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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 32–41
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Picosecond time scale modification of forward scattered light induced by absorption inside particles

Myriam Kervella, Françoix-Xavier d’Abzac, François Hache, Laurent Hespel, and Thibault Dartigalongue  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 32-41 (2012)
http://dx.doi.org/10.1364/OE.20.000032


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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

1. Introduction

The understanding of interactions between light and scattering dense media such as clouds, paints or biological tissues is a major issue as far as optical diagnosis is concerned. In order to carry out such investigation, model systems made up of spherical particles in suspension in a host medium have been widely studied [1

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

, 2

2. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

]. Femtosecond lasers are bright enough to go through very thick media with tunable wavelength [3

3. 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]

, 4

4. M. Barthélémy, N. Rivière, L. Hespel, and T. Dartigalongue, “Pump probe experiment for high scattering media diagnostics,” in SPIE Optics and Photonics; San Diego, CA, USA, 2008; Conference Proceedings; Vol. 7065.

], and are used in a wide variety of optical diagnosis and imaging techniques (SHG [5

5. 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]

], THG [6

6. 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]

], CARS [7

7. S. A. Malinovskaya and V. S. Malinovsky, “Chirped-pulse adiabatic control in coherent anti-Stokes Raman scattering for imaging of biological structure and dynamics,” Opt. Lett. 32(6), 707–709 (2007). [CrossRef] [PubMed]

], …). Furthermore, thanks to Optical Kerr Gate (OKG) measurements [8

8. 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]

] or up-conversion technique [9

9. 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]

], it is possible to temporally sample the light going out of the sample with a resolution of approximately 100 fs [10

10. 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]

] (i.e. less than 20 microns spatially). Such experiments are used to isolate ballistic and scattered light (ballistic imaging [11

11. D. Sedarsky, E. Berrocal, and M. Linne, “Quantitative image contrast enhancement in time-gated transillumination of scattering media,” Opt. Express 19(3), 1866–1883 (2011). [CrossRef] [PubMed]

, 12

12. L. Wang, X. Liang, P. A. Galland, P. P. Ho, and R. R. Alfano, “Detection of objects hidden in highly scattering media using time-gated imaging methods,” in Optical Sensing, Imaging, and Manipulation for Biological and Biomedical Applications, Conference SPIE Proceeding, Vol. 4082 (2000).

], optical density measurement [13

13. 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).

]) or to study the temporal scattering process itself in order to get information about the sample [14

14. 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]

16

16. C. J. Lee, P. J. van der Slot, and K. J. Boller, “Using ultra-short pulses to determine particle size and density distributions,” Opt. Express 15(19), 12483–12497 (2007). [CrossRef] [PubMed]

].

The aim of this work is to evaluate the Time Of Flight (TOF) of light going through a scattering medium on a femtosecond time scale when the particles are absorbing. The influence of absorption processes has been widely studied on longer time scale (nanosecond) and backscattered direction [17

17. 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]

, 18

18. 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]

]. This will not be the goal of our study as we only focus on the forward direction (few 10−4 Sr around the laser beam). We will demonstrate that absorption inside the particle induces a decrease of the TOF on a picosecond time scale. This effect appears to be very sensitive to the imaginary part of the particle refractive index.

The influence of absorption inside the particles is not straightforward as it profoundly affects all the microscopic properties of particles: albedo, phase function, absorption and scattering cross sections. We will present a complete numerical scheme in order to evaluate the TOF of light scattered out of a system made up of absorbing particles in the forward direction. We will fully describe how absorption modifies the temporal phase function, the weight of Debye modes, the asymmetry factor, and the albedo. We will show that all these effects should contribute to a global decrease of the TOF on a picosecond time scale. We will then carry out a Monte-Carlo simulation to evaluate the order of magnitude of this effect. We will compare the case of large particles (50 µm radii), exhibiting a neat temporal separation of the Debye mode, with the case of small particles (5 µm radii).

2. Temporal phase function

3. Debye mode weight

We have carried out calculation of temporal phase functions of the different Debye modes for a significant and arbitrary imaginary part of the refractive index of the particle, kpa. The two key results of our study are the following. First, we have compared different temporal profiles Pθ (t) with and without absorption. No significant change can be observed. However, kpa profoundly affects the relative weight of the Debye modes. To show this second result, we have calculated the energy Ip scattered for the modes p:
Ip=2π|k|2n=1(2n+1)(|anp|2+|bnp|2)
(3)
where k is the wave number. We have calculated the weight of the different modes on a large domain of particle size. As soon as the radii are bigger than 1 µm, all the energy is scattered either in mode 0 or 1. We represent (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.
) the ratio I1/I0. When kpa = 0, the energy is almost equally shared between mode 0 and mode 1, I1/I0 is very close to 1. When kpa increased, the weight of mode 1 strongly decreases as it corresponds to a mode going through the absorbing bulk of the particle. Only mode 0 remains as it propagates at the interface. This effect is more important for large particles as the energy loss inside the particle is larger.

