Abstract

The aim of this work is to evaluate the influence of absorption processes on the Time Of Flight (TOF) of the light scattered out of a thick medium in the forward direction. We use a Monte-Carlo simulation with temporal phase function and Debye modes. The main result of our study is that absorption inside the particle induces a decrease of the TOF on a picosecond time scale, measurable with a femtosecond laser apparatus. This decrease, which exhibits a neat sensitivity to the absorption coefficient of particles, could provide an efficient way to measure this absorption.

© 2011 OSA

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    [CrossRef]

2011

2010

J. Shen and H. Wang, “Calculation of Debye series expansion of light scattering,” Appl. Opt. 49(13), 2422–2428 (2010).
[CrossRef]

W. Tan, Y. Yang, J. Si, J. Tong, W. Yi, F. Chen, and X. Hou, “Shape measurement of objects using an ultrafast optical Kerr gate of bismuth glass,” J. Appl. Phys. 107(4), 043104 (2010).
[CrossRef]

2009

M. Barthélémy, L. Hespel, N. Rivière, B. Chatel, and T. Dartigalongue, “Pump probe experiment for optical diagnosis of very thick scattering media,” Aerospace Lab J. 1, 155–200 (2009).

2008

N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” Proc. SPIE 7065, 70650X, 70650X-9 (2008).
[CrossRef]

C. Calba, L. Méès, C. Rozé, and T. Girasole, “Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments,” J. Opt. Soc. Am. A 25(7), 1541–1550 (2008).
[CrossRef] [PubMed]

2007

2006

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

C. Calba, C. Rozé, T. Girasole, and L. Méès, “Monte Carlo simulation of the interaction between an ultra short pulse and a strongly scattering medium: the case of large particles,” Opt. Commun. 265(2), 373–382 (2006).
[CrossRef]

2005

A. M. Pena, T. Boulesteix, T. Dartigalongue, and M. C. Schanne-Klein, “Chiroptical effects in the second harmonic signal of collagens I and IV,” J. Am. Chem. Soc. 127(29), 10314–10322 (2005).
[CrossRef] [PubMed]

2003

C. Gributs and D. Burns, “Multiresolution analysis for quantification of optical properties in scattering media using pulsed photon time-of-flight measurements,” Anal. Chim. Acta 490(1-2), 185–195 (2003).
[CrossRef]

C. Das, A. Trivedi, K. Mitra, and T. Vo-Dinh, “Short pulse laser propagation through tissues for biomedical imaging,” J. Phys. D Appl. Phys. 36(14), 1714–1721 (2003).
[CrossRef]

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).
[CrossRef] [PubMed]

2002

T. Gustavsson, A. Sharonov, and D. Markovitsi, “Thymine, thymidine and thimidine 5′-monophosphate studied by femtosecond fluorescence upconversion spectroscopy,” Chem. Phys. Lett. 351(3-4), 195–200 (2002).
[CrossRef]

2001

L. Méès, G. Gréhan, and G. Gouesbet, “Time-resolved scattering diagram for a sphere illuminated by plane wave and focused short pulses,” Opt. Commun. 194(1-3), 59–65 (2001).
[CrossRef]

W. Long and D. Burns, “Particle sizing and optical constant measurement in granular samples using statistical descriptors of photon time-of-flight distributions,” Anal. Chim. Acta 434(1), 113–123 (2001).
[CrossRef]

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40(9), 1354–1361 (2001).
[CrossRef] [PubMed]

1999

F. Onofri, “Critical angle refractometry for simultaneous measurement of particles in flow: size and relative refractive index,” Part. Part. Syst. Charact. 16(3), 119–127 (1999).
[CrossRef]

1996

S. Avrillier, E. Tinet, and J. M. Tualle, “Fast semianalytical monte carlo simulation for time resolved light propagation in turbid media,” J. Opt. Soc. Am. A 9, 1903–1915 (1996).

1992

1991

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[CrossRef] [PubMed]

1990

Alfano, R. R.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[CrossRef] [PubMed]

K. M. Yoo, G. C. Tang, and R. R. Alfano, “Coherent backscattering of light from biological tissues,” Appl. Opt. 29(22), 3237–3239 (1990).
[CrossRef] [PubMed]

Avrillier, S.

S. Avrillier, E. Tinet, and J. M. Tualle, “Fast semianalytical monte carlo simulation for time resolved light propagation in turbid media,” J. Opt. Soc. Am. A 9, 1903–1915 (1996).

Barthélémy, M.

M. Barthélémy, L. Hespel, N. Rivière, B. Chatel, and T. Dartigalongue, “Pump probe experiment for optical diagnosis of very thick scattering media,” Aerospace Lab J. 1, 155–200 (2009).

N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” Proc. SPIE 7065, 70650X, 70650X-9 (2008).
[CrossRef]

Beaurepaire, E.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

Berrocal, E.

