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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 9604–9615
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Experimental and numerical analysis of ballistic and scattered light using femtosecond optical Kerr gating: a way for the characterization of strongly scattering media

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


Optics Express, Vol. 20, Issue 9, pp. 9604-9615 (2012)
http://dx.doi.org/10.1364/OE.20.009604


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Abstract

We have developed a new experimental setup based on optical Kerr gating in order to isolate either the transmitted or the scattered light going through an optically thick medium. This selectivity can be obtained by finely tuning the focusing of the different laser beams in the Kerr medium. We have developed an experimental setup. A Monte Carlo simulation scheme generates an accurate model of scattering processes taking into account the time of flight, the geometry of the Kerr gating and the polarization. We show that our experimental setup is capable of analyzing the transmitted light with optical densities up to OD = 9.7, and scattered light beyond OD = 347 in poly-disperse silica spheres in water (distribution centered on ~0.9µm radius) at λ = 550 nm. Strongly positive correlations are obtained with simulations.

© 2012 OSA

1. Introduction

The propagation of light in strongly scattering media such as clouds, paints or biological tissues has been receiving increasing attention. This research is mainly driven by a need for characterization of such media (particle sizing, chemical characterization, fine physical measurements, etc.). This often requires an instantaneous and accurate in situ measurement, using light/matter interaction. Depending on the application, the goal is to focus either on the transmitted light (i.e. the light which goes through the sample and does not interact with it) or on the scattered light. Transmitted light characterization is very useful for ballistic imaging [1

1. M. Paciaroni and M. Linne, “Single-shot, two-dimensional ballistic imaging through scattering media,” Appl. Opt. 43(26), 5100–5109 (2004). [CrossRef] [PubMed]

], detection of objects hidden in turbid media [2

2. 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 for spray imaging [3

3. C. Schultz, J. Gronki, and S. Andersson, “Multi-species laser-based imaging measurements in a diesel spray,” SAE Transactions 113(4), 1032–1042 (2004).

]. It can also be used for spectral extinction measurement of optically thick media [4

4. M. Barthélémy, N. Rivière, L. Hespel, and T. Dartigalongue, “Pump probe experiment for high scattering media diagnostics,” in Reflection, scattering, and diffraction from surfaces, Z.-H. Gu and L.M. Hanssen, eds., Proc SPIE 7065, 70650Z (2008).

] such as combustion chambers and rocket motors. The goal is to accurately measure the transmitted fraction of energy while removing the scattered parasitic part, however this becomes difficult with increasing OD (Optical Density). The other approach consists of carefully analyzing the scattered part itself. A considerable variety of information on the microphysical structure of the system can be gained from the temporal profile analysis of the scattered light. Thanks to femtosecond lasers and techniques such as up conversion [5

5. A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up conversion,” J. Mod. Opt. 51(9–10), 1433–1445 (2009).

] or optical Kerr gating (OKG) [6

6. P. P. Ho, N. L. Yang, T. Jimbo, Q. Z. Wang, and R. R. Alfano, “Ultrafast resonant optical Kerr effect in 4-butoxycarbonylmethylurethane polydiacetylene,” J. Opt. Soc. Am. B 4(6), 1025–1029 (1987). [CrossRef]

], it is now possible to perform Time Of Flight (TOF) measurements and to characterize the temporal scattered intensity profile. A careful analysis of the forward scattered light gives access to the optical depth and/or the particle sizes, even if the ballistic contribution is negligible [7

7. 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]

]. In a recent work, Barthélémy [8

8. M. Barthélémy, Apport d’une source laser femtoseconde amplifiée pour la mesure de spectre d’extinction d’un milieu diffusant optiquement épais. PhD thesis, Université de Toulouse, 2009.

] has shown the great benefit of using femtosecond laser sources and OKG experiments for optical diagnosis: the high temporal resolution and increased power allow for spectral extinction measurements of thick media. In this present study, we will experimentally demonstrate that optical Kerr gating is a well suited technique to measure independently scattered or ballistic intensities of light travelling through optically thick media. This selectivity allows us to study, thanks to a unique set up, a great variety of scattering samples displaying a large range of optical densities. At small OD, spectral extinction measurements should give, after inversion, the particle size distribution of the sample [4

4. M. Barthélémy, N. Rivière, L. Hespel, and T. Dartigalongue, “Pump probe experiment for high scattering media diagnostics,” in Reflection, scattering, and diffraction from surfaces, Z.-H. Gu and L.M. Hanssen, eds., Proc SPIE 7065, 70650Z (2008).

