Abstract

In Part I of this study [1], good agreement between experimental measurements and results from Monte Carlo simulations were obtained for the spatial intensity distribution of a laser beam propagating within a turbid environment. In this second part, the validated Monte Carlo model is used to investigate spatial and temporal effects from distinct scattering orders on image formation. The contribution of ballistic photons and the first twelve scattering orders are analyzed individually by filtering the appropriate data from simulation results. Side-scattering and forward-scattering detection geometries are investigated and compared. We demonstrate that the distribution of positions for the final scattering events is independent of particle concentration when considering a given scattering order in forward detection. From this observation, it follows that the normalized intensity distribution of each order, in both space and time, is independent of the number density of particles. As a result, the amount of transmitted information is constant for a given scattering order and is directly related to the phase function in association with the detection acceptance angle. Finally, a contrast analysis is performed in order to quantify this information at the image plane.

© 2009 Optical Society of America

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  1. E. Berrocal, D. L. Sedarsky, M. E. Paciaroni, I. V. Meglinski, and M. A. Linne, "Laser light scattering in turbid media Part I: Experimental and simulated results for the spatial intensity distribution," Opt. Express 15, 10649-10665 (2007)
    [CrossRef] [PubMed]
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  3. C. Bohren and D. Huffman, Absorption and scattering of light by small particles (Wiley, N.Y., 1983)
  4. M. A. Linne M. Paciaroni, E. Berrocal and D. Sedarsky, "Ballistic imaging of liquid breakup processes in dense sprays," Proc. Combust. Inst. 32, 2147-2161 (2009)
    [CrossRef]
  5. B. Kaldvee, A. Ehn, J. Bood, and M. Aldén, "Development of a picosecond lidar system for large-scale combustion diagnostics," Appl. Opt. 48, B65-B72 (2009)
    [CrossRef] [PubMed]
  6. G. E. Anderson, F. Liu, and R. R. Alfano, "Microscope imaging through highly scattering media," Opt. Lett. 19, 981 (1994)
    [CrossRef] [PubMed]
  7. L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano, "True scattering coefficients of turbid matter measured by early-time gating," Opt. Lett. 20, 913-915 (1995)
    [CrossRef] [PubMed]
  8. J. C. Hebden, R. A. Kruger, and K. S. Wong, " Time resolved imaging through a highly scattering medium," Appl. Opt. 30, 788- (1991)
    [CrossRef] [PubMed]
  9. O. Emile, F. Bretenaker, and A. Le Floch, "Rotating polarization imaging in turbid media," Opt. Lett. 21, 1706-1708 (1996)
    [CrossRef] [PubMed]
  10. V. Sankaran, K. Schnenberger, J. T. Walsh, and D. J. Maitland, "Polarization Discrimination of Coherently Propagating Light in Turbid Media," Appl. Opt. 38, 4252-4261 (1999)
    [CrossRef]
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    [CrossRef]
  13. R. M. Measures, Laser Remote Sensing: Fundamentals and applications (Krieger, Florida, 1992)
  14. M. Gai, M. Gurioli, P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Laboratory simulations of lidar returns from clouds," Appl. Opt. 35, 5435-5442 (1996)
    [CrossRef] [PubMed]
  15. E. Berrocal, D. Y. Churmakov, V. P. Romanov, M. C. Jermy, and I. V. Meglinski, "Crossed source/detector geometry for novel spray diagnostic: Monte Carlo and analytical results", Appl. Opt. 44, 2519-2529 (2005)
    [CrossRef] [PubMed]
  16. I. M. Sobol, The Monte Carlo Method (University of Chicago, Chicago, Ill., 1974)
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    [CrossRef] [PubMed]
  18. G. Zaccanti, "Monte Carlo study of light propagation in optically thick media: point source case," Appl. Opt. 30, 2031-2041 (1991)
    [CrossRef] [PubMed]
  19. E. Berrocal, Multiple scattering of light in optical diagnostics of dense sprays and other complex turbid media (PhD Thesis, Cranfield University, 2006)
  20. V. P.  Romanov, D. Yu.  Churmakov, E.  Berrocal and I. V.  Meglinski, "Low-order light scattering in multiple scattering disperse media," Opt. Spectros. 97, 847-854 (2004)
  21. I. Meglinski, M. Kirillin, V. Kuzmin, and R. Myllylä, "Simulation of polarization-sensitive optical coherence tomography images by a Monte Carlo method," Opt. Lett. 33, 1581-1583 (2008)
    [CrossRef] [PubMed]
  22. L. R. Poole, D. D. Venable, and J. W. Campbell, "Semianalytic Monte Carlo radiative transfer model for oceanographic lidar systems," Appl. Opt. 20, 3653-3656 (1981)
    [CrossRef] [PubMed]
  23. P. Bruscaglioni, P. Donelli, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of the modulation transfer function of an optical system operating in a turbid medium," Appl. Opt. 32, 2813-2824 (1993)
    [CrossRef] [PubMed]
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    [CrossRef]
  26. C. Calba, C. Rozé, T. Girasole, 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, 373-382, (2006)
    [CrossRef]
  27. Q1. 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, 1541-1550 (2008)
    [CrossRef]
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    [CrossRef]
  29. K. M. Yoo and R. R. Alfano, "Time-resolved coherent and incoherent components of forward light scattering in random media," Opt. Lett. 15, 320- (1990)
    [CrossRef] [PubMed]
  30. G. Zaccanti, P. Bruscaglioni, A. Ismaelli, L. Carraresi, M. Gurioli, and Q. Wei, "Transmission of a pulsed thin light beam through thick turbid media: experimental results," Appl. Opt. 31, 2141-2147 (1992)
    [CrossRef] [PubMed]
  31. Feng Liu, K. M. Yoo, and R. R. Alfano, "Transmitted photon intensity through biological tissues within various time windows," Opt. Lett. 19, 740-742 (1994)
    [CrossRef] [PubMed]
  32. S. G. Demos and R. R. Alfano, "Temporal gating in highly scattering media by the degree of optical polarization," Opt. Lett. 21, 161-163 (1996)
    [CrossRef] [PubMed]
  33. V. M. Podgaetsky, S. A. Tereshchenko, A. V. Smirnov, and N. S. Vorob'ev, "Bimodal temporal distribution of photons in ultrashort laser pulse passed through a turbid medium," Opt. Commun. 180, 217-223 (2000)
    [CrossRef]

