Abstract

An improved method used to determine the absorption and scattering characteristics of a weakly absorbing substance containing bubbles is suggested. The identification procedure is based on a combination of directional-hemispherical measurements and predictions of Mie-scattering theory including approximate relations for a medium with polydisperse bubbles. A modified two-flux approximation is suggested for the calculation of directional-hemispherical transmittance and reflectance of a refracting and scattering medium. The complete identification procedure gives not only the spectral radiative properties but also the volume fraction of bubbles and the characteristics of possible impurity of the medium. This procedure is used to obtain new data on near-infrared properties of fused-quartz samples containing bubbles.

© 2005 Optical Society of America

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2005

A. M. Papadopoulos, “State of the art in thermal insulation materials and aims for future developments,” Energy Build. 37, 77–86 (2005).
[CrossRef]

L. A. Dombrovsky, “Modeling of thermal radiation of a polymer coating containing hollow microspheres,” High Temp. 43, 247–258 (2005).
[CrossRef]

T. Kournyts’kyi, R. V. N. Melnik, A. Gachkevich, “Thermal behavior of absorbing and scattering glass media containing molecular water impurity,” Int. J. Thermal Sci. 44, 107–114 (2005).
[CrossRef]

2004

L. A. Dombrovsky, “The propagation of infrared radiation in a semitransparent liquid containing gas bubbles,” High Temp. 42, 133–139 (2004).

W. Sun, N. S. Loeb, Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

S. S. Moiseev, V. A. Petrov, S. V. Stepanov, “The optical properties of heat-insulating ceramics made of microballoons of aluminum oxide,” High Temp. 42, 127–132 (2004).
[CrossRef]

D. Baillis, L. Pilon, H. Randrianalisoa, R. Gomez, R. Viskanta, “Measurements of radiation characteristics of fused quartz containing bubbles,” J. Opt. Soc. Am. A 21, 149–159 (2004).
[CrossRef]

2003

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

L. A. Dombrovsky, S. S. Sazhin, S. V. Mikhalovsky, R. Wood, M. R. Heikal, “Spectral properties of diesel fuel droplets,” Fuel 82, 15–22 (2003).
[CrossRef]

L. Hespel, S. Mainguy, J.-J. Greffet, “Radiative properties of scattering and absorbing dense media: theory and experimental study,” J. Quant. Spectrosc. Radiat. Transfer 77, 193–210 (2003).
[CrossRef]

2002

L. A. Dombrovsky, “A modified differential approximation for thermal radiation of semitransparent nonisothermal particles: application to optical diagnostics of plasma spraying,” J. Quant. Spectrosc. Radiat. Transfer 73, 433–441 (2002).
[CrossRef]

P. J. Coelho, “Bounded skew high order resolution schemes for the discrete ordinates method,” J. Comput. Phys. 175, 412–437 (2002).
[CrossRef]

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

A. G. Fedorov, L. Pilon, “Glass foam: formation, transport properties, and heat, mass, and radiation transfer,” J. Non-Cryst. Solids 311, 154–173 (2002).
[CrossRef]

M. L. German, P. S. Grinchuk, “Mathematical model for calculating the heat-protection properties of the composite coating ceramic microspheres—binder,” J. Eng. Phys. Thermophys. 75, 1301–1313 (2002).
[CrossRef]

J.-F. Sacadura, D. Baillis, “Experimental characterization of thermal radiation properties of disperse media,” Int. J. Thermal Sci. 41, 699–707 (2002).
[CrossRef]

2001

C. Rosé, T. Girasole, G. Gréhan, G. Gouesbet, B. Maheu, “Average crossing parameter and forward scattering ratio values in four-flux model for multiple scattering media,” Opt. Commun. 194, 251–263 (2001).
[CrossRef]

M. A. Khashan, A. Y. Nassif, “Dispersion of the optical constants of quartz and polymethyl methacrylate glasses in a wide spectral range: 0.2–3 µm,” Opt. Commun. 188, 129–139 (2001).
[CrossRef]

M. Caldas, V. Semião, “A new approximate phase function for isolated particles and polydispersions,” J. Quant. Spectrosc. Radiat. Transfer 68, 521–542 (2001).
[CrossRef]

I. W. Sudiarta, P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

M. Tomozawa, D.-L. Kim, V. Lou, “Preparation of high purity, low water content fused silica glass,” J. Non-Cryst. Solids 296, 102–106 (2001).
[CrossRef]

C. Z. Tan, J. Arndt, “Refractive index, optical dispersion, and group velocity of infrared waves in silica glass,” J. Phys. Chem. Solids 62, 1087–1092 (2001).
[CrossRef]