]. At high OD, scattered light shows variable time delay depending on OD and particles sizes and could be used as a tool of characterization [7

7. 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]

]. We validate our results using a Monte Carlo simulation scheme. In the first section, we describe the experimental set up we have developed and show how fine-tuning the focusing of the beam increases either the ballistic or the scattered fraction of the signal. In the second section, the numerical Monte Carlo scheme is introduced and used to evaluate the range of accessible OD and the efficiency of OKG filter. Finally, experimental measurements are carried out and compared with various numerical simulations in scattered and ballistic configurations. Correlations are quantified and limits of detection are discussed.

2. Optical Kerr gate experiment: two possible configurations

When a femtosecond laser pulse impinges on a dense scattering medium, the ballistic light (transmitted light) goes straight through the sample. It is linearly delayed only by the eventual refractive index changes through its pathway (Fig. 1
Fig. 1 Interaction of an ultra short scattering pulse and a scattering medium, and resulting temporal intensity of the signal.
). The scattered light undergoes a more complex pathway and is consequently more delayed.

It is possible to temporally sample the forward scattered and/or ballistic light thanks to the optical Kerr gating method. The laser source generates two pulses (pump and probe (Fig. 2
Fig. 2 Schematic representation of the sampling set up. The probe beam crosses the scattering sample S, and the iris I1 constrains the area of interest. The iris I2 defines the angle of collection of the scattered light. A convergent lens Lpr focuses both the ballistic and scattered light. The ballistic light follows a Gaussian propagation and focuses at the focal point F’. The scattered light follows a geometric propagation and the sample is imaged at plane (A’). The OKG plate is placed either at F’ or A’. P1 and P2 are two crossed polarizers.
)). The linearly polarized probe (using polarizer P1) goes through the sample. The pump is optically delayed and is used as a temporal gate as it induces an instantaneous birefringence [6

6. P. P. Ho, N. L. Yang, T. Jimbo, Q. Z. Wang, and R. R. Alfano, “Ultrafast resonant optical Kerr effect in 4-butoxycarbonylmethylurethane polydiacetylene,” J. Opt. Soc. Am. B 4(6), 1025–1029 (1987). [CrossRef]

] in a BK7 plate. A crossed polarizer P2 lets the probe pulse reach the detector only if the two pulses (pump and probe) perfectly overlap spatially and temporally as shown on Fig. 2. The pump is linearly polarized at 45° with respect to the probe for optimal efficiency. This is strictly equivalent to a virtual pinhole which stops all the probe light that does not overlap the pump light. When the delay between the two pulses is adjusted, it is possible to sample either the ballistic or the scattered light. The sampling is performed along a defined delay range in order to obtain the temporal profile of the scattered light. A typical gate of 100 fs should discriminate pathway differences of 30 µm. In comparison with up conversion, there is no need for phase matching which is convenient when the probe is tunable over a large spectrum as is the case in our setup (tunable OPA). The only limit is the transmission of the OKG plate (0.3 to 2 µm for BK7). Furthermore, this method allows the sampling of photons with different linear polarization states simply by adjusting the two polarizers (P1 and P2). Optical Kerr gating also provides optimized sampling either of the scattered or the ballistic light, obtained with a fine adjustment of the focusing of the pump and probe beams on the Kerr plate (lenses Lpp and Lpr). Hence, two experimental configurations arise:

  • 1) Ballistic photon measurement (BPM). The smallest possible virtual pinhole is set up to filter out as much scattered light as possible. Ideally, the Kerr plate should be placed at the focal plane of both lenses Lpp and Lpr. This necessitates a strong attenuation of the pump energy. Practically, the pump is slightly defocused to avoid any damage to the plate. This also makes the adjustment of the spatial overlap of both beams easier.
  • 2) Scattered light measurement (SLM). The Kerr plate is placed at the image plane A’ of the sample. The pump is enlarged to overlap the majority of the sample image on the Kerr plate (i.e. the image of the iris I1). Here, the pump energy is raised to its maximum to maintain the same Kerr efficiency (7% at the ballistic peak for both configurations).