For non absorbing particles, 50% of the energy goes through mode 1 and is delayed of Δt = (npa-nhm)*(2R/c). For absorbing particles, 100% of the energy should be scattered through mode 0 and not be delayed. As a result, the global TOF should decrease when kpa increases. In addition to the scattering process itself, we have to consider the TOF between two scattering events. When the phase function is mainly directed in the forward direction, the trajectory of light is very straight, and the TOF is very small. As the contrary, when the phase function is isotropic, the trajectory of the light is more complex, and the global time of flight is longer. As a result, we need to understand the dependence between the angular distribution and kpa.

4. Asymmetry factor

The angular dependence is modified when kpa strongly increases [22

22. 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]

]. We introduce the asymmetry factor g defined and calculated as followed [1

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

]:

g=120πP(cosθ)sinθcosθdθg=2n=1n(n+2)n+1Re(anan+1*+bnbn+1*)+2n+1n(n+1)Re(anbn*)n=1(2n+1)(|an|2+|bn|2)
(4)

This factor g gives information about the sharpness of the phase function (i.e., g very close to 1 for sharp phase function and close to 0 for isotropic phase function). By using decomposition (2) in this formula, we are able to calculate the asymmetry factor of the total and partial phase functions. The results are represented (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)).
) for increasing value of kpa. For mode 0, g is a constant and almost equal to 1. The phase function of mode 0 is very sharp and peaked in the forward direction and the absorption of the bulk does not modify this surface mode. On the opposite, mode 1 is more isotropic than mode 0. The total phase function becomes more and more peaked in the forward direction when kpa increases (complete overlap with mode 0 for great value of kpa as observed in [23

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

]).

The TOF should decrease even more when kpa increases as the angular distribution of the scattered light is sharper for mode 0 compared to mode 1. The trajectory of light through the medium will be straighter. The time of flight decreases because the asymmetry factor increases (straighter trajectory), and because mode 1 is killed (no more Δt at the crossing of the particle). In the following section, we show that the decrease of TOF can be also due to the modification of the scattering/absorbing cross section.

5. Scattering and absorption cross sections

One needs to evaluate the influence of kpa over the different cross sections: scattering σsca, absorption σabs, and extinction σext. Partial extinction cross-section σextpverifies the following formula:
σextp=2πk2n=1(2n+1)Re{anp+bnp}
(5)
where anp and bnp can be found in the Eq. (2). We have also carried out similar calculations for σextmieusing regular expressions for an and bn based on Mie theory, still valid for absorbing particles [1

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

]. We define the different extinction efficiencies qextp:
qextp=σextp/(πR2)
(6)
qextmie denotes the efficiency obtained with the regular Mie theory. We represent (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.
) the evolution of three different extinction efficiencies (qext0, qext0+qext1 and qextmie) for increasing radii. Without absorption, one can observe 3 regimes: (i) the increase of qextmie with R for small particles corresponds to the Rayleigh regime, (ii) oscillations of qextmie with R belong to the Mie regime and (iii) qextmie is very close to 2 for large particles in the so-called non selective regime. The agreement between qext0+qext1 and qextmie is very good except for Rayleigh regime where more than 2 Debye modes are needed to describe the scattering process. For increasing value of kpa, mode 1 is killed. The qext curve overlaps the one obtained for mode 0 only, and oscillations disappear. The consequence is a slight increase or decrease of qextmie when kpa increases, depending on the particle radius. This is the well known process called absorption edge [1

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

].

We now evaluate the impact of kpa over the scattering and absorbing cross sections when we calculate the albedo Ω:

Ω=σscamieσextmie
(7)

When there is no absorption, all the energy is scattered: σscamie=σextmie (Ω = 1). When kpa increases, σextmie is not modified (if we neglect the absorption edge effect described above). Half of the total energy that should have been scattered in mode 1 is now absorbed inside the particle. As a result, we expect that σabsmie=σscamieσextmie/2. Indeed, when kpa increases, the albedo decreases from 1 to 0,5 (Fig. 6
Fig. 6 albedo Ω (Eq. (7)) as a function of kpa for different particle radii.
). The main consequence for the time of flight is that single scattering trajectory will have a more important weight compared to multiple scattering trajectory, as there are energy losses after every scattering event. The energy decay is roughly equal to 2-m where m is the number of the scattering events. One can note that single scattering trajectory corresponds to a shorter pathway, and shows up for earlier delay than multiple scattering one. Hence, the absorption inside the particle induces a decrease of the global TOF of the light.

6. Monte Carlo scheme

In order to evaluate the TOF decrease, we developed a Monte Carlo simulation scheme. A great part of random tests is explained in [21

21. 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]

]: this complex process is simulated by a succession of elementary events (scattering, absorption by the particle). In order to simplify our study, we consider a medium without interfaces. We have carefully compared our simulation code with published result in the case of non absorbing particle [3

3. 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]

,24

24. 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]

]. In order to obtain the best signal to noise ratio, we use a semi-analytical Monte Carlo approach [25

25. 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).

] for small particles, and a full Monte Carlo for large particles [26

26. 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]

]. We have carefully checked the agreement of these two approaches for a great variety of radii. We consider a small detector in the forward direction. The solid angle is equal to 5.10−4 Sr. We consider an optical path of 1 cm, and an Optical Thickness O.T. = 20. We verified that O.T. is not significantly modified for the value of kpa we considered.

In Fig. 7
Fig. 7 Relative scattered intensity as a function of TOF for different values of kpa and for a 5 µm particle radius.
, we report the relative scattered intensity as a function of time delay for particles of 5 µm. For kpa = 0.001, we observe a global decrease of the intensity, and a small but yet measurable decrease of TOF (few picoseconds can be detected with a streak camera [14

14. 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]

] or femtosecond laser experiment [11

11. D. Sedarsky, E. Berrocal, and M. Linne, “Quantitative image contrast enhancement in time-gated transillumination of scattering media,” Opt. Express 19(3), 1866–1883 (2011). [CrossRef] [PubMed]

]). For stronger value (kpa = 0.01), the reduction of TOF is more visible. The scattered light tends to overlap the ballistic light (ballistic distribution is centred on zero-delay and has 100 fs line width (FWHM)).

Within the same conditions as above, we now study larger particles (R = 50 µm). With no absorption, two separated lobes can be observed (Fig. 8
Fig. 8 Relative scattered intensity as a function of TOF for different values of kpa, and for a 50 µm particle radius.
). In order to understand the physical origin of these two lobes, we represent (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.
) the partial TOF curve, as we have kept track of the amount of mode 0 and mode 1 scattering events in our modelling scheme. The first lobe corresponds to pathways with only “0 mode” scattering events. A single “mode 1 scattering” event in the pathway greatly reduces the efficiency of collection. This is due to the asymmetry factor of mode 1 that spreads the angular distribution of the scattered light. As we only detect energy in the forward direction with a small solid angle, the collection efficiency dramatically decreases. The high efficiency of collection in “pure mode 0 pathway” completely balances its very poor probability of occurrence. As a result, a very neat temporal separation between the 2 lobes can be observed. Indeed, the delay shift observed between pure 0 scattering pathway and single mode 1 event scattering pathway is roughly equal to Δt. The “0 lobe”, also called “snake-like photon”, completely overlaps the ballistic contribution (not represented here as it is thousand times smaller compared to the “snake-like contribution”). A slight increase of the absorption (kpa = 10−5) induces a detectable change in the temporal distribution: we can observe a neat decrease of the delayed lobe. Here again, for high values of kpa, only the mode 0 remains whereas higher modes are absorbed.

7. Discussion

We want to evaluate independently the influence of the 3 phenomena (albedo, Debye mode weight and asymmetry factor). Though, it is not possible to dissociate the angular and temporal dependence of the phase function. As a result, we have studied 2 cases. Case a/ kpa modifies the angular and temporal distribution (sections 3&4), but we consider that there is no energy loss during the scattering process. Case b/ the photon can be lost during the scattering process (section 5), but we keep the temporal phase function as if the particles were non absorbing. We report (Table 1

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

table-icon
View This Table
) the corresponding average delay τ, τa and τb.

For small and large particles, both effects (albedo and phase function) induce a decrease of τ. While considering the two processes, the effect is even stronger. For small particles (Fig. 7), the average intensity of scattered light decreases a lot with kpa. This effect could be tracked thanks to a non-temporal measurement which is more straightforward. Nevertheless, the TOF is an absolute measurement, less sensitive to the fluctuation of the intensity of the laser or other experimental noise. This could be relevant to measure kpa bigger than 10−3. For large particles, a measurement of TOF is even more sensitive as the snake like peak remains unchanged and can be used as a reference: it precisely defines the 0 delay, and it allows a measurement of the ratio of intensity of the 2 lobes. We have checked that the slight attenuation of the snake like peak when kpa = 10−3 is only induced by the increase of O.T. from 20 to 20.18 (absorption edge). When kpa = 10−5, absorption is not detectable with classical technique, there is no variation of the optical thickness or modification of the phase function (Table 1).

