## Picosecond time scale modification of forward scattered light induced by absorption inside particles |

Optics Express, Vol. 20, Issue 1, pp. 32-41 (2012)

http://dx.doi.org/10.1364/OE.20.000032

Acrobat PDF (1201 KB)

### 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

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]

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]

*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]

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. 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]

*10*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.

^{−4}Sr*µm*radii), exhibiting a neat temporal separation of the Debye mode, with the case of small particles (5

*µm*radii).

## 2. Temporal phase function

*i.e.*, the probability for a photon to be scattered out of the particle with a given angle

*θ*, and a given delay

*t*. The scattering angle

*θ*is the angle between the incident and scattered vectors (0° corresponds to the forward scattering direction). The time delay

*t*corresponds to the time difference between the outgoing scattered beam and a reference beam propagating through the centre of the particle where the particle has been replaced by the host medium. For our entire study, we consider ultra short laser pulses (

*FWHM*=100

*fs*) impinging on spherical particles (refractive index

*n*=1.5) in suspension in a host medium (

_{pa}*n*=1.33). This short laser pulse has a spectral bandwidth centred at

_{hm}*λ*=0.8

*µm*. For every frequency

*ω*of the laser pulse, we calculate the Jones coefficients

*S*and

_{1}*S*thanks to Mie decomposition:

_{2}*a*and

_{n}*b*are the Mie scattering coefficients and can be found in [1]. The angular phase function

_{n}*P(ω,θ)*is directly proportional to

*|S*The temporal and angular phase function

_{1}(ω,θ)|^{2}+|S_{2}(ω,θ)|^{2}.*P(t,θ)*is obtained by Fourier transformation of

*P(ω,θ)*[19

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]

*a*(and

_{n}*b*) can be rewritten as followed:where

_{n}*p*denotes the order of the Debye mode.

*T*and

*R*denote transmission and reflection coefficients through the interface particle/host medium which can be found in [20

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]

*a*and

*n (R*refer to the coefficient

_{n,a}, T_{n,a})*a*and an equivalent formula can be written for

_{n}*b*. By using decomposition (2) in Eq. (1), it is now possible to calculate the partial phase function of the different modes. A schematic representation [21

_{n}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]

*i.e.*before the “zero” reference beam) as it corresponds to light reflected at the front interface. The mode 1 (Fig. 1(c)) mainly corresponds to a transmission of energy through the bulk of the particle. It is approximately delayed of

*Δt = (n*, compared to the mode 0, where

_{pa}-n_{hm})*(2R/c)*R*is the radius of the particle,

*c*the speed of light in vacuum,

*n*, and

_{pa}*n*denote the refractive index of the particle and of the host medium respectively. Mode 2 (Fig. 1(d)) undergoes 1 internal reflection and is responsible of the rainbow effect. Mode

_{hm}*n*undergoes

*n-1*internal reflections. One of the key points of our study is to evaluate how absorption modifies the temporal phase function and this will be done in the next section.

## 3. Debye mode weight

*Δt = (n*. 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

_{pa}-n_{hm})*(2R/c)*k*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

_{pa}*k*.

_{pa}## 4. Asymmetry factor

*k*strongly increases [22

_{pa}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]

*g*defined and calculated as followed [1]:

*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 ) for increasing value of

*k*For mode 0,

_{pa}.*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

*k*increases (complete overlap with mode 0 for great value of

_{pa}*k*as observed in [23

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

*k*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.

_{pa}## 5. Scattering and absorption cross sections

*k*over the different cross sections: scattering

_{pa}*σ*, absorption

_{sca}*σ*, and extinction

_{abs}*σ*. Partial extinction cross-section

_{ext}*a*and

_{n}*b*based on Mie theory, still valid for absorbing particles [1]. We define the different extinction efficiencies

_{n}*R*for small particles corresponds to the Rayleigh regime, (ii) oscillations of

*R*belong to the Mie regime and (iii)

*k*, mode 1 is killed. The

_{pa}*q*curve overlaps the one obtained for mode 0 only, and oscillations disappear. The consequence is a slight increase or decrease of

_{ext}*k*increases, depending on the particle radius. This is the well known process called absorption edge [1].

_{pa}*k*over the scattering and absorbing cross sections when we calculate the albedo

_{pa}*Ω*:

*Ω =*1). When

*k*increases,

_{pa}*k*increases, the albedo decreases from 1 to 0,5 (Fig. 6 ). 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

_{pa}*2*where

^{-m}*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

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]

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. 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]

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]

*5.10*. We consider an optical path of 1 cm, and an Optical Thickness

^{−4}Sr*O.T.*= 20. We verified that

*O.T.*is not significantly modified for the value of

*k*we considered.

