Abstract

The electromagnetic far field, as well as the near field, originating from light interaction with a red blood cell (RBC) volume-equivalent spheroid, was analyzed by utilizing the T-matrix theory. This method is a powerful tool that makes it possible to study the influence of cell shape on the angular distribution of scattered light. General observations were that the three-dimensional shape, as well as the optical thickness apparent to the incident field, affects the forward scattering. The backscattering was influenced by the shape of the surface facing the incident beam. Furthermore sphering as well as elongation of an oblate RBC into a volume-equivalent sphere or a prolate spheroid, respectively, was theoretically modeled to imitate physiological phenomena caused, e.g., by heat or the increased shear stress of flowing blood. Both sphering and elongation were shown to decrease the intensity of the forward-directed scattering, thus yielding lower g factors. The sphering made the scattering pattern independent of azimuthal scattering angle ϕs, whereas the elongation induced more apparent ϕs-dependent patterns. The light scattering by a RBC volume-equivalent spheroid was thus found to be highly influenced by the shape of the scattering object. A near-field radius r nf was evaluated as the distance to which the maximum intensity of the total near field had decreased to 2.5 times that of the incident field. It was estimated to 2–24.5 times the maximum radius of the scattering spheroid, corresponding to 12–69 μm. Because the near-field radius was shown to be larger than a simple estimation of the distance between the RBC’s in whole blood, the assumption of independent scattering, frequently employed in optical measurements on whole blood, seems inappropriate. This also indicates that one cannot extrapolate the results obtained from diluted blood to whole blood by multiplying with a simple concentration factor.

© 1998 Optical Society of America

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1998

1997

A. M. K. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, M. J. C. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65, 366–373 (1997).
[CrossRef] [PubMed]

1996

H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

A. Kienle, M. S. Patterson, L. Ott, R. Steiner, “Determination of the scattering coefficient and the anisotropy factor from laser Doppler spectra of liquids including blood,” Appl. Opt. 35, 3404–3412 (1996).
[CrossRef] [PubMed]

1995

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

A. Quirantes Sierra, A. V. Delgado Mora, “Size-shape determination of nonspherical particles in suspension by means of full and depolarized static light scattering,” Appl. Opt. 34, 6256–6262 (1995).
[CrossRef]

S. Kashima, A. Sohda, Y. Yagyu, T. Ohsawa, “Determination of deformability of erythrocytes by change in scattering cross section,” Jpn. J. Appl. Phys. 34, 680–682 (1995).
[CrossRef]

B. Chance, H. Liu, T. Kitai, Y. Zhang, “Effects of solutes on optical properties of biological materials: models, cells, and tissues,” Anal. Biochem. 227, 351–362 (1995).
[CrossRef] [PubMed]

1994

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

1993

1990

Y. Mendelson, A. C. Clermont, R. A. Peura, B.-C. Lin, “Blood glucose measurement by multiple attenuated total reflection and infrared absorption spectroscopy,” IEEE Trans. Biomed. Eng. 37, 458–465 (1990).
[CrossRef] [PubMed]

1988

1987

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

J. M. Steinke, A. P. Shepherd, “Reflectance measurements of hematocrit and oxyhemoglobin saturation,” Am. J. Physiol. 253, H147–H153 (1987).
[PubMed]

1986

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

M. Bitbol, “Red blood cell orientation in orbit C = 0,” Biophys. J. 49, 1055–1068 (1986).
[CrossRef] [PubMed]

1985

M. Sugihara, “Motion and deformation of a red blood cell in a shear flow: a two-dimensional simulation of the wall effect,” Biorheology 22, 1–19 (1985).
[PubMed]

1984

1983

M. Tomita, M. Gotoh, M. Yamamoto, N. Tanahashi, M. Kobari, “Effects of hemolysis, hematocrit, RBC swelling, and flow rate on light scattering by blood in a 0.26 cm ID transparent tube,” Biorheology 20, 485–494 (1983).
[PubMed]

1979

1977

R. A. Meyer, “Light scattering from red blood cell ghosts: sensitivity of angular dependent structure to membrane thickness and refractive index,” Appl. Opt. 16, 2036–2038 (1977).
[CrossRef] [PubMed]

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef] [PubMed]

1976

1975

1974

J. C. Lin, A. W. Guy, “A note on the optical scattering characteristics of whole blood,” IEEE Trans. Biomed. Eng. 21, 43–45 (1974).
[CrossRef] [PubMed]