The beam size has been measured using a beam profiler (WincamD-UD23, Datary Inc., Boulder Creek, CA, USA). The different spot sizes ωpump and ωprobe on the OKG plate are reported in Table 1

Table 1. Beam waist at 1/e (in µm) of pump (ωpump) and probe (ωprobe) and spot size Rspot on the OKG plate in the two sampling configurations

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(ω denotes the waist of the beam at 1/e). We have furthermore calculated the size of the scattered light spot Rspot on the OKG plate, induced by a single particle situated on the optical axis (red spot on Fig. 2). This diameter (2* Rspot) is equal to I2 at the lens position (O), and linearly decreases to almost 0 at the image plane (A’) (the Point Spread Function of our optical apparatus is less than 30 µm).

From these parameters, we evaluate the transmission of ballistic (Tbal) and scattered (Tscatt) photons through the OKG plate. Ballistic photons have a Gaussian transverse energy repartition Iprobe(r). The transmission at any point of the OKG plate is directly proportional to the pump energy Ipump. Integration of the transverse transmitted intensity profile ∫Iprobe(r)Ipump(r)dr gives, after a straightforward derivation and normalization, Tbalωpump2/(ωpump2+ωprobe2). The transmission of scattered light Tscatt is obtained using a similar derivation assuming that we have a homogeneous energy distribution all over the scattered disk. We then define and calculate the ratio η of these two transmissions:
η=TbalTscatt=ωpump2ωpump2+ωprobe2×u1eu
(1)
where u = (Rspotpump)2 . In the SLM configuration, η=0.75, i.e. transmissions of scattered and ballistic photons have the same order of magnitude. In the BPM configuration, η = 180 and the transmission of ballistic light is greatly enhanced. This analysis of efficiency has to be extended to every particle situated at a given distance r from the optical axis. In the BPM configuration, since Rspot>>ωpump, efficiency of OKG is homogeneous all over the sample and does not depend on r. In the SLM configuration, Kerr efficiency decreases with r. Indeed, it is directly governed by the pump profile intensity. One needs to project the Gaussian pump profile from the OKG plane, back to the sample plane, using Γ, the optical magnification of the probe line. The OKG efficiency is therefore equal to η(r) = η(0).exp(-r2η2) where ωη = ωpump*Γ. Hence, the optimization of the scattered flux is a two step process. The first step consists of minimizing η by placing the OKG plate at A’. The second step consists of collecting the scattered flux coming from the largest part of the sample (i.e. by enlarging ωpump and consequently ωη ).

3. Numerical simulations

In order to evaluate the relative efficiency of the temporal and spatial filtering, we have developed a temporal Monte Carlo scheme [9

9. N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” in Reflection, scattering, and diffraction from surfaces, Z.-H. Gu and L.M. Hanssen, eds., Proc SPIE 7065, 70650X (2008).

]. Using a computer simulation, we randomly send particles of light (that we call photons) through the sample. Their pathway through the sample is randomly built toward the detector, keeping track of their time of flight. We calculate the different density functions. The distance between two scattering events is governed by the extinction coefficients. The phase function determines the scattering angle. To model the time spent in the particle, one needs to introduce temporal phase functions [10

10. 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]

] and Debye modes [11

11. 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]

]. For basic geometries, a good agreement between our simulations and those found in Calba et al. [7

7. 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]

] was obtained. Our model also takes into account the depolarization effect, and further results on this subject will be presented in a dedicated study. In order to carefully understand and predict the relative weight of the ballistic and scattered light, a very accurate description of the geometry of the system is required. We measured the size of the probe beam ωsample at the sample position and the pulse duration (FWHMprobe) was obtained from the laser specifications. Given these data, initialization of the photon is then done spatially and temporally on a Gaussian profile. After every initialization, the photon position is checked. If it remains within the iris I1, the corresponding ballistic contribution reaching the detector is calculated by multiplying by η.10-OD. Every scattering event is checked to be within the iris I1. We use a semi Monte Carlo detection by multiplying the corresponding intensity by the solid angle of collection Ω (defined by the iris I2). We also multiply the contribution by the radial Gaussian attenuation (ωη) due to the pump spatial profile. The photon is “killed” when it comes to the interface. We then sum the ballistic and scattered contributions and convolute the result with a temporal Gaussian profile (FWHMconvol) in order to reproduce the signal obtained experimentally for a pure ballistic signal. This last convolution merges the temporal size of the pump beam and other effects due to the non compensated dispersions in lenses, polarizer or the sample itself and the electronic response of the Kerr medium which is known to be faster than the 100 fs pulse duration [12

12. R. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear susceptibilities of glasses,” Phys. Rev. B 11(2), 964–967 (1975). [CrossRef]

]. The parameters used for the simulation are given in Table 2

Table 2. Geometrical parameters of the experimental setup

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.