Q. Fu, W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
[CrossRef]

2000

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

L. A. Dombrovsky, “Thermal radiation from nonisothermal spherical particle,” Int. J. Heat Mass Transfer 43, 1661–1672 (2000).
[CrossRef]

W. E. Vargas, P. Greenwood, J. E. Otterstedt, G. A. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transfer 67, 327–363 (2000).
[CrossRef]

1999

G. M. Campbell, E. Mougeot, “Creation and characterisation of aerated food products,” Trends Food Sci. Technol. 10, 283–296 (1999).
[CrossRef]

1998

C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelength by IR spectroscopy,” J. Non-Cryst. Solids 223, 158–163 (1998).
[CrossRef]

X. Zhang, M. Lewis, B. Johnson, “Influence of bubbles on scattering of light in the ocean,” Appl. Opt. 37, 6525–6536 (1998).
[CrossRef]

1997

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka-Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

1996

L. A. Dombrovsky, “Approximate methods for calculating radiation heat transfer in dispersed systems,” Thermal Eng. 43, 235–243 (1996).

B.-T. Liou, C.-Y. Wu, “Radiative transfer in a multi-layer medium with Fresnel interfaces,” Heat Mass Transfer 32, 103–107 (1996).
[CrossRef]

1994

V. A. Petrov, “Solution of inverse problems of radiation transfer in semitransparent scattering materials based on the radiation diffusion approximation,” High Temp.—High Pressures 26, 339–351 (1994).

1984

M. M. Gurevich, E. F. Itsko, M. M. Seredenko, Optical Properties of Paint Coatings (Chemistry, 1984) (in Russian).

1977

1974

W. C. Mundy, J. A. Roux, A. M. Smith, “Mie scattering in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
[CrossRef]

1973

1971

1965

Arndt, J.

C. Z. Tan, J. Arndt, “Refractive index, optical dispersion, and group velocity of infrared waves in silica glass,” J. Phys. Chem. Solids 62, 1087–1092 (2001).
[CrossRef]

Baillis, D.

D. Baillis, L. Pilon, H. Randrianalisoa, R. Gomez, R. Viskanta, “Measurements of radiation characteristics of fused quartz containing bubbles,” J. Opt. Soc. Am. A 21, 149–159 (2004).
[CrossRef]

J.-F. Sacadura, D. Baillis, “Experimental characterization of thermal radiation properties of disperse media,” Int. J. Thermal Sci. 41, 699–707 (2002).
[CrossRef]

D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transfer 67, 327–363 (2000).
[CrossRef]

Bass, C. D.

Baum, B. A.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Beder, E. C.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1968).

Caldas, M.

M. Caldas, V. Semião, “A new approximate phase function for isolated particles and polydispersions,” J. Quant. Spectrosc. Radiat. Transfer 68, 521–542 (2001).
[CrossRef]

Campbell, G. M.

G. M. Campbell, E. Mougeot, “Creation and characterisation of aerated food products,” Trends Food Sci. Technol. 10, 283–296 (1999).
[CrossRef]

Chylek, P.

I. W. Sudiarta, P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

P. Chylek, “Light scattering by small particles in an absorbing medium,” J. Opt. Soc. Am. 67, 561–563 (1977).
[CrossRef]

Coelho, P. J.

P. J. Coelho, “Bounded skew high order resolution schemes for the discrete ordinates method,” J. Comput. Phys. 175, 412–437 (2002).
[CrossRef]

Dianov, E. M.

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

Dombrovsky, L. A.

L. A. Dombrovsky, “Modeling of thermal radiation of a polymer coating containing hollow microspheres,” High Temp. 43, 247–258 (2005).
[CrossRef]

L. A. Dombrovsky, “The propagation of infrared radiation in a semitransparent liquid containing gas bubbles,” High Temp. 42, 133–139 (2004).

L. A. Dombrovsky, S. S. Sazhin, S. V. Mikhalovsky, R. Wood, M. R. Heikal, “Spectral properties of diesel fuel droplets,” Fuel 82, 15–22 (2003).
[CrossRef]

L. A. Dombrovsky, “A modified differential approximation for thermal radiation of semitransparent nonisothermal particles: application to optical diagnostics of plasma spraying,” J. Quant. Spectrosc. Radiat. Transfer 73, 433–441 (2002).
[CrossRef]

L. A. Dombrovsky, “Thermal radiation from nonisothermal spherical particle,” Int. J. Heat Mass Transfer 43, 1661–1672 (2000).
[CrossRef]

L. A. Dombrovsky, “Approximate methods for calculating radiation heat transfer in dispersed systems,” Thermal Eng. 43, 235–243 (1996).