Boller, K. J.

Boulesteix, T.

A. M. Pena, T. Boulesteix, T. Dartigalongue, and M. C. Schanne-Klein, “Chiroptical effects in the second harmonic signal of collagens I and IV,” J. Am. Chem. Soc. 127(29), 10314–10322 (2005).
[CrossRef] [PubMed]

Burns, D.

C. Gributs and D. Burns, “Multiresolution analysis for quantification of optical properties in scattering media using pulsed photon time-of-flight measurements,” Anal. Chim. Acta 490(1-2), 185–195 (2003).
[CrossRef]

W. Long and D. Burns, “Particle sizing and optical constant measurement in granular samples using statistical descriptors of photon time-of-flight distributions,” Anal. Chim. Acta 434(1), 113–123 (2001).
[CrossRef]

Calba, C.

C. Calba, L. Méès, C. Rozé, and T. Girasole, “Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments,” J. Opt. Soc. Am. A 25(7), 1541–1550 (2008).
[CrossRef] [PubMed]

C. Calba, C. Rozé, T. Girasole, and L. Méès, “Monte Carlo simulation of the interaction between an ultra short pulse and a strongly scattering medium: the case of large particles,” Opt. Commun. 265(2), 373–382 (2006).
[CrossRef]

Chatel, B.

M. Barthélémy, L. Hespel, N. Rivière, B. Chatel, and T. Dartigalongue, “Pump probe experiment for optical diagnosis of very thick scattering media,” Aerospace Lab J. 1, 155–200 (2009).

Chen, F.

W. Tan, Y. Yang, J. Si, J. Tong, W. Yi, F. Chen, and X. Hou, “Shape measurement of objects using an ultrafast optical Kerr gate of bismuth glass,” J. Appl. Phys. 107(4), 043104 (2010).
[CrossRef]

Combettes, L.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

Dartigalongue, T.

M. Barthélémy, L. Hespel, N. Rivière, B. Chatel, and T. Dartigalongue, “Pump probe experiment for optical diagnosis of very thick scattering media,” Aerospace Lab J. 1, 155–200 (2009).

N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” Proc. SPIE 7065, 70650X, 70650X-9 (2008).
[CrossRef]

A. M. Pena, T. Boulesteix, T. Dartigalongue, and M. C. Schanne-Klein, “Chiroptical effects in the second harmonic signal of collagens I and IV,” J. Am. Chem. Soc. 127(29), 10314–10322 (2005).
[CrossRef] [PubMed]

Das, C.

C. Das, A. Trivedi, K. Mitra, and T. Vo-Dinh, “Short pulse laser propagation through tissues for biomedical imaging,” J. Phys. D Appl. Phys. 36(14), 1714–1721 (2003).
[CrossRef]

Débarre, D.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

Fabre, A.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

Fu, Q.

Girasole, T.

C. Calba, L. Méès, C. Rozé, and T. Girasole, “Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments,” J. Opt. Soc. Am. A 25(7), 1541–1550 (2008).
[CrossRef] [PubMed]

C. Calba, C. Rozé, T. Girasole, and L. Méès, “Monte Carlo simulation of the interaction between an ultra short pulse and a strongly scattering medium: the case of large particles,” Opt. Commun. 265(2), 373–382 (2006).
[CrossRef]

Gouesbet, G.

L. Méès, G. Gréhan, and G. Gouesbet, “Time-resolved scattering diagram for a sphere illuminated by plane wave and focused short pulses,” Opt. Commun. 194(1-3), 59–65 (2001).
[CrossRef]

Gréhan, G.

L. Méès, G. Gréhan, and G. Gouesbet, “Time-resolved scattering diagram for a sphere illuminated by plane wave and focused short pulses,” Opt. Commun. 194(1-3), 59–65 (2001).
[CrossRef]

Gributs, C.

C. Gributs and D. Burns, “Multiresolution analysis for quantification of optical properties in scattering media using pulsed photon time-of-flight measurements,” Anal. Chim. Acta 490(1-2), 185–195 (2003).
[CrossRef]

Gustavsson, T.

T. Gustavsson, A. Sharonov, and D. Markovitsi, “Thymine, thymidine and thimidine 5′-monophosphate studied by femtosecond fluorescence upconversion spectroscopy,” Chem. Phys. Lett. 351(3-4), 195–200 (2002).
[CrossRef]

Hespel, L.

M. Barthélémy, L. Hespel, N. Rivière, B. Chatel, and T. Dartigalongue, “Pump probe experiment for optical diagnosis of very thick scattering media,” Aerospace Lab J. 1, 155–200 (2009).

N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” Proc. SPIE 7065, 70650X, 70650X-9 (2008).
[CrossRef]

Ho, P. P.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[CrossRef] [PubMed]

Hou, X.