2009

M. A. Linne M. Paciaroni, E. Berrocal and D. Sedarsky, "Ballistic imaging of liquid breakup processes in dense sprays," Proc. Combust. Inst. 32, 2147-2161 (2009)
[CrossRef]

B. Kaldvee, A. Ehn, J. Bood, and M. Aldén, "Development of a picosecond lidar system for large-scale combustion diagnostics," Appl. Opt. 48, B65-B72 (2009)
[CrossRef] [PubMed]

2008

2007

2006

C. Calba, C. Rozé, T. Girasole, 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, 373-382, (2006)
[CrossRef]

2005

2004

V. P.  Romanov, D. Yu.  Churmakov, E.  Berrocal and I. V.  Meglinski, "Low-order light scattering in multiple scattering disperse media," Opt. Spectros. 97, 847-854 (2004)

2003

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

C. Dunsby and P. M. W. French, "Techniques for Depth-Resolved Imaging through Turbid Media including Coherence-gated Imaging," J. Phys. D: Appl. Phys. 36R207-R227 (2003)
[CrossRef]

2000

V. M. Podgaetsky, S. A. Tereshchenko, A. V. Smirnov, and N. S. Vorob'ev, "Bimodal temporal distribution of photons in ultrashort laser pulse passed through a turbid medium," Opt. Commun. 180, 217-223 (2000)
[CrossRef]

1999

1996

1995

L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano, "True scattering coefficients of turbid matter measured by early-time gating," Opt. Lett. 20, 913-915 (1995)
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, L. Zheng, "MCML - Monte Carlo modelling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

1994

1993

1992

1991

1983

1981

1967

Aldén, M.

Alfano, R. R.

Anderson, G. E.

Berrocal, E.

Bood, J.

Bretenaker, F.

Bruckner, A. P.

Bruscaglioni, P.

Calba, C.

Q1. 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, 1541-1550 (2008)
[CrossRef]

C. Calba, C. Rozé, T. Girasole, 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, 373-382, (2006)
[CrossRef]

Campbell, J. W.

Carraresi, L.

Churmakov, D. Y.

Churmakov, D. Yu.