L. A. Dombrovsky, Radiation Heat Transfer in Disperse Systems (Begell, 1996).

Fedorov, A. G.

A. G. Fedorov, L. Pilon, “Glass foam: formation, transport properties, and heat, mass, and radiation transfer,” J. Non-Cryst. Solids 311, 154–173 (2002).
[CrossRef]

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

Fu, Q.

W. Sun, N. S. Loeb, Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

Q. Fu, W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
[CrossRef]

Gachkevich, A.

T. Kournyts’kyi, R. V. N. Melnik, A. Gachkevich, “Thermal behavior of absorbing and scattering glass media containing molecular water impurity,” Int. J. Thermal Sci. 44, 107–114 (2005).
[CrossRef]

Gao, B.-C.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

German, M. L.

M. L. German, P. S. Grinchuk, “Mathematical model for calculating the heat-protection properties of the composite coating ceramic microspheres—binder,” J. Eng. Phys. Thermophys. 75, 1301–1313 (2002).
[CrossRef]

Girasole, T.

C. Rosé, T. Girasole, G. Gréhan, G. Gouesbet, B. Maheu, “Average crossing parameter and forward scattering ratio values in four-flux model for multiple scattering media,” Opt. Commun. 194, 251–263 (2001).
[CrossRef]

Gomez, R.

Gouesbet, G.

C. Rosé, T. Girasole, G. Gréhan, G. Gouesbet, B. Maheu, “Average crossing parameter and forward scattering ratio values in four-flux model for multiple scattering media,” Opt. Commun. 194, 251–263 (2001).
[CrossRef]

Greenwood, P.

W. E. Vargas, P. Greenwood, J. E. Otterstedt, G. A. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

Greffet, J.-J.

L. Hespel, S. Mainguy, J.-J. Greffet, “Radiative properties of scattering and absorbing dense media: theory and experimental study,” J. Quant. Spectrosc. Radiat. Transfer 77, 193–210 (2003).
[CrossRef]

Gréhan, G.

C. Rosé, T. Girasole, G. Gréhan, G. Gouesbet, B. Maheu, “Average crossing parameter and forward scattering ratio values in four-flux model for multiple scattering media,” Opt. Commun. 194, 251–263 (2001).
[CrossRef]

Grinchuk, P. S.

M. L. German, P. S. Grinchuk, “Mathematical model for calculating the heat-protection properties of the composite coating ceramic microspheres—binder,” J. Eng. Phys. Thermophys. 75, 1301–1313 (2002).
[CrossRef]

Gunde, M. K.

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka-Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

Gurevich, M. M.

M. M. Gurevich, E. F. Itsko, M. M. Seredenko, Optical Properties of Paint Coatings (Chemistry, 1984) (in Russian).

Hale, G. M.

Heikal, M. R.

L. A. Dombrovsky, S. S. Sazhin, S. V. Mikhalovsky, R. Wood, M. R. Heikal, “Spectral properties of diesel fuel droplets,” Fuel 82, 15–22 (2003).
[CrossRef]

Hespel, L.

L. Hespel, S. Mainguy, J.-J. Greffet, “Radiative properties of scattering and absorbing dense media: theory and experimental study,” J. Quant. Spectrosc. Radiat. Transfer 77, 193–210 (2003).
[CrossRef]

Hu, Y. X.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Huang, H.-L.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Hulst, H. C. van de

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Itsko, E. F.

M. M. Gurevich, E. F. Itsko, M. M. Seredenko, Optical Properties of Paint Coatings (Chemistry, 1984) (in Russian).

Johnson, B.

Khashan, M. A.

M. A. Khashan, A. Y. Nassif, “Dispersion of the optical constants of quartz and polymethyl methacrylate glasses in a wide spectral range: 0.2–3 µm,” Opt. Commun. 188, 129–139 (2001).
[CrossRef]

Kim, D.-L.

M. Tomozawa, D.-L. Kim, V. Lou, “Preparation of high purity, low water content fused silica glass,” J. Non-Cryst. Solids 296, 102–106 (2001).
[CrossRef]

Kournyts’kyi, T.

T. Kournyts’kyi, R. V. N. Melnik, A. Gachkevich, “Thermal behavior of absorbing and scattering glass media containing molecular water impurity,” Int. J. Thermal Sci. 44, 107–114 (2005).
[CrossRef]

Lewis, M.

Liou, B.-T.

B.-T. Liou, C.-Y. Wu, “Radiative transfer in a multi-layer medium with Fresnel interfaces,” Heat Mass Transfer 32, 103–107 (1996).
[CrossRef]

Loeb, N. S.

W. Sun, N. S. Loeb, Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

Lou, V.