1972

P. Latimer, B. E. Pyle, “Light scattering at various angles. Theoretical predictions of the effects of particle volume changes,” Biophys. J. 12, 764–773 (1972).
[CrossRef] [PubMed]

E. Evans, Y.-C. Fung, “Improved measurements of the erythrocyte geometry,” Microvasc. Res. 4, 335–347 (1972).
[CrossRef] [PubMed]

1971

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

1968

P. Latimer, D. M. Moore, F. Dudley Bryant, “Changes in total light scattering and absorption caused by changes in particle conformation,” J. Theor. Biol. 21, 348–367 (1968).
[CrossRef] [PubMed]

1941

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Alter, C. A.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Andersson-Engels, S.

A. M. K. Nilsson, C. Sturesson, D. L. Liu, S. Andersson-Engels, “Changes in spectral shape of tissue optical properties in conjunction with laser-induced thermotherapy,” Appl. Opt. 37, 1256–1267 (1998).
[CrossRef]

A. M. K. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, M. J. C. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65, 366–373 (1997).
[CrossRef] [PubMed]

Asano, S.

Barber, P. W.

Bäumler, H.

H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

Bitbol, M.

M. Bitbol, “Red blood cell orientation in orbit C = 0,” Biophys. J. 49, 1055–1068 (1986).
[CrossRef] [PubMed]

Chance, B.

B. Chance, H. Liu, T. Kitai, Y. Zhang, “Effects of solutes on optical properties of biological materials: models, cells, and tissues,” Anal. Biochem. 227, 351–362 (1995).
[CrossRef] [PubMed]

Clermont, A. C.

Y. Mendelson, A. C. Clermont, R. A. Peura, B.-C. Lin, “Blood glucose measurement by multiple attenuated total reflection and infrared absorption spectroscopy,” IEEE Trans. Biomed. Eng. 37, 458–465 (1990).
[CrossRef] [PubMed]

Cope, M.

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

Cruz, L.

Delgado Mora, A. V.

Delpy, D. T.

M. Cope, D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination,” Med. Biol. Eng. Comput. 26, 289–294 (1988).
[CrossRef] [PubMed]

Dudley Bryant, F.

P. Latimer, D. M. Moore, F. Dudley Bryant, “Changes in total light scattering and absorption caused by changes in particle conformation,” J. Theor. Biol. 21, 348–367 (1968).
[CrossRef] [PubMed]

Evans, E.

E. Evans, Y.-C. Fung, “Improved measurements of the erythrocyte geometry,” Microvasc. Res. 4, 335–347 (1972).
[CrossRef] [PubMed]

Fonseca, L. F.

Fung, Y.-C.

E. Evans, Y.-C. Fung, “Improved measurements of the erythrocyte geometry,” Microvasc. Res. 4, 335–347 (1972).
[CrossRef] [PubMed]

Gómez, M.

Gotoh, M.

M. Tomita, M. Gotoh, M. Yamamoto, N. Tanahashi, M. Kobari, “Effects of hemolysis, hematocrit, RBC swelling, and flow rate on light scattering by blood in a 0.26 cm ID transparent tube,” Biorheology 20, 485–494 (1983).
[PubMed]

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Groner, W.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Guy, A. W.

J. C. Lin, A. W. Guy, “A note on the optical scattering characteristics of whole blood,” IEEE Trans. Biomed. Eng. 21, 43–45 (1974).
[CrossRef] [PubMed]

Hahn, H.

H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

Heethaar, R. M.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hill, A. C.

Hill, S. C.

S. C. Hill, A. C. Hill, P. W. Barber, “Light scattering by size/shape distributions of soil particles and spheroids,” Appl. Opt. 23, 1025–1031 (1984).
[CrossRef] [PubMed]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Hoekstra, A. G.

Ishimaru, A.

Jacques, S. L.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Jöbsis, F. F.

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef] [PubMed]

Johnson, C.

Kashima, S.

S. Kashima, A. Sohda, Y. Yagyu, T. Ohsawa, “Determination of deformability of erythrocytes by change in scattering cross section,” Jpn. J. Appl. Phys. 34, 680–682 (1995).
[CrossRef]

Kienle, A.

Kim, Y. R.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Kitai, T.

B. Chance, H. Liu, T. Kitai, Y. Zhang, “Effects of solutes on optical properties of biological materials: models, cells, and tissues,” Anal. Biochem. 227, 351–362 (1995).
[CrossRef] [PubMed]

Kobari, M.