_{pa}*µm*. For

*k*= 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

_{pa}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]

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]

*k*= 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

_{pa}*fs*line width (FWHM)).

*R =*50

*µm*). With no absorption, two separated lobes can be observed (Fig. 8 ). In order to understand the physical origin of these two lobes, we represent (Fig. 9 ) 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 (

*k*= 10

_{pa}^{−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

*k*, only the mode 0 remains whereas higher modes are absorbed.

_{pa}## 7. Discussion

*k*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 ) the corresponding average delay τ, τ

_{pa}_{a}and τ

_{b}.

*k*. 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

_{pa}*k*bigger than 10

_{pa}^{−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

*k*10

_{pa}=^{−3}is only induced by the increase of

*O.T.*from 20 to 20.18 (absorption edge). When

*k*= 10

_{pa}^{−5}, absorption is not detectable with classical technique, there is no variation of the optical thickness or modification of the phase function (Table 1).

*n*compared to

_{pa}*k*, we have considered a variation of these two parameters of the same magnitude (Δ

_{pa}*n*Δ

_{pa}=*k*) and calculated the impact on the average time of flight τ. For particle of 50

_{pa}= 10^{−5}*µm*, the impact of

*k*is 40 times bigger than the impact of

_{pa}*n*(20 times for particle of 5

_{pa}*µm*). This method could be coupled with other methods more sensitive to

*n*

_{p}_{a}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]

*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

*R*= 5

*µm*and large particles

*R*= 50

*µm*. For small particles, TOF is reduced for value of

*k*(≥10

_{pa}^{−3}) only. For large particles, the effect can be tracked for value of

*k*(≥10

_{pa}^{−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, |

2. | M. I. Mishchenko, L. D. Travis, and A. A. Lacis, |

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 |

4. | M. Barthélémy, N. Rivière, L. Hespel, and T. Dartigalongue, “Pump probe experiment for high scattering media diagnostics,” in |

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. |

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 |

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. |

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 |

9. | T. Gustavsson, A. Sharonov, and D. Markovitsi, “Thymine, thymidine and thimidine 5′-monophosphate studied by femtosecond fluorescence upconversion spectroscopy,” Chem. Phys. Lett. |

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. |

11. | D. Sedarsky, E. Berrocal, and M. Linne, “Quantitative image contrast enhancement in time-gated transillumination of scattering media,” Opt. Express |

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. |

14. | K. M. Yoo, G. C. Tang, and R. R. Alfano, “Coherent backscattering of light from biological tissues,” Appl. Opt. |

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. |

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 |

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 |

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 |

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. |

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 |

21. | N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” Proc. SPIE |

22. | Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. |

23. | J. Shen and H. Wang, “Calculation of Debye series expansion of light scattering,” Appl. Opt. |

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. |

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 |

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. |

27. | F. Onofri, “Critical angle refractometry for simultaneous measurement of particles in flow: size and relative refractive index,” Part. Part. Syst. Charact. |

**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

Sort: Year | Journal | Reset

### References

- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, 1983).
- M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University Press, 2002).
- C. Calba, L. Méès, C. Rozé, and T. Girasole, “Ultrashort pulse propagation through a strongly scattering medium: simulation and experiments,” J. Opt. Soc. Am. A25(7), 1541–1550 (2008). [CrossRef] [PubMed]
- 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.
- 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]
- 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. Methods3(1), 47–53 (2006). [CrossRef] [PubMed]
- 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]
- 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,” Science253(5021), 769–771 (1991). [CrossRef] [PubMed]
- 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]
- 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]
- D. Sedarsky, E. Berrocal, and M. Linne, “Quantitative image contrast enhancement in time-gated transillumination of scattering media,” Opt. Express19(3), 1866–1883 (2011). [CrossRef] [PubMed]
- 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).
- 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).
- 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]
- 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]
- C. J. Lee, P. J. van der Slot, and K. J. Boller, “Using ultra-short pulses to determine particle size and density distributions,” Opt. Express15(19), 12483–12497 (2007). [CrossRef] [PubMed]
- 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. Acta434(1), 113–123 (2001). [CrossRef]
- C. Gributs and D. Burns, “Multiresolution analysis for quantification of optical properties in scattering media using pulsed photon time-of-flight measurements,” Anal. Chim. Acta490(1-2), 185–195 (2003). [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]
- 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. A9(5), 781–795 (1992). [CrossRef]
- N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” Proc. SPIE7065, 70650X, 70650X-9 (2008). [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]
- J. Shen and H. Wang, “Calculation of Debye series expansion of light scattering,” Appl. Opt.49(13), 2422–2428 (2010). [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]
- 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. A9, 1903–1915 (1996).
- 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]
- 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.