sensing of algal bloom dynamics,” BioScience 46, 492-501 (1996). [CrossRef]
  17. R. Drezek, K. Sokolov, U. Utzinger, I. Boiko, A. Malpica, M. Follen, and R. Richards-Kortum, “Understanding the contributions of NADH and collagen to cervical tissue fluorescence spectra: Modeling, measurements, and implications,” J. Biomed. Opt. 6, 385-396 (2001). [CrossRef]
  18. G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43, 113-122 (1996). [CrossRef]
  19. S. H. Tseng, A. Grant, and A. J. Durkin, “In-vivo determination of skin near-infrared optical properties using diffuse optical spectroscopy,” J. Biomed. Opt. 13, 014016(2008). [CrossRef]
  20. K. J. Zuzak, M. D. Schaeberle, E. N. Lewis, and I. W. Levin, “Visible reflectance hyperspectral imaging: characterization of a noninvasive, in-vivo system for determining tissue perfusion,” Anal. Chem. 74, 2021-2028 (2002). [CrossRef]
  21. M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003).
  22. M. J. C. van Gemert and W. M. Star, “Relations between the Kubelka-Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 98 (1987).
  23. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70-83 (1941). [CrossRef]
  24. M. J. C. Van Gemert, S. L. Jacques, H. Sterenborg, and W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146-1154(1989). [CrossRef]
  25. S. L. Jacques, C. A. Alter, and S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309-333 (1987).
  26. K. Zhou, Z. Ren, S. Lin, H. Bao, B. Guo, and H. Y. Shum, “Real-time smoke rendering using compensated ray marching,” in Proceedings of the Association for Computing Machinery's Special Interest Group on Graphics and Interactive Techniques, Vol. 1, pp. 1-12 (2008).
  27. D. Q. Nguyen, R. Fedkiw, and H. W. Jensen, “Physically based modeling and animation of fire,” in Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques (Association for Computing Machinery, 2002), pp. 721-728.
  28. D. Calzetti, “The dust opacity of star-forming galaxies,” Publ. Astron. Soc. Pac. 113, 1449-1485 (2001). [CrossRef]
  29. J. M. Carvano, “Compositional interpretation of the geometric albedo of asteroids,” Astron. Astrophys. 486, 1031-1038(2008). [CrossRef]
  30. S. Chandrasekhar, Radiative Transfer (Courier Dover, 1960).
  31. P. Kubelka and F. Munk, “A contribution to the optics of pigments,” Zeit. Technol. Phys. 12, 593-599 (1931).
  32. A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1-22 (1905). [CrossRef]
  33. P. Edström, “Examination of the revised Kubelka-Munk theory: considerations of modeling strategies,” J. Opt. Soc. Am. 24), 548-556 (2007). [CrossRef]
  34. J. L. Saunderson, “Calculation of the color of pigmented plastics,” J. Opt. Soc. Am. 32, 727-736 (1942). [CrossRef]
  35. W. E. Vargas and G. A. Niklasson, “Applicability conditions of the Kubelka-Munk theory,” Appl. Opt. 36, 5580-5586(1997). [CrossRef]
  36. A. Gershun, “Fresnel reflection of diffusely incident light,” J. Opt. Soc. Am. 35, 162 (1945). [CrossRef]
  37. W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166-2185 (1990). [CrossRef]
  38. G. Yoon, S. A. Prahl, and A. J. Welch, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. 28, 2250-2255 (1989). [CrossRef]
  39. S. L. Jacques, “Modeling tissue optics using Monte Carlo modeling: a tutorial,” Proc. SPIE 6854, 68540T (2008). [CrossRef]
  40. I. V. Meglinski and S. J. Matcher, “Modeling of skin reflectance spectra,” Proc. SPIE 4241, 78-87 (2001). [CrossRef]
  41. C. M. Gardner, S. L. Jacques, and A. J. Welch, “Light transport in tissue: accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation,” Lasers Surg. Med. 18, 129-138 (1996). [CrossRef]
  42. J. Wu, F. Partovi, M. S. Field, and R. P. Rava, “Diffuse reflectance from turbid media: an analytical model of photon migration,” Appl. Opt. 32, 1115-1121 (1993). [CrossRef]
  43. H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, “Monte Carlo modeling of tissue autofluorescence measurement and imaging,” Proc. SPIE 2135, 94-104 (1994). [CrossRef]