W. Tan, Y. Yang, J. Si, J. Tong, W. Yi, F. Chen, and X. Hou, “Shape measurement of objects using an ultrafast optical Kerr gate of bismuth glass,” J. Appl. Phys. 107(4), 043104 (2010).
[CrossRef]

Hovenac, A. E.

Lee, C. J.

Linne, M.

Liu, C.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[CrossRef] [PubMed]

Lock, J. A.

Long, W.

W. Long and D. Burns, “Particle sizing and optical constant measurement in granular samples using statistical descriptors of photon time-of-flight distributions,” Anal. Chim. Acta 434(1), 113–123 (2001).
[CrossRef]

Malinovskaya, S. A.

Malinovsky, V. S.

Markovitsi, D.

T. Gustavsson, A. Sharonov, and D. Markovitsi, “Thymine, thymidine and thimidine 5′-monophosphate studied by femtosecond fluorescence upconversion spectroscopy,” Chem. Phys. Lett. 351(3-4), 195–200 (2002).
[CrossRef]

Méès, L.

C. Calba, L. Méès, C. Rozé, and T. Girasole, “Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments,” J. Opt. Soc. Am. A 25(7), 1541–1550 (2008).
[CrossRef] [PubMed]

C. Calba, C. Rozé, T. Girasole, and L. Méès, “Monte Carlo simulation of the interaction between an ultra short pulse and a strongly scattering medium: the case of large particles,” Opt. Commun. 265(2), 373–382 (2006).
[CrossRef]

L. Méès, G. Gréhan, and G. Gouesbet, “Time-resolved scattering diagram for a sphere illuminated by plane wave and focused short pulses,” Opt. Commun. 194(1-3), 59–65 (2001).
[CrossRef]

Mitra, K.

C. Das, A. Trivedi, K. Mitra, and T. Vo-Dinh, “Short pulse laser propagation through tissues for biomedical imaging,” J. Phys. D Appl. Phys. 36(14), 1714–1721 (2003).
[CrossRef]

Onofri, F.

F. Onofri, “Critical angle refractometry for simultaneous measurement of particles in flow: size and relative refractive index,” Part. Part. Syst. Charact. 16(3), 119–127 (1999).
[CrossRef]

Pena, A. M.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

A. M. Pena, T. Boulesteix, T. Dartigalongue, and M. C. Schanne-Klein, “Chiroptical effects in the second harmonic signal of collagens I and IV,” J. Am. Chem. Soc. 127(29), 10314–10322 (2005).
[CrossRef] [PubMed]

Rivière, N.

M. Barthélémy, L. Hespel, N. Rivière, B. Chatel, and T. Dartigalongue, “Pump probe experiment for optical diagnosis of very thick scattering media,” Aerospace Lab J. 1, 155–200 (2009).

N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” Proc. SPIE 7065, 70650X, 70650X-9 (2008).
[CrossRef]

Rozé, C.

C. Calba, L. Méès, C. Rozé, and T. Girasole, “Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments,” J. Opt. Soc. Am. A 25(7), 1541–1550 (2008).
[CrossRef] [PubMed]

C. Calba, C. Rozé, T. Girasole, and L. Méès, “Monte Carlo simulation of the interaction between an ultra short pulse and a strongly scattering medium: the case of large particles,” Opt. Commun. 265(2), 373–382 (2006).
[CrossRef]

Schanne-Klein, M. C.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

A. M. Pena, T. Boulesteix, T. Dartigalongue, and M. C. Schanne-Klein, “Chiroptical effects in the second harmonic signal of collagens I and IV,” J. Am. Chem. Soc. 127(29), 10314–10322 (2005).
[CrossRef] [PubMed]

Sedarsky, D.

Sharonov, A.

T. Gustavsson, A. Sharonov, and D. Markovitsi, “Thymine, thymidine and thimidine 5′-monophosphate studied by femtosecond fluorescence upconversion spectroscopy,” Chem. Phys. Lett. 351(3-4), 195–200 (2002).
[CrossRef]

Shen, J.

Si, J.

W. Tan, Y. Yang, J. Si, J. Tong, W. Yi, F. Chen, and X. Hou, “Shape measurement of objects using an ultrafast optical Kerr gate of bismuth glass,” J. Appl. Phys. 107(4), 043104 (2010).
[CrossRef]

Sun, C.-W.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).
[CrossRef] [PubMed]

Sun, W.

Supatto, W.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

Tan, W.

W. Tan, Y. Yang, J. Si, J. Tong, W. Yi, F. Chen, and X. Hou, “Shape measurement of objects using an ultrafast optical Kerr gate of bismuth glass,” J. Appl. Phys. 107(4), 043104 (2010).
[CrossRef]

Tang, G. C.

Tinet, E.