M. Tomozawa, D.-L. Kim, V. Lou, “Preparation of high purity, low water content fused silica glass,” J. Non-Cryst. Solids 296, 102–106 (2001).
[CrossRef]

Maheu, B.

C. Rosé, T. Girasole, G. Gréhan, G. Gouesbet, B. Maheu, “Average crossing parameter and forward scattering ratio values in four-flux model for multiple scattering media,” Opt. Commun. 194, 251–263 (2001).
[CrossRef]

Mainguy, S.

L. Hespel, S. Mainguy, J.-J. Greffet, “Radiative properties of scattering and absorbing dense media: theory and experimental study,” J. Quant. Spectrosc. Radiat. Transfer 77, 193–210 (2003).
[CrossRef]

Malitson, I. H.

Melnik, R. V. N.

T. Kournyts’kyi, R. V. N. Melnik, A. Gachkevich, “Thermal behavior of absorbing and scattering glass media containing molecular water impurity,” Int. J. Thermal Sci. 44, 107–114 (2005).
[CrossRef]

Mikhalovsky, S. V.

L. A. Dombrovsky, S. S. Sazhin, S. V. Mikhalovsky, R. Wood, M. R. Heikal, “Spectral properties of diesel fuel droplets,” Fuel 82, 15–22 (2003).
[CrossRef]

Mishchenko, M. I.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Modest, M. F.

M. F. Modest, Radiative Heat Transfer, 2nd ed.(Academic, 2003).

Moiseev, S. S.

S. S. Moiseev, V. A. Petrov, S. V. Stepanov, “The optical properties of heat-insulating ceramics made of microballoons of aluminum oxide,” High Temp. 42, 127–132 (2004).
[CrossRef]

Mougeot, E.

G. M. Campbell, E. Mougeot, “Creation and characterisation of aerated food products,” Trends Food Sci. Technol. 10, 283–296 (1999).
[CrossRef]

Mundy, W. C.

W. C. Mundy, J. A. Roux, A. M. Smith, “Mie scattering in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
[CrossRef]

Nassif, A. Y.

M. A. Khashan, A. Y. Nassif, “Dispersion of the optical constants of quartz and polymethyl methacrylate glasses in a wide spectral range: 0.2–3 µm,” Opt. Commun. 188, 129–139 (2001).
[CrossRef]

Niklasson, G. A.

W. E. Vargas, P. Greenwood, J. E. Otterstedt, G. A. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

Orel, B.

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka-Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

Orel, Z. C.

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka-Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

Otterstedt, J. E.

W. E. Vargas, P. Greenwood, J. E. Otterstedt, G. A. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

Papadopoulos, A. M.

A. M. Papadopoulos, “State of the art in thermal insulation materials and aims for future developments,” Energy Build. 37, 77–86 (2005).
[CrossRef]

Park, S. K.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Petrov, V. A.

S. S. Moiseev, V. A. Petrov, S. V. Stepanov, “The optical properties of heat-insulating ceramics made of microballoons of aluminum oxide,” High Temp. 42, 127–132 (2004).
[CrossRef]

V. A. Petrov, “Solution of inverse problems of radiation transfer in semitransparent scattering materials based on the radiation diffusion approximation,” High Temp.—High Pressures 26, 339–351 (1994).

Pilon, L.

D. Baillis, L. Pilon, H. Randrianalisoa, R. Gomez, R. Viskanta, “Measurements of radiation characteristics of fused quartz containing bubbles,” J. Opt. Soc. Am. A 21, 149–159 (2004).
[CrossRef]

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

A. G. Fedorov, L. Pilon, “Glass foam: formation, transport properties, and heat, mass, and radiation transfer,” J. Non-Cryst. Solids 311, 154–173 (2002).
[CrossRef]

Platnick, S. E.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Plotnichenko, V. G.

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

Querry, M. P.

Randrianalisoa, H.

Rosé, C.

C. Rosé, T. Girasole, G. Gréhan, G. Gouesbet, B. Maheu, “Average crossing parameter and forward scattering ratio values in four-flux model for multiple scattering media,” Opt. Commun. 194, 251–263 (2001).
[CrossRef]

Roux, J. A.

W. C. Mundy, J. A. Roux, A. M. Smith, “Mie scattering in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
[CrossRef]

Sacadura, J.-F.

J.-F. Sacadura, D. Baillis, “Experimental characterization of thermal radiation properties of disperse media,” Int. J. Thermal Sci. 41, 699–707 (2002).
[CrossRef]

D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transfer 67, 327–363 (2000).
[CrossRef]

Sazhin, S. S.

L. A. Dombrovsky, S. S. Sazhin, S. V. Mikhalovsky, R. Wood, M. R. Heikal, “Spectral properties of diesel fuel droplets,” Fuel 82, 15–22 (2003).
[CrossRef]

Semião, V.

M. Caldas, V. Semião, “A new approximate phase function for isolated particles and polydispersions,” J. Quant. Spectrosc. Radiat. Transfer 68, 521–542 (2001).
[CrossRef]

Seredenko, M. M.

M. M. Gurevich, E. F. Itsko, M. M. Seredenko, Optical Properties of Paint Coatings (Chemistry, 1984) (in Russian).

Shackleford, W. L.

Smith, A. M.

W. C. Mundy, J. A. Roux, A. M. Smith, “Mie scattering in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
[CrossRef]

Sokolov, V. O.

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

Stepanov, S. V.

S. S. Moiseev, V. A. Petrov, S. V. Stepanov, “The optical properties of heat-insulating ceramics made of microballoons of aluminum oxide,” High Temp. 42, 127–132 (2004).
[CrossRef]

Sudiarta, I. W.

I. W. Sudiarta, P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

Sun, W.

W. Sun, N. S. Loeb, Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

Q. Fu, W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
[CrossRef]

Tan, C. Z.

C. Z. Tan, J. Arndt, “Refractive index, optical dispersion, and group velocity of infrared waves in silica glass,” J. Phys. Chem. Solids 62, 1087–1092 (2001).
[CrossRef]

C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelength by IR spectroscopy,” J. Non-Cryst. Solids 223, 158–163 (1998).
[CrossRef]

Tomozawa, M.

M. Tomozawa, D.-L. Kim, V. Lou, “Preparation of high purity, low water content fused silica glass,” J. Non-Cryst. Solids 296, 102–106 (2001).
[CrossRef]

Tsay, S.-C.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Vargas, W. E.

W. E. Vargas, P. Greenwood, J. E. Otterstedt, G. A. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

Viskanta, R.

D. Baillis, L. Pilon, H. Randrianalisoa, R. Gomez, R. Viskanta, “Measurements of radiation characteristics of fused quartz containing bubbles,” J. Opt. Soc. Am. A 21, 149–159 (2004).
[CrossRef]

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

Winker, D. M.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Wiscombe, W. J.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1968).

Wood, R.

L. A. Dombrovsky, S. S. Sazhin, S. V. Mikhalovsky, R. Wood, M. R. Heikal, “Spectral properties of diesel fuel droplets,” Fuel 82, 15–22 (2003).
[CrossRef]

Wu, C.-Y.

B.-T. Liou, C.-Y. Wu, “Radiative transfer in a multi-layer medium with Fresnel interfaces,” Heat Mass Transfer 32, 103–107 (1996).
[CrossRef]

Yang, P.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Zhang, X.

Appl. Opt.

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[CrossRef] [PubMed]

Appl. Opt.

Energy Build.

A. M. Papadopoulos, “State of the art in thermal insulation materials and aims for future developments,” Energy Build. 37, 77–86 (2005).
[CrossRef]

Fuel

L. A. Dombrovsky, S. S. Sazhin, S. V. Mikhalovsky, R. Wood, M. R. Heikal, “Spectral properties of diesel fuel droplets,” Fuel 82, 15–22 (2003).
[CrossRef]

Heat Mass Transfer

B.-T. Liou, C.-Y. Wu, “Radiative transfer in a multi-layer medium with Fresnel interfaces,” Heat Mass Transfer 32, 103–107 (1996).
[CrossRef]

High Temp.—High Pressures

V. A. Petrov, “Solution of inverse problems of radiation transfer in semitransparent scattering materials based on the radiation diffusion approximation,” High Temp.—High Pressures 26, 339–351 (1994).

High Temp.

S. S. Moiseev, V. A. Petrov, S. V. Stepanov, “The optical properties of heat-insulating ceramics made of microballoons of aluminum oxide,” High Temp. 42, 127–132 (2004).
[CrossRef]

L. A. Dombrovsky, “The propagation of infrared radiation in a semitransparent liquid containing gas bubbles,” High Temp. 42, 133–139 (2004).

L. A. Dombrovsky, “Modeling of thermal radiation of a polymer coating containing hollow microspheres,” High Temp. 43, 247–258 (2005).
[CrossRef]

Int. J. Heat Mass Transfer

L. A. Dombrovsky, “Thermal radiation from nonisothermal spherical particle,” Int. J. Heat Mass Transfer 43, 1661–1672 (2000).
[CrossRef]

Int. J. Thermal Sci.