  44. I. Lux and L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, 1991), p. 650.
  45. L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995). [CrossRef]
  46. M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9, 148-154(1989). [CrossRef]
  47. G. M. Hale and M. R. Querry, “Optical constants of water in the 200 nm to 200 μm wavelength region,” Appl. Opt. 12, 555-563 (1973). [CrossRef]
  48. L. Wang and S. L. Jacques, “Monte Carlo modeling of light transport in multi-layered tissues in standard C,” last accessed 31 March 2009, http://labs.seas.wustl.edu/bme/Wang/mcr5/Mcman.pdf.
  49. S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329-340 (2002). [CrossRef]
  50. K. M. Katika and L. Pilon, “Steady-state directional diffuse reflectance and fluorescence of human skin,” Appl. Opt. 45, 4174-4183 (2006). [CrossRef]
  51. S. Prahl, “Optical absorption of hemoglobin” (2002), http://omlc.ogi.edu/spectra/hemoglobin/hemestruct/index.html.
  52. S. L. Jacques, “Origins of tissue optical properties in the UVA, visible, and NIR regions,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano and J. G. Fujimoto, eds. (Optical Society of America, 1996), Vol. 2, pp. 364-370.
  53. I. S. Saidi, “Transcutaneous optical measurement of hyperbilirubinemia in neonates,” Ph.D. dissertation (Rice University, 1992).
  54. S. L. Jacques and D. J. McAuliffe, “The melanosome: threshold temperature for explosive vaporization and internal absorption coefficient during pulsed laser irradiation,” Photochem. Photobiol. 53, 769-775 (1991).
  55. R. R. Anderson and J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13-19 (1981). [CrossRef]
  56. M. J. C. Van Gemert, A. J. Welch, W. M. Star, M. Motamedi, and W. F. Cheong, “Tissue optics for a slab geometry in the diffusion approximation,” Lasers Med. Sci. 2, 295-302(1987). [CrossRef]
  57. A. Krishnaswamy and G. V. G. Baranoski, “A biophysically-based spectral model of light interaction with human skin,” in Computer Graphics Forum (Blackwell, 2004), Vol. 23, pp. 331-340.
  58. A. N. Yaroslavsky, A. V. Priezzhev, J. R. I. V. Yaroslavsky, and H. Battarbee, “Optics of blood,” in Handbook of Optical Biomedical Diagnostics, V. V. Tuchin, ed. (SPIE, 2002), pp. 169-216.
  59. R. Flewelling, “Noninvasive optical monitoring,” in The Biomedical Engineering Handbook, J. Bronzion, ed. (IEEE, 1981), pp. 1-11.
  60. S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, and E. O. Reynolds, “Characterization of the near infrared absorption spectra of cytochrome aa3 and haemoglobin for the non-invasive monitoring of cerebral oxygenation.,” Biochim. Biophys. Acta Bioenergetics 933, 184-192 (1988). [CrossRef]
  61. A. P. Harris, M. J. Sendak, R. T. Donham, M. Thomas, and D. Duncan, “Absorption characteristics of human fetal hemoglobin at wavelengths used in pulse oximetry,” J. Clin. Monit. Comput. 4, 175-177 (1988). [CrossRef]
  62. S. Takatani and M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. bme-26, 656-664 (1979). [CrossRef]
  63. O. W. Van Assendelft, Spectrophotometry of Haemoglobin Derivatives (Thomas, Springfield, 1970).
  64. J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. 37, 3586-3593 (1998). [CrossRef]
  65. S. L. Jacques, “Skin optics,” Oregon Medical Laser Center News 1998, pp. 1-9 (1998).
  66. Y. Lee and K. Hwang, “Skin thickness of Korean adults,” Surg. Radiol. Anat. 24, 183-189 (2002). [CrossRef]
  67. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. SIAM Control 11, 431-441(1963).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited