Abstract

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

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

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]

2010

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]

2009

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).

2008

2007

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]

2006

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]

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]

2005

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]

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]

2004

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]

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]

2003

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]

2001

1995

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).

1989

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]

1974

1973

1962

1931

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Anderson, C. A.

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]

Arakawa, H.

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]

Brioude, A.

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]

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]

Butler, W. L.

Cao, Y.

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]

Christy, A. A.

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).

Chumanov, G.

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]

Cornell, R. M.

R. M. Cornell and U. Schwertmann, The Iron Oxides: Structure, Properties, Reactions, Occurrences and Uses (Wiley-VCH, 2003).

El-Sayed, M. A.

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]

Evanoff, D. D.

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]

Flock, S. T.

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]

Fu, Q.

Gaonkar, H. A.

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]

Gate, L. F.

Germain, V.

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]

Hao, E.

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]

Ingert, D.

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]

Jiang, X. C.

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]

Jin, R.

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]

Kasemo, B.

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]

Kashima, T.

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]

Kawauchi, H.

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]

Kortüm, G.

G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, 1969).

Kubelka, P.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Kvalheim, O. M.

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).

Langhammer, C.

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]

Lee, K. S.

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]

Lim, B.

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).

Métraux, G. S.

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]

Mirkin, C. A.

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]

Munk, F.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Patterson, M. S.

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]

Pileni, M. P.

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]

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]

Pilon, L.

Ramasubramaniam, R.

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]

Reichman, J.

Roy, A.

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]

Schatz, G. C.

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]

Schwertmann, U.

R. M. Cornell and U. Schwertmann, The Iron Oxides: Structure, Properties, Reactions, Occurrences and Uses (Wiley-VCH, 2003).

Shaath, N.

N. Shaath, Sunscreens: Regulations and Commercial Development, 3rd ed. (Taylor & Francis, 2005).

Skrabalak, S. E.

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).

Sun, W.

Thennadil, S. N.

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Velapoldi, R. A.

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).

Wang, Z.

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]

Wilson, B. C.

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]

Xia, Y.

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).

Xiong, Y.

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).

Yin, J.

Zhi, Z.

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]

Zoric, I.

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]

Angew. Chem. Int. Ed.

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).

Appl. Opt.

Coord. Chem. Rev.

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]

IEEE Trans. Biomed. Eng.

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]

J. Biomed. Opt.

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]

J. Chem. Phys.

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]

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]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Pharm. Sci.

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]

J. Phys. Chem. B

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]

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]

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]

Nature

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]

Vib. Spectrosc.

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).

Z. Tech. Phys.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Other

G. Kortüm, Reflectance Spectroscopy (Springer-Verlag, 1969).

N. Shaath, Sunscreens: Regulations and Commercial Development, 3rd ed. (Taylor & Francis, 2005).

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).

P. Laven, “A computer program for scattering of light from a sphere using Mie theory & the Debye series,” http://www.philiplaven.com/mieplot.htm .

R. M. Cornell and U. Schwertmann, The Iron Oxides: Structure, Properties, Reactions, Occurrences and Uses (Wiley-VCH, 2003).

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Figures (5)

Fig. 1.
Fig. 1.

Measurement configuration used to measure (a) total reflectance and (b) total transmittance.

Fig. 2.
Fig. 2.

K-M scattering coefficient S as a function of reduced scattering coefficient μs of the polystyrene microspheres. Each cluster of points corresponds to different concentration of polystyrene spheres and different points in a cluster correspond to different wavelengths. The solid line is the best linear fit obtained.

Fig. 3.
Fig. 3.

Actual (circles) and extracted (solid line) values of (a) absorption coefficient of the dye and (b) linear fit between actual and extracted absorption coefficient of the dye showing less than 2% variation. (c) Reduced scattering coefficient of pure polystyrene spheres (solid line) and polystyrene spheres in the presence of dye (circles).

Fig. 4.
Fig. 4.

Decoupled values of (a) absorption coefficient μa and (b) reduced scattering coefficient μs of the dispersions containing different concentrations of iron oxide.

Fig. 5.
Fig. 5.

(a) Specific absorption and (b) specific reduced scattering coefficient of the iron oxide particles. The error bars indicate standard error in measurement.

Tables (1)

Tables Icon

Table 1. Samples with Different Concentrations of Dye and Polystyrene Microspheres Used to Obtain the Empirical Relation Shown in Eq. (5)

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

R=(1β2)(exp(αt)exp(αt))(1+β)2exp(αt)(1β)2exp(αt),T=4β(1+β)2exp(αt)(1β)2exp(αt),
S=aμs;K=μa+b(μaμs)c,
S=0.59μs.
K=μa+(μabμsc).
S=0.59μs,K=μa+(μa0.72μs0.4).

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