T. Kournyts’kyi, R. V. N. Melnik, A. Gachkevich, “Thermal behavior of absorbing and scattering glass media containing molecular water impurity,” Int. J. Thermal Sci. 44, 107–114 (2005).
[CrossRef]

J.-F. Sacadura, D. Baillis, “Experimental characterization of thermal radiation properties of disperse media,” Int. J. Thermal Sci. 41, 699–707 (2002).
[CrossRef]

J. Non-Cryst. Solids

V. G. Plotnichenko, V. O. Sokolov, E. M. Dianov, “Hydroxyl groups in high-purity silica glass,” J. Non-Cryst. Solids 261, 186–194 (2000).
[CrossRef]

J. Am. Ceram. Soc.

A. G. Fedorov, R. Viskanta, “Radiative characteristics of glass foams,” J. Am. Ceram. Soc. 83, 2769–2776 (2000).
[CrossRef]

J. Am. Ceram. Soc.

L. Pilon, R. Viskanta, “Radiation characteristics of glass containing bubbles,” J. Am. Ceram. Soc. 86, 1313–1320 (2003).
[CrossRef]

J. Comput. Phys.

P. J. Coelho, “Bounded skew high order resolution schemes for the discrete ordinates method,” J. Comput. Phys. 175, 412–437 (2002).
[CrossRef]

J. Eng. Phys. Thermophys.

M. L. German, P. S. Grinchuk, “Mathematical model for calculating the heat-protection properties of the composite coating ceramic microspheres—binder,” J. Eng. Phys. Thermophys. 75, 1301–1313 (2002).
[CrossRef]

J. Non-Cryst. Solids

A. G. Fedorov, L. Pilon, “Glass foam: formation, transport properties, and heat, mass, and radiation transfer,” J. Non-Cryst. Solids 311, 154–173 (2002).
[CrossRef]

M. Tomozawa, D.-L. Kim, V. Lou, “Preparation of high purity, low water content fused silica glass,” J. Non-Cryst. Solids 296, 102–106 (2001).
[CrossRef]

C. Z. Tan, “Determination of refractive index of silica glass for infrared wavelength by IR spectroscopy,” J. Non-Cryst. Solids 223, 158–163 (1998).
[CrossRef]

J. Opt. Soc. Am.

W. C. Mundy, J. A. Roux, A. M. Smith, “Mie scattering in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. Chem. Solids

C. Z. Tan, J. Arndt, “Refractive index, optical dispersion, and group velocity of infrared waves in silica glass,” J. Phys. Chem. Solids 62, 1087–1092 (2001).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

W. Sun, N. S. Loeb, Q. Fu, “Light scattering by coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

I. W. Sudiarta, P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

L. A. Dombrovsky, “A modified differential approximation for thermal radiation of semitransparent nonisothermal particles: application to optical diagnostics of plasma spraying,” J. Quant. Spectrosc. Radiat. Transfer 73, 433–441 (2002).
[CrossRef]

M. Caldas, V. Semião, “A new approximate phase function for isolated particles and polydispersions,” J. Quant. Spectrosc. Radiat. Transfer 68, 521–542 (2001).
[CrossRef]

L. Hespel, S. Mainguy, J.-J. Greffet, “Radiative properties of scattering and absorbing dense media: theory and experimental study,” J. Quant. Spectrosc. Radiat. Transfer 77, 193–210 (2003).
[CrossRef]

D. Baillis, J.-F. Sacadura, “Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization,” J. Quant. Spectrosc. Radiat. Transfer 67, 327–363 (2000).
[CrossRef]

Opt. Commun.

C. Rosé, T. Girasole, G. Gréhan, G. Gouesbet, B. Maheu, “Average crossing parameter and forward scattering ratio values in four-flux model for multiple scattering media,” Opt. Commun. 194, 251–263 (2001).
[CrossRef]

M. A. Khashan, A. Y. Nassif, “Dispersion of the optical constants of quartz and polymethyl methacrylate glasses in a wide spectral range: 0.2–3 µm,” Opt. Commun. 188, 129–139 (2001).
[CrossRef]

Optical Properties of Paint Coatings

M. M. Gurevich, E. F. Itsko, M. M. Seredenko, Optical Properties of Paint Coatings (Chemistry, 1984) (in Russian).

Prog. Org. Coat.

Z. C. Orel, M. K. Gunde, B. Orel, “Application of the Kubelka-Munk theory for the determination of the optical properties of solar absorbing paints,” Prog. Org. Coat. 30, 59–66 (1997).
[CrossRef]

Sol. Energy

W. E. Vargas, P. Greenwood, J. E. Otterstedt, G. A. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

Thermal Eng.

L. A. Dombrovsky, “Approximate methods for calculating radiation heat transfer in dispersed systems,” Thermal Eng. 43, 235–243 (1996).

