OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 13 — May. 1, 2014
  • pp: 2892–2898

Decoupling scattering and absorption of turbid samples using a simple empirical relation between coefficients of the Kubelka–Munk and radiative transfer theories

Harshavardhan Ashok Gaonkar, Dinesh Kumar, Rajagopal Ramasubramaniam, and Arindam Roy  »View Author Affiliations

Applied Optics, Vol. 53, Issue 13, pp. 2892-2898 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (521 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Efforts are underway to better understand the absorption properties of micro- and nano-sized particles due to their potential in various photonic applications. However, most of these particles exhibit strong scattering in the spectral regions of interest in addition to absorption. Due to strong interference from scattering, the absorption of these turbid samples cannot be directly measured using conventional spectroscopy techniques. The optical properties of these particles are also different from that of the bulk due to quantum confinement and plasmon resonance effects and cannot be inferred from their bulk properties. By measuring the total transmittance and total reflectance (diffuse and collimated) of turbid samples and using an empirical relation between the coefficients of the Kubelka–Munk and radiative transfer theories, we have demonstrated a method to calculate the absorption and reduced scattering coefficients of turbid samples. This method is capable of extracting the absorption coefficient of turbid samples with an error of 2%. Using this method, we have decoupled the specific absorption and specific reduced scattering coefficients of commercially available micro-sized iron oxide particles. The current method can be used to measure the optical properties of irregularly shaped particle dispersions, which are otherwise difficult to estimate theoretically.

© 2014 Optical Society of America

OCIS Codes
(170.7050) Medical optics and biotechnology : Turbid media
(290.0290) Scattering : Scattering
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(290.7050) Scattering : Turbid media
(160.4236) Materials : Nanomaterials

ToC Category:

Original Manuscript: December 4, 2013
Revised Manuscript: March 27, 2014
Manuscript Accepted: March 29, 2014
Published: April 30, 2014

Virtual Issues
Vol. 9, Iss. 7 Virtual Journal for Biomedical Optics

Harshavardhan Ashok Gaonkar, Dinesh Kumar, Rajagopal Ramasubramaniam, and Arindam Roy, "Decoupling scattering and absorption of turbid samples using a simple empirical relation between coefficients of the Kubelka–Munk and radiative transfer theories," Appl. Opt. 53, 2892-2898 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. Shaath, Sunscreens: Regulations and Commercial Development, 3rd ed. (Taylor & Francis, 2005).
  2. K. S. Lee and M. A. El-Sayed, “Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition,” J. Phys. Chem. B 110, 19220–19225 (2006). [CrossRef]
  3. Y. Xia, Y. Xiong, B. Lim, and S. E. Skrabalak, “Shape-controlled synthesis of metal nanocrystals: simple chemistry meets complex physics?” Angew. Chem. Int. Ed. 48, 60–103 (2009).
  4. Z. Wang, H. Kawauchi, T. Kashima, and H. Arakawa, “Significant influence of TiO2 photoelectrode morphology on the energy conversion efficiency of N719 dye-sensitized solar cell,” Coord. Chem. Rev. 248, 1381–1389 (2004). [CrossRef]
  5. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  6. A. Brioude, X. C. Jiang, and M. P. Pileni, “Optical properties of gold nanorods: DDA simulations supported by experiments,” J. Phys. Chem. B 109, 13138–13142 (2005). [CrossRef]
  7. R. Jin, Y. Cao, E. Hao, G. S. Métraux, G. C. Schatz, and C. A. Mirkin, “Controlling anisotropic nanoparticle growth through plasmon excitation,” Nature 425, 487–490 (2003). [CrossRef]
  8. V. Germain, A. Brioude, D. Ingert, and M. P. Pileni, “Silver nanodisks: size selection via centrifugation and optical properties,” J. Chem. Phys. 122, 124707 (2005). [CrossRef]
  9. Z. Zhi and C. A. Anderson, “Pharmaceutical applications of separation of absorption and scattering in near-infrared spectroscopy (NIRS),” J. Pharm. Sci. 99, 4766–4783 (2010). [CrossRef]
  10. D. D. Evanoff and G. Chumanov, “Size-controlled synthesis of nanoparticles. 2. Measurement of extinction, scattering and absorption cross sections,” J. Phys. Chem. B 108, 13957–13962 (2004). [CrossRef]
  11. W. L. Butler, “Absorption of light by turbid materials,” J. Opt. Soc. Am. 52, 292–299 (1962). [CrossRef]
  12. C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007). [CrossRef]
  13. S. T. Flock, M. S. Patterson, and B. C. Wilson, “Monte Carlo modeling of light propagation in highly scattering tissues. I. Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989). [CrossRef]
  14. P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  15. A. A. Christy, O. M. Kvalheim, and R. A. Velapoldi, “Quantitative analysis in diffuse reflectance spectrometry: a modified Kubelka–Munk equation,” Vib. Spectrosc. 9, 19–27 (1995).
  16. G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, 1969).
  17. A. Roy, R. Ramasubramaniam, and H. A. Gaonkar, “Empirical relationship between Kubelka–Munk and radiative transfer coefficients for extracting optical parameters of tissues in diffusive and nondiffusive regimes,” J. Biomed. Opt. 17, 115006 (2012). [CrossRef]
  18. P. Laven, “A computer program for scattering of light from a sphere using Mie theory & the Debye series,” http://www.philiplaven.com/mieplot.htm .
  19. S. N. Thennadil, “Relationship between the Kubelka–Munk scattering and radiative transfer coefficients,” J. Opt. Soc. Am. A 25, 1480–1485 (2008). [CrossRef]
  20. L. F. Gate, “Comparison of the photon diffusion model and Kubelka–Munk equation with the exact solution of the radiative transport equation,” Appl. Opt. 13, 236–238 (1974). [CrossRef]
  21. J. Reichman, “Determination of absorption and scattering coefficients for non-homogeneous media. 1: theory,” Appl. Opt. 12, 1811–1815 (1973). [CrossRef]
  22. J. Yin and L. Pilon, “Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium,” J. Opt. Soc. Am. A 23, 2784–2796 (2006). [CrossRef]
  23. Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001). [CrossRef]
  24. R. M. Cornell and U. Schwertmann, The Iron Oxides: Structure, Properties, Reactions, Occurrences and Uses (Wiley-VCH, 2003).

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