S. Avrillier, E. Tinet, and J. M. Tualle, “Fast semianalytical monte carlo simulation for time resolved light propagation in turbid media,” J. Opt. Soc. Am. A 9, 1903–1915 (1996).

Tong, J.

W. Tan, Y. Yang, J. Si, J. Tong, W. Yi, F. Chen, and X. Hou, “Shape measurement of objects using an ultrafast optical Kerr gate of bismuth glass,” J. Appl. Phys. 107(4), 043104 (2010).
[CrossRef]

Tordjmann, T.

D. Débarre, W. Supatto, A. M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M. C. Schanne-Klein, and E. Beaurepaire, “Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy,” Nat. Methods 3(1), 47–53 (2006).
[CrossRef] [PubMed]

Trivedi, A.

C. Das, A. Trivedi, K. Mitra, and T. Vo-Dinh, “Short pulse laser propagation through tissues for biomedical imaging,” J. Phys. D Appl. Phys. 36(14), 1714–1721 (2003).
[CrossRef]

Tualle, J. M.

S. Avrillier, E. Tinet, and J. M. Tualle, “Fast semianalytical monte carlo simulation for time resolved light propagation in turbid media,” J. Opt. Soc. Am. A 9, 1903–1915 (1996).

van der Slot, P. J.

Vo-Dinh, T.

C. Das, A. Trivedi, K. Mitra, and T. Vo-Dinh, “Short pulse laser propagation through tissues for biomedical imaging,” J. Phys. D Appl. Phys. 36(14), 1714–1721 (2003).
[CrossRef]

Wang, H.

Wang, L.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-d imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253(5021), 769–771 (1991).
[CrossRef] [PubMed]

Wang, L. V.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).
[CrossRef] [PubMed]

Wang, X.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).
[CrossRef] [PubMed]

Yang, C.-C.

X. Wang, L. V. Wang, C.-W. Sun, and C.-C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).
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Figures (9)

Fig. 1
Fig. 1

2D plot of normalized temporal phase functions P(t,θ) ((a) total, (b) for mode 0, (c) for mode 1 and (d) for mode 2) for a 50 µm particle radius. More than 80% of energy is contained inside the rings, i.e. in the forward direction. The mode 1 is delayed by Δt compared with the mode 0.

Fig. 2
Fig. 2

Schematic representation of the first four Debye modes. Mode 0 is a surface reflection mode at the interface of the particle. Mode 1 is a transmission mode through the bulk of the particle. For information, we also show the second and the third modes which undergo respectively one and two internal reflections.

Fig. 3
Fig. 3

Ratio Ι10 between the weight of the mode 0 and the mode 1 (Eq. (3)) as a function of kpa for different particle radii.

Fig. 4
Fig. 4

Total asymmetry factor (solid black line), asymmetry factors of mode 0 (dotted red line) and mode 1 (dotted green line) as a function of kpa for a 50µm particle radius (Eq. (4)).

Fig. 5
Fig. 5

Extinction efficiency qext (Eq. (6)) as a function of the particle radius. Total (solid black and dotted red lines) and partial (dotted green and blue lines) extinction efficiencies are plotted for different values of kpa.

Fig. 6
Fig. 6

albedo Ω (Eq. (7)) as a function of kpa for different particle radii.

Fig. 7
Fig. 7

Relative scattered intensity as a function of TOF for different values of kpa and for a 5 µm particle radius.

Fig. 8
Fig. 8

Relative scattered intensity as a function of TOF for different values of kpa, and for a 50 µm particle radius.

Fig. 9
Fig. 9

Relative scattered intensity as a function of TOF for different amount of mode 1’s event when kpa = 0 and for a 50 µm particle radius.

Tables (1)

Tables Icon

Table 1 Results of the simulation. Index a and b denotes respectively the influence of albedo and phase function.

Equations (7)

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S 1 (ω,θ)= n 2n+1 n(n+1) ( τ n 1 (θ) a n (ω,θ) τ n 2 (θ) b n (ω,θ)) S 2 (ω,θ)= n 2n+1 n(n+1) ( τ n 2 (θ) a n (ω,θ) τ n 1 (θ) b n (ω,θ))
a n p = 1 2 (1 R n,a hm p=1 T n,a hm ( R n,a pa ) p1 T n,a pa )
I p = 2π | k | 2 n=1 (2n+1)( | a n p | 2 + | b n p | 2 )
g= 1 2 0 π P(cosθ)sinθcosθdθ g= 2 n=1 n(n+2) n+1 Re( a n a n+1 * + b n b n+1 * )+ 2n+1 n(n+1) Re( a n b n * ) n=1 (2n+1)( | a n | 2 + | b n | 2 )
σ ext p = 2π k 2 n=1 (2n+1)Re{ a n p + b n p }
q ext p = σ ext p / (π R 2 )
Ω= σ sca mie σ ext mie

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