Trends Food Sci. Technol.

G. M. Campbell, E. Mougeot, “Creation and characterisation of aerated food products,” Trends Food Sci. Technol. 10, 283–296 (1999).
[CrossRef]

Other

M. F. Modest, Radiative Heat Transfer, 2nd ed.(Academic, 2003).

L. A. Dombrovsky, Radiation Heat Transfer in Disperse Systems (Begell, 1996).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

M. Born, E. Wolf, Principles of Optics (Pergamon, 1968).

Y. S. Touloukian, D. P. DeWitt, eds, Thermal Radiative Properties: Nonmetallic Solids, Vol. 8 of Thermophysical Properties of Matter (Plenum, 1972).

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Figures (9)

Fig. 1
Fig. 1

Effect of the absorbing and refracting medium inside a bubble on its efficiency factor of absorption for n0 = 1.4: a, κi = 10−4; b, κi = 10−3; 1, ni = 1.1; 2, ni = 1.2.

Fig. 2
Fig. 2

Effect of refracting medium inside a bubble on its transport efficiency factor of scattering: a, n0 = 1.4; b, n0 = 1.5; 1, ni = 1; 2, ni = 1.2; 3, ni = 1.3.

Fig. 3
Fig. 3

Normalized size distribution of bubbles in the fused-quartz sample.

Fig. 4
Fig. 4

Directional-hemispherical transmittance and reflectance for two samples of fused quartz containing bubbles: 1, z0 = 5 mm; 2, z0 = 10 mm.

Fig. 5
Fig. 5

Comparison of different experimental data for the absorption index of fused quartz: 1, Beder et al.34; 2, Touloukian and DeWitt35; 3, Khashan and Nassif36; 4, present paper.

Fig. 6
Fig. 6

Effect of the scattering function on the directional-hemispherical transmittance and reflectance. CDOM calculations for n0 = 1.4: a, transport approximation; b, Henyey–Greenstein approximation; 1, τtr0 = 0.2; 2, τtr0 = 0.5; 3, τtr0 = 1.

Fig. 7
Fig. 7

Directional-hemispherical reflectance for two samples of fused quartz containing bubbles: a, z0 = 5 mm; b, 10 mm; 1, measurement; 2, calculation for fν = 3.5%; 3, fν = 4.5%.

Fig. 8
Fig. 8

Transport albedo of fused quartz containing bubbles (fν = 4%): 1, z0 = 5 mm; 2, 10 mm.

Fig. 9
Fig. 9

Absorption coefficient of fused quartz containing bubbles (fν = 4%): a, z0 = 5 mm; b, z0 = 10 mm; 1, experiment; 2, theoretical prediction.

Tables (1)

Tables Icon

Table 1 Directional-Hemispherical Characteristics for n0 = 1.4

Equations (52)