4. Experimental study

4.1 Samples investigated and principle of measurement

4.2 Experimental setup

The laser source is a 3mJ - 1 kHz - 800 nm - 100 fs amplified Ti:Sapphire laser (Coherent “Libra HE”, Santa Clara, CA, USA). The laser beam is split in two before the compression stage: the two lines are compressed independently through identical compressor stages in order to avoid self phase modulation in the beam splitter. The pump beam (1 mJ/pulse) can be optically delayed using a motorized delay line kit (Newport, Irvine, CA, USA). The pulse energy is adjusted depending on the set configuration (1 mJ/pulse in SLM, few µJ/pulse for BPM) in order to have a similar laser fluence on the OKG plate. The probe beam (2 mJ/pulse) goes through a commercial optical parametric amplifier (TOPAS, Light Conversion Ltd., Vilnius, Lithuania) and a harmonic generator. This setup makes the 800 nm initial beam tunable continuously from 0.23 to 20 µm. This study presents results obtained for a single 550 nm SFI output (sum frequency between 800 nm and a produced Idler). The output energy is ~200 µJ/pulse. The probe beam is then routed through the sample, towards the OKG plate. As OKG sampling is based on the birefringence effects inside the Kerr medium, the extinction level of the crossed polarizer P2 should be sufficient to significantly reduce the amount of non-sampled probe beam, actually identified as background. This is particularly true in the SLM configuration when very low signals are acquired from very thick scattering media. After precise alignment of the probe line through lenses and plates and ensuring that the optics are birefringence free (i.e. constraint free), we find an extinction coefficient of ~10−6 which is close to the specification of a single polarizer (10−5). In other words, the background signal can be reduced to this value, meaning that P2 has a “leak” of one photon out of 106. The resulting ballistic and scattered sampled light are finally directed towards a spectrometer made of a monochromator (Newport, Oriel Instruments 74125, Stratford, MT, USA) and a PMT detector (Perkin Elmer MH973, Waltham, MA, USA). This additional spectral filter is imperative in order to eliminate the pump parasitic light and to spectrally filter the output of the TOPAS. Indeed, different wavelengths are generated in the TOPAS and the provided harmonic separators are not sufficient.

5. Results

Figure 4a
Fig. 4 Experimental and simulated temporal scattering diagrams in BPM configuration, for samples OD8, OD8.6 and OD9. Intensities and zero time delay are normalized to the experimental ballistic light peak. Scattered light is represented in (a) with a zoom on ballistic photons in (b).
shows the results obtained for OD8, OD8.6 and OD9 in the ballistic configuration. Experimental pump/probe scanning clearly reveals a ballistic peak of intensity, placed at the zero delay (Fig. 4b). Here after, the temporal lobe of scattered photons grows with OD and the maximum intensity is delayed: 0.8 ps (OD8), 0.9 ps (OD8.6), and 1 ps (OD9). Simulations fit the experimental data for all samples well, with computed OD of 8.1, 8.7 and 9.1 respectively for the three samples. For the sake of clarity, the curves are normalized to the experimental ballistic peak. Yet the great step forward of these experiments is the absolute agreement between experiments and simulations. Indeed, the latter are normalized to the same calibrated ODref as that used experimentally. We were able to reproduce the absolute level of both ballistic peak and scattered lobe with a slight adjustment of the critical parameters (η, Ω) within uncertainties measured on our setup. Only one set of parameters were sufficient to reproduce accurately all the different experiments.

Figure 5
Fig. 5 Experimental and simulated temporal scattering diagrams in SLM configuration, for samples OD8.6, OD10.5, OD18 and OD42.7. Intensities are normalized to the maximum measured signal for each sample. Zero delay is the previously detected ballistic peak of OD8.6, not visible anymore in SLM.
represents a compilation of experimental and simulated temporal scattering profiles in the SLM configuration. No ballistic light can be detected because of the high optical densities studied and the lack of efficiency of the SLM configuration for such detection. Whereas the OD8.6 sample clearly exhibits a ballistic peak in the BPM configuration, it is not visible here. Therefore, signals are normalized to the maximum peak intensity for all samples. We observe an increase of Δt1 with OD: 1.6ps (OD8.6), 2.4ps (OD10.5), 4.3ps (OD18) and 10.6ps (OD42.7). The simulations were computed with OD of 8.2, 11.8, 19.5 and 42.1 respectively. These adjustments are slightly higher than the 7% uncertainty over measured the OD (section 4.1) but could be explained by the sample instability (i.e. sedimentation, agglomeration). We have calculated the 3 first orders of Δtn, and deviations between the simulations and experiments are below 2%.