M. Tomita, M. Gotoh, M. Yamamoto, N. Tanahashi, M. Kobari, “Effects of hemolysis, hematocrit, RBC swelling, and flow rate on light scattering by blood in a 0.26 cm ID transparent tube,” Biorheology 20, 485–494 (1983).
[PubMed]

Latimer, P.

P. Latimer, B. E. Pyle, “Light scattering at various angles. Theoretical predictions of the effects of particle volume changes,” Biophys. J. 12, 764–773 (1972).
[CrossRef] [PubMed]

P. Latimer, D. M. Moore, F. Dudley Bryant, “Changes in total light scattering and absorption caused by changes in particle conformation,” J. Theor. Biol. 21, 348–367 (1968).
[CrossRef] [PubMed]

Lin, B.-C.

Y. Mendelson, A. C. Clermont, R. A. Peura, B.-C. Lin, “Blood glucose measurement by multiple attenuated total reflection and infrared absorption spectroscopy,” IEEE Trans. Biomed. Eng. 37, 458–465 (1990).
[CrossRef] [PubMed]

Lin, J. C.

J. C. Lin, A. W. Guy, “A note on the optical scattering characteristics of whole blood,” IEEE Trans. Biomed. Eng. 21, 43–45 (1974).
[CrossRef] [PubMed]

Lindberg, L.-G.

L.-G. Lindberg, P. Å. Öberg, “Optical properties of blood in motion,” Opt. Eng. 32, 253–257 (1993).
[CrossRef]

Liu, D. L.

Liu, H.

B. Chance, H. Liu, T. Kitai, Y. Zhang, “Effects of solutes on optical properties of biological materials: models, cells, and tissues,” Anal. Biochem. 227, 351–362 (1995).
[CrossRef] [PubMed]

Lucassen, G. W.

A. M. K. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, M. J. C. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65, 366–373 (1997).
[CrossRef] [PubMed]

Mackowski, D. W.

Mendelson, Y.

Y. Mendelson, A. C. Clermont, R. A. Peura, B.-C. Lin, “Blood glucose measurement by multiple attenuated total reflection and infrared absorption spectroscopy,” IEEE Trans. Biomed. Eng. 37, 458–465 (1990).
[CrossRef] [PubMed]

Meyer, R. A.

Mishchenko, M. I.

Mohandas, N.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Moore, D. M.

P. Latimer, D. M. Moore, F. Dudley Bryant, “Changes in total light scattering and absorption caused by changes in particle conformation,” J. Theor. Biol. 21, 348–367 (1968).
[CrossRef] [PubMed]

Nijhof, E.-J.

Nilsson, A. M. K.

A. M. K. Nilsson, C. Sturesson, D. L. Liu, S. Andersson-Engels, “Changes in spectral shape of tissue optical properties in conjunction with laser-induced thermotherapy,” Appl. Opt. 37, 1256–1267 (1998).
[CrossRef]

A. M. K. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, M. J. C. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65, 366–373 (1997).
[CrossRef] [PubMed]

Öberg, P. Å.

L.-G. Lindberg, P. Å. Öberg, “Optical properties of blood in motion,” Opt. Eng. 32, 253–257 (1993).
[CrossRef]

Ohsawa, T.

S. Kashima, A. Sohda, Y. Yagyu, T. Ohsawa, “Determination of deformability of erythrocytes by change in scattering cross section,” Jpn. J. Appl. Phys. 34, 680–682 (1995).
[CrossRef]

Orlik, J.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

Ott, L.

Patterson, M. S.

Peura, R. A.

Y. Mendelson, A. C. Clermont, R. A. Peura, B.-C. Lin, “Blood glucose measurement by multiple attenuated total reflection and infrared absorption spectroscopy,” IEEE Trans. Biomed. Eng. 37, 458–465 (1990).
[CrossRef] [PubMed]

Prahl, S. A.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of He–Ne laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Pyle, B. E.

P. Latimer, B. E. Pyle, “Light scattering at various angles. Theoretical predictions of the effects of particle volume changes,” Biophys. J. 12, 764–773 (1972).
[CrossRef] [PubMed]

Quirantes Sierra, A.

Reynolds, L.

Roggan, A.

H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

Schädel, D.

H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

Shepherd, A. P.

Sohda, A.