V. P.  Romanov, D. Yu.  Churmakov, E.  Berrocal and I. V.  Meglinski, "Low-order light scattering in multiple scattering disperse media," Opt. Spectros. 97, 847-854 (2004)

Delfour, A.

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

Demos, S. G.

Donelli, P.

Dunsby, C.

C. Dunsby and P. M. W. French, "Techniques for Depth-Resolved Imaging through Turbid Media including Coherence-gated Imaging," J. Phys. D: Appl. Phys. 36R207-R227 (2003)
[CrossRef]

Ehn, A.

Emile, O.

Feng Liu,

French, P. M. W.

C. Dunsby and P. M. W. French, "Techniques for Depth-Resolved Imaging through Turbid Media including Coherence-gated Imaging," J. Phys. D: Appl. Phys. 36R207-R227 (2003)
[CrossRef]

Gai, M.

Galland, P.

Gan, X.

Girasole, T.

Q1. 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, 1541-1550 (2008)
[CrossRef]

C. Calba, C. Rozé, T. Girasole, 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, 373-382, (2006)
[CrossRef]

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

Gréhan, G.

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

Gu, M.

Gurioli, M.

Hespel, L.

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

Ho, P. P.

Ishimaru, A.

Ismaelli, A.

Jacques, S. L.

L. Wang, S. L. Jacques, L. Zheng, "MCML - Monte Carlo modelling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

Jermy, M. C.

Kaldvee, B.

Kirillin, M.

Kuga, Y.

Kuzmin, V.

Le Floch, A.

Liang, X.

Linne, M. A.

Liu, F.

Maitland, D. J.

Méès, L.

Q1. 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, 1541-1550 (2008)
[CrossRef]

C. Calba, C. Rozé, T. Girasole, 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, 373-382, (2006)
[CrossRef]

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

Meglinski, I.

Meglinski, I. V.

Meglinski, I. V.

V. P.  Romanov, D. Yu.  Churmakov, E.  Berrocal and I. V.  Meglinski, "Low-order light scattering in multiple scattering disperse media," Opt. Spectros. 97, 847-854 (2004)

Myllylä, R.

Paciaroni, M. E.

Podgaetsky, V. M.

V. M. Podgaetsky, S. A. Tereshchenko, A. V. Smirnov, and N. S. Vorob'ev, "Bimodal temporal distribution of photons in ultrashort laser pulse passed through a turbid medium," Opt. Commun. 180, 217-223 (2000)
[CrossRef]

Poole, L. R.

Romanov, V. P.

Romanov, V. P.

V. P.  Romanov, D. Yu.  Churmakov, E.  Berrocal and I. V.  Meglinski, "Low-order light scattering in multiple scattering disperse media," Opt. Spectros. 97, 847-854 (2004)

Rozé, C.

Q1. 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, 1541-1550 (2008)
[CrossRef]

C. Calba, C. Rozé, T. Girasole, 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, 373-382, (2006)
[CrossRef]

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

Sankaran, V.

Schnenberger, K.

Sedarsky, D. L.

Smirnov, A. V.

V. M. Podgaetsky, S. A. Tereshchenko, A. V. Smirnov, and N. S. Vorob'ev, "Bimodal temporal distribution of photons in ultrashort laser pulse passed through a turbid medium," Opt. Commun. 180, 217-223 (2000)
[CrossRef]

Stetson, K. A.

Tereshchenko, S. A.

V. M. Podgaetsky, S. A. Tereshchenko, A. V. Smirnov, and N. S. Vorob'ev, "Bimodal temporal distribution of photons in ultrashort laser pulse passed through a turbid medium," Opt. Commun. 180, 217-223 (2000)
[CrossRef]

Venable, D. D.

Vorob'ev, N. S.

V. M. Podgaetsky, S. A. Tereshchenko, A. V. Smirnov, and N. S. Vorob'ev, "Bimodal temporal distribution of photons in ultrashort laser pulse passed through a turbid medium," Opt. Commun. 180, 217-223 (2000)
[CrossRef]

Walsh, J. T.

Wang, L.

L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano, "True scattering coefficients of turbid matter measured by early-time gating," Opt. Lett. 20, 913-915 (1995)
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, L. Zheng, "MCML - Monte Carlo modelling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

Wei, Q.

Zaccanti, G