Figure 6
Fig. 6 Experimental temporal scattering diagram in SLM configuration, for sample OD347.
represents the experimental result of the temporal scattering in the OD347 sample. The signal to background ratio is ~1. For this OD, it was not possible to perform the simulation. Three main reasons could be given. First, side interfaces of the sample modify the temporal signal even if the forward direction is considered. This point is under investigation and we have evidenced modification of temporal profiles for OD greater than 50 (for this geometry and PSD). Moreover, the charge rate of this last sample exceeds a few percent and for this regime, dependent scattering has to be considered. Finally, such an optical density requires enormous calculation resources. The estimated time needed for such a simulation is nearly a month using a 3GHz CPU, 16GB RAM personal computer. Meanwhile, a similar single in situ measurement is performed in five minutes.

4. Discussion

5. Conclusions

The present study reports a temporal analysis of scattered and ballistic light on a very large OD range [0, 347]. The extremely short acquisition time (compared to simulations) makes the present setup a reliable tool to compile a reference data bank of temporal signatures of scattered light emitted from calibrated very thick media. This opens a way for further possible optical diagnostics of very thick unknown samples (particle sizing, OD determination…). Furthermore, our study allows the validation of our Monte Carlo code. We are thus able to precisely model two different configurations, optimized either for ballistic or scattered light collection. The OKG filtering efficiency for spectral extinction measurements has been numerically evaluated and appears to work well for particles up to 50 µm radii. We are currently performing further experiments at different wavelengths and particle sizes. The temporal depolarization could provide additional information about the sample [19

19. S. G. Demos and R. R. Alfano, “Temporal gating in highly scattering media by the degree of optical polarization,” Opt. Lett. 21(2), 161–163 (1996). [CrossRef] [PubMed]

] and should be meticulously investigated.

Acknowledgments

This work is supported by the ONERA - The French Aerospace Lab Research Project “FEMTO”. The authors would like to thank Nicolas Rivière for his great technical and scientific support.

References and links

1.

M. Paciaroni and M. Linne, “Single-shot, two-dimensional ballistic imaging through scattering media,” Appl. Opt. 43(26), 5100–5109 (2004). [CrossRef] [PubMed]

2.

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]

3.

C. Schultz, J. Gronki, and S. Andersson, “Multi-species laser-based imaging measurements in a diesel spray,” SAE Transactions 113(4), 1032–1042 (2004).

4.

M. Barthélémy, N. Rivière, L. Hespel, and T. Dartigalongue, “Pump probe experiment for high scattering media diagnostics,” in Reflection, scattering, and diffraction from surfaces, Z.-H. Gu and L.M. Hanssen, eds., Proc SPIE 7065, 70650Z (2008).

5.

A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up conversion,” J. Mod. Opt. 51(9–10), 1433–1445 (2009).

6.

P. P. Ho, N. L. Yang, T. Jimbo, Q. Z. Wang, and R. R. Alfano, “Ultrafast resonant optical Kerr effect in 4-butoxycarbonylmethylurethane polydiacetylene,” J. Opt. Soc. Am. B 4(6), 1025–1029 (1987). [CrossRef]

7.

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]

8.

M. Barthélémy, Apport d’une source laser femtoseconde amplifiée pour la mesure de spectre d’extinction d’un milieu diffusant optiquement épais. PhD thesis, Université de Toulouse, 2009.

9.

N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” in Reflection, scattering, and diffraction from surfaces, Z.-H. Gu and L.M. Hanssen, eds., Proc SPIE 7065, 70650X (2008).

10.

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]

11.

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]

12.

R. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear susceptibilities of glasses,” Phys. Rev. B 11(2), 964–967 (1975). [CrossRef]

13.