S. Kashima, A. Sohda, Y. Yagyu, T. Ohsawa, “Determination of deformability of erythrocytes by change in scattering cross section,” Jpn. J. Appl. Phys. 34, 680–682 (1995).
[CrossRef]

Steiner, R.

Steinke, J. M.

Stock, U.

H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

Streekstra, G. J.

Sturesson, C.

Sugihara, M.

M. Sugihara, “Motion and deformation of a red blood cell in a shear flow: a two-dimensional simulation of the wall effect,” Biorheology 22, 1–19 (1985).
[PubMed]

Tanahashi, N.

M. Tomita, M. Gotoh, M. Yamamoto, N. Tanahashi, M. Kobari, “Effects of hemolysis, hematocrit, RBC swelling, and flow rate on light scattering by blood in a 0.26 cm ID transparent tube,” Biorheology 20, 485–494 (1983).
[PubMed]

Tomita, M.

M. Tomita, M. Gotoh, M. Yamamoto, N. Tanahashi, M. Kobari, “Effects of hemolysis, hematocrit, RBC swelling, and flow rate on light scattering by blood in a 0.26 cm ID transparent tube,” Biorheology 20, 485–494 (1983).
[PubMed]

Travis, L. D.

M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, “T-matrix computations of light scattering by large spheroidal particles,” Opt. Commun. 109, 16–21 (1994).
[CrossRef]

Tycko, D. H.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

van de Hulst, H. C.

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

van Gemert, M. J. C.

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H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

Wyatt, J.

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
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S. Kashima, A. Sohda, Y. Yagyu, T. Ohsawa, “Determination of deformability of erythrocytes by change in scattering cross section,” Jpn. J. Appl. Phys. 34, 680–682 (1995).
[CrossRef]

Yamamoto, M.

M. Tomita, M. Gotoh, M. Yamamoto, N. Tanahashi, M. Kobari, “Effects of hemolysis, hematocrit, RBC swelling, and flow rate on light scattering by blood in a 0.26 cm ID transparent tube,” Biorheology 20, 485–494 (1983).
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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

Biorheology

M. Tomita, M. Gotoh, M. Yamamoto, N. Tanahashi, M. Kobari, “Effects of hemolysis, hematocrit, RBC swelling, and flow rate on light scattering by blood in a 0.26 cm ID transparent tube,” Biorheology 20, 485–494 (1983).
[PubMed]

M. Sugihara, “Motion and deformation of a red blood cell in a shear flow: a two-dimensional simulation of the wall effect,” Biorheology 22, 1–19 (1985).
[PubMed]

Blood

N. Mohandas, Y. R. Kim, D. H. Tycko, J. Orlik, J. Wyatt, W. Groner, “Accurate and independent measurement of volume and hemoglobin concentration of individual red cells by laser light scattering,” Blood 68, 506–513 (1986).
[PubMed]

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S. Kashima, A. Sohda, Y. Yagyu, T. Ohsawa, “Determination of deformability of erythrocytes by change in scattering cross section,” Jpn. J. Appl. Phys. 34, 680–682 (1995).
[CrossRef]

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Minimal Invasive Medizin

H. Hahn, A. Roggan, D. Schädel, U. Stock, H. Bäumler, F. Wondrazek, “Die Optischen Eigenschaften von dicken Schichten zirkulierenden Humanblutes,” Minimal Invasive Medizin 7, 79–90 (1996).

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[CrossRef]

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[CrossRef]

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A. M. K. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, M. J. C. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65, 366–373 (1997).
[CrossRef] [PubMed]

Phys. Rev. D

P. C. Waterman, “Symmetry, unitarity and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971).
[CrossRef]

Science

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Other

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

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

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991).

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Figures (7)

Fig. 1
Fig. 1

Reference systems used (a) for derivation of the T-matrix formalism, (b) to describe the geometry of the incident and the scattered light in conjunction with T-matrix computations, and (c) when one is presenting the results of the T-matrix computations as the intensity of scattered light on a planar grid.

Fig. 2
Fig. 2

Geometric shape of the RBC volume-equivalent spheroids used for T-matrix computations. (a) The volume-equivalent oblate spheroid (axial ratio, 0.375; size parameter, 19.6 at a wavelength of 632.8 nm) and the sphere (axial ratio, 1; size parameter, 37.7 at 632.8 nm). (b) Three prolate spheroids (I–III) with different elongations. Prolate I (left) has an axial ratio of 1.63 and a size parameter of 35.2 at a wavelength of 940 nm and Prolates II and III have the corresponding parameters 2.64/3.5 and 48.4/58.4, respectively. Computations were performed at a 940-nm wavelength for the two particles in (a) as well, and the corresponding size parameters were 13.2 for the oblate spheroid and 25.4 for the sphere.