In order to evaluate the impact of the real part of the refractive index npa compared to kpa, we have considered a variation of these two parameters of the same magnitude (Δnpa = Δkpa = 10−5) and calculated the impact on the average time of flight τ. For particle of 50 µm, the impact of kpa is 40 times bigger than the impact of npa (20 times for particle of 5 µm). This method could be coupled with other methods more sensitive to npa such as refractometry or rainbow [27

27. 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]

] and might be a powerful tool to measure the absorption coefficient of particle. This could be very useful to evaluate the water content of particle, the concentration of absorbing molecule at the surface of a particle or the temperature of a water droplet.

The phenomenon we have simulated is observed on a picosecond time scale and could not be observed with a nanosecond apparatus. It is representative of the amount of events “one photon crosses the bulk of one particle”. The consequence on the TOF is a delay Δt = 60 fs per event (case of large particles). For an optical thickness of 20, the global effect is roughly equal to 20*60 = 1.2 ps. The real simulation we have carried gives the same order of magnitude (2.54 ps). The impact of the global TOF is very small but as soon as it is measurable, it exhibits a neat sensitivity to the absorption coefficient of particles.

8. Conclusion

We have carried a detailed study of TOF of light going through a scattering media when the particles are absorbing. We have demonstrated that TOF is significantly reduced by the absorption process inside the particle for 3 main reasons. First, the absorption inside the bulk of the particle kills delayed Debye modes. Then, phase functions are more peaked in the forward direction. Finally, single scattering trajectories are enhanced compared to multiple ones due to the albedo of particles and the energy losses observed for every scattering event. We have focused on two particular regimes: small particles R = 5 µm and large particles R = 50 µm. For small particles, TOF is reduced for value of kpa (≥10−3) only. For large particles, the effect can be tracked for value of kpa (≥10−5). Measurements of the time of flight, coupled with other techniques, could be a good way to measure the absorption coefficient of a particle with a good sensitivity.

References and links

1.

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

2.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).

3.

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]

4.

M. Barthélémy, N. Rivière, L. Hespel, and T. Dartigalongue, “Pump probe experiment for high scattering media diagnostics,” in SPIE Optics and Photonics; San Diego, CA, USA, 2008; Conference Proceedings; Vol. 7065.

5.

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]

6.

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]

7.

S. A. Malinovskaya and V. S. Malinovsky, “Chirped-pulse adiabatic control in coherent anti-Stokes Raman scattering for imaging of biological structure and dynamics,” Opt. Lett. 32(6), 707–709 (2007). [CrossRef] [PubMed]

8.

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]

9.

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]

10.

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]

11.

D. Sedarsky, E. Berrocal, and M. Linne, “Quantitative image contrast enhancement in time-gated transillumination of scattering media,” Opt. Express 19(3), 1866–1883 (2011). [CrossRef] [PubMed]

12.

L. Wang, X. Liang, P. A. Galland, P. P. Ho, and R. R. Alfano, “Detection of objects hidden in highly scattering media using time-gated imaging methods,” in Optical Sensing, Imaging, and Manipulation for Biological and Biomedical Applications, Conference SPIE Proceeding, Vol. 4082 (2000).

13.

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).

14.

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]

15.

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]

16.

C. J. Lee, P. J. van der Slot, and K. J. Boller, “Using ultra-short pulses to determine particle size and density distributions,” Opt. Express 15(19), 12483–12497 (2007). [CrossRef] [PubMed]

17.

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]

18.

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]

19.

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]

20.

A. E. Hovenac and J. A. Lock, “Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” J. Opt. Soc. Am. A 9(5), 781–795 (1992). [CrossRef]

21.

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]

22.

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]

23.

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

24.

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]

25.

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).

26.

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]

27.

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]

OCIS Codes
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles
(290.7050) Scattering : Turbid media
(320.7120) Ultrafast optics : Ultrafast phenomena

ToC Category:
Scattering

History
Original Manuscript: September 16, 2011
Revised Manuscript: October 28, 2011
Manuscript Accepted: October 28, 2011
Published: December 20, 2011

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Myriam Kervella, Françoix-Xavier d’Abzac, François Hache, Laurent Hespel, and Thibault Dartigalongue, "Picosecond time scale modification of forward scattered light induced by absorption inside particles," Opt. Express 20, 32-41 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-32


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