N. Pfeiffer and G. H. Chapman, “Monte Carlo simulations of the growth and decay of quasi-ballistic photon fractions with depth in an isotropic medium,” in Optical Interactions with Tissue and Cells XVI, S.L. Jacques and W.P. Roach, eds. Proc. SPIE 5695, 136–147 (2005).

14.

W. F. Long and D. H. 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]

15.

L. Hespel and A. Delfour, “Mie light-scattering granulometer with adaptive numerical filtering. I. Theory,” Appl. Opt. 39(36), 6897–6917 (2000). [CrossRef] [PubMed]

16.

G. P. Box, K. M. Sealey, and M. A. Box, “Inversion of Mie extinction measurement using analytic eigenfunction theory,” J. Atmos. Sci. 49(22), 2074–2081 (1992). [CrossRef]

17.

J. P. Butler, J. A. Reeds, and S. V. Dawson, “Estimating solutions of first kind integral equation with nonnegative constraints and optimal smoothing,” SIAM J. Numer. Anal. 18(3), 381–397 (1981). [CrossRef]

18.

M. Kervella, F.-X. d’Abzac, F. Hache, L. Hespel, and T. Dartigalongue, “Picosecond time scale modification of forward scattered light induced by absorption inside particles,” Opt. Express 20(1), 32–41 (2012). [CrossRef] [PubMed]

19.

S. G. Demos and R. R. Alfano, “Temporal gating in highly scattering media by the degree of optical polarization,” Opt. Lett. 21(2), 161–163 (1996). [CrossRef] [PubMed]

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: January 18, 2012
Revised Manuscript: February 10, 2012
Manuscript Accepted: February 11, 2012
Published: April 11, 2012

Virtual Issues
Vol. 7, Iss. 6 Virtual Journal for Biomedical Optics

Citation
François-Xavier d’Abzac, Myriam Kervella, Laurent Hespel, and Thibault Dartigalongue, "Experimental and numerical analysis of ballistic and scattered light using femtosecond optical Kerr gating: a way for the characterization of strongly scattering media," Opt. Express 20, 9604-9615 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-9604


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References

  1. M. Paciaroni and M. Linne, “Single-shot, two-dimensional ballistic imaging through scattering media,” Appl. Opt.43(26), 5100–5109 (2004). [CrossRef] [PubMed]
  2. 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]
  3. C. Schultz, J. Gronki, and S. Andersson, “Multi-species laser-based imaging measurements in a diesel spray,” SAE Transactions113(4), 1032–1042 (2004).
  4. M. Barthélémy, N. Rivière, L. Hespel, and T. Dartigalongue, “Pump probe experiment for high scattering media diagnostics,” in Reflection, scattering, and diffraction from surfaces, Z.-H. Gu and L.M. Hanssen, eds., Proc SPIE 7065, 70650Z (2008).
  5. A. P. Vandevender and P. G. Kwiat, “High efficiency single photon detection via frequency up conversion,” J. Mod. Opt.51(9–10), 1433–1445 (2009).
  6. P. P. Ho, N. L. Yang, T. Jimbo, Q. Z. Wang, and R. R. Alfano, “Ultrafast resonant optical Kerr effect in 4-butoxycarbonylmethylurethane polydiacetylene,” J. Opt. Soc. Am. B4(6), 1025–1029 (1987). [CrossRef]
  7. 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]
  8. M. Barthélémy, Apport d’une source laser femtoseconde amplifiée pour la mesure de spectre d’extinction d’un milieu diffusant optiquement épais. PhD thesis, Université de Toulouse, 2009.
  9. N. Rivière, M. Barthélémy, T. Dartigalongue, and L. Hespel, “Modeling of femtosecond pulse propagation through dense scattering media,” in Reflection, scattering, and diffraction from surfaces, Z.-H. Gu and L.M. Hanssen, eds., Proc SPIE 7065, 70650X (2008).
  10. 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]
  11. 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]
  12. R. Hellwarth, J. Cherlow, and T. Yang, “Origin and frequency dependence of nonlinear susceptibilities of glasses,” Phys. Rev. B11(2), 964–967 (1975). [CrossRef]
  13. N. Pfeiffer and G. H. Chapman, “Monte Carlo simulations of the growth and decay of quasi-ballistic photon fractions with depth in an isotropic medium,” in Optical Interactions with Tissue and Cells XVI, S.L. Jacques and W.P. Roach, eds. Proc. SPIE 5695, 136–147 (2005).
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