Fig. 3
Fig. 3

Planar grids of the angular distribution of the scattered light resulting from T-matrix computations in which parallel polarization of the incident plane wave with a wavelength of 632.8 nm is employed. The intensity is shown on a logarithmic scale (base 10), and relative units versus the azimuthal scattering angle ϕ s and the zenith scattering angle θs are mapped onto the normal azimuthal angle and the radius in the planar grid, respectively. (a) The scattering pattern originating from the RBC volume-equivalent oblate spheroid with θ i = 0° with a value of 3.25 (relative units) for the log intensity of the forward scattering (ϕs = θs = 0°) and -2.18 for the log intensity of the backscattering (θs = 180°). Corresponding planar grids: (b) θ i = 45° with a log intensity of forward scattering and backscattering of 3.19 and -4.29; (c) θ i = 90° with values of 2.83 and -2.64, respectively. (d) Distribution of the scattered light from the RBC volume-equivalent sphere with a log intensity of forward scattering and backscattering of 2.48 and -3.95.

Fig. 4
Fig. 4

Planar grids of the angular distribution of the scattered light resulting from T-matrix computations of prolate spheroids in which parallel polarization of the incident light with a zenith incident angle of 90° and a wavelength of 940 nm is employed. The intensity is presented on a logarithmic scale (base 10) and relative units. The results (a) of Prolate I with a log intensity of forward scattering and backscattering of 1.72 and -4.31 (relative units), (b) of Prolate II with corresponding values of 1.46 and -4.05, and (c) of Prolate III with a log intensity of forward scattering and backscattering of 1.31 and -3.81.

Fig. 5
Fig. 5

Scattering probability plotted versus the zenith scattering angle for the oblate spheroid with incident angles θ i = 0°, 45°, and 90° at a wavelength of 632.8 nm (gray curves). The black curve represents the scattering probability of the volume-equivalent sphere.

Fig. 6
Fig. 6

Scattering probability is plotted versus the zenith scattering angle for the oblate spheroid with incident angles θ i = 0°, 45°, and 90° at a 940-nm wavelength (gray curves). The black curves correspond to results for the volume-equivalent prolate spheroids I–III with an incident angle of 90° and the same wavelength.

Fig. 7
Fig. 7

Near fields computed at 940 nm with a parallel polarization of the incident light surrounding the five spheroids depicted in Fig. 2. The incident plane wave propagates in the +x direction, and the intensity of the near field is given in relative units in the equatorial plane of the scattering object. Arrows indicate the position of the spheroid, and the scales of the x and the y axes are expressed in terms of the major axis of the spheroid, r csc. Near field of (a) the sphere, (b) the oblate spheroid, (c) the prolate spheroid I, (d) the prolate spheroid II, and (e) the prolate spheroid III. Note that the scale on the z axis in (a) differs from those in (b)–(e).

Tables (2)

Tables Icon

Table 1 Influence of Particle Shape and Incident Angle on the g Factora

Tables Icon

Table 2 Near-Field Radius rnr for the Volume Equivalents of a RBC Evaluated as the Distance from the Center of the Particle to Where the Maximum Intensity of the Total Field Decreased to 2.5 Times that of the Incident Fielda

Equations (14)

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

× × E - k 2 E = 0     k = 2 π / λ .
M ν o r = × r   exp - im ϕ P n m cos   θ × j n kr + in n kr ,
N ν o r = k - 1 × M ν r ,
E i k surmed r = E 0 ν   D ν a ν M ν r k surmed r + b ν N ν r k surmed r .
E int k object r = E 0 μ c μ M μ r k object r + d μ N μ r k object r ,
E s k surmed r = E 0 ν   D ν f ν M ν o k surmed r + g ν N ν o k surmed r ,
f ν g ν = - T - matrix a ν b ν .
f ν g ν = - i B - matrix c μ d μ .
A - matrix c μ d μ = - i a ν b ν .
f ν g ν = - B - matrix A - matrix - 1 × a ν b ν = - T - matrix a ν b ν .
m r + im i = n object / n surmed .
P θ s = 0 2 π   P diff   sin   θ s   d ϕ ,
0 2 π 0 π   P diff   sin   θ   d θ d ϕ = 1 .
g = cos   θ s .

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