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

α λ = 4 π κ 0 λ + 0.75 f ν a 30 0 Q a a 2 F ( a ) d a ,
σ λ tr = 0.75 f ν a 30 0 Q s tr a 2 F ( a ) d a ,
a i j = 0 a i F ( a ) d a / 0 a j F ( a ) d a .
Φ λ ( μ ) σ λ = 0.75 f ν a 30 0 Q s ϕ λ ( μ ) a 2 F ( a ) d a ,
σ λ = 0.75 f ν a 30 0 Q s a 2 F ( a ) d a .
Q a = 8 κ 0 x / 3 , Q s tr = 0.9 ( n 0 1 ) .
α λ = ( 1 f ν ) α λ 0 , σ λ tr = 0.675 ( n 0 1 ) ( f ν / a 32 ) ,
μ ¯ = 1 0.45 ( n 0 1 ) .
Q a i = 0.9 ( 3 n i / n 0 1 ) κ i x , Q s tr ( i ) = 0.9 ( n 0 / n i 1 ) .
Q a i = 1 exp [ 0.9 ( 3 n i / n 0 1 ) κ i x ] .
α λ = ( 1 f ν + f ν i ) α λ 0 + 0.675 f ν i ( 3 n i / n 0 1 ) α λ i / 2 , σ λ tr = 0.675 ( n 0 / n i 1 ) ( f ν / a 32 ) ,
f ν = ( 4 π / 3 ) a 30 / d 3 ,
f s = 2 a 10 / d 3 ,
f ν = ( 2 π / 3 ) f s a 32 a 21 .
f ν = ( 4 π / 3 ) N a 30 / ( z 0 S ) ,
μ τ + = ω 4 π 1 1 ( τ , μ ) [ 0 2 π Φ ( μ 0 ) d ψ ] d μ ,
( 0 , μ ) = R ( 0 , μ ) + ( 1 R ) δ ( 1 μ ) , ( τ 0 , μ ) = R ( τ 0 , μ ) for μ > 0 ,
= I λ / ( n 0 2 I λ e ) , ω = σ λ / β λ , τ = β λ z ,
μ 0 = μ μ + ( 1 μ 2 ) 1 / 2 ( 1 μ 2 ) 1 / 2 cos ( ψ ψ ) .
Φ ( μ 0 ) = 1 μ ¯ + 2 μ ¯ δ ( 1 μ 0 ) ,
μ τ tr + = ω tr 2 1 1 d μ ,
( 0 , μ ) = R ( 0 , μ ) + ( 1 R ) δ ( 1 μ ) , ( τ tr 0 , μ ) = R ( τ tr 0 , μ ) μ > 0 ,
= J ¯ + 1 R 1 1 R 1 C [ exp ( τ tr ) δ ( 1 μ ) + C exp ( τ tr ) δ ( 1 + μ ) ] ,
μ J ¯ τ tr + J ¯ = ω tr 2 { 1 1 J ¯ d μ + 1 R 1 1 R 1 C × [ exp ( τ tr ) + C exp ( τ tr ) ] } ,
J ¯ ( 0 , μ ) = R ( μ ) J ¯ ( 0 , μ ) , J ¯ ( τ tr 0 , μ ) = R ( μ ) J ¯ ( τ tr 0 , μ ) for μ > 0 .
R d h = R d h 0 + 0 1 [ 1 R ( μ ) ] J ¯ ( 0 , μ ) μ d μ , T d h = T d h 0 + 0 1 [ 1 R ( μ ) ] J ¯ ( τ tr 0 , μ ) μ d μ ,
R d h 0 = R 1 + ( 1 R 1 ) 2 C 1 R 1 C , T d h 0 = R 1 + ( 1 R 1 ) 2 1 R 1 C exp ( τ tr 0 ) .
Φ ( μ 0 ) = ( 1 μ ¯ 2 ) / ( 1 + μ ¯ 2 2 μ ¯ μ 0 ) 3 / 2 .
J ( τ tr , μ ) = { φ 0 ( τ tr ) , 1 μ < μ c ψ 0 ( τ tr ) , μ c < μ < μ c with μ c ( 1 1 / n 0 2 ) 1 / 2 . φ 0 + ( τ tr ) , μ c < μ 1
g 0 + β 2 g 0 = β 2 χ [ exp ( τ tr ) + C exp ( τ tr ) ] , ( 1 + μ c ) g 0 ( 0 ) = 2 γ g 0 ( 0 ) , ( 1 + μ c ) g 0 ( τ tr 0 ) = 2 γ g 0 ( τ tr 0 ) ,
β 2 = 4 ( 1 + μ c ) 2 1 ω tr 1 ω tr μ c , γ = ( 1 R 1 ) / ( 1 + R 1 ) , χ = ω tr 1 ω tr 1 R 1 1 R 1 C .
R d h = R d h 0 + γ ( 1 μ c 2 ) g 0 ( 0 ) / 2 , T d h = T d h 0 + γ ( 1 μ c 2 ) g 0 ( τ tr 0 ) / 2 .
R d h = R d h 0 + D ( 1 + B / β + C ) / 2 , T d h = T d h 0 + D [ ( 1 + R 1 ) exp ( τ tr 0 ) + A / β ] / 2 ,
D = γ ( 1 μ c 2 ) χ β 2 / ( β 2 1 ) , A = ( γ 1 γ 2 R 1 ) ( φ s + c ) exp ( τ tr 0 ) ( γ 2 γ 1 C ) ( 1 + φ 2 ) s + 2 φ c , B = ( γ 1 γ 2 R 1 ) exp ( τ tr 0 ) ( γ 2 γ 1 C ) ( φ s + c ) ( 1 + φ 2 ) s + 2 φ c , γ 1 = 1 2 γ ¯ , γ 2 = 1 + 2 γ ¯ , φ = 2 γ ¯ / β , γ ¯ = γ / ( 1 + μ c ) , s = sinh ( β τ tr 0 ) , c = cosh ( β τ tr 0 ) .
Δ α λ = 4 f ν i κ i ( 3 n i / n 0 1 ) / λ .
T d h ( % ) R d h ( % )
78.0 5.1
78.0 5.1
35.9 4.5
35.9 4.5
78.8 5.9
78.8 5.9
37.7 6.6
37.7 6.4
80.0 7.1
80.0 7.1
40.7 10.0
40.6 9.6
82.1 9.2
82.0 9.2
46.6 16.8
46.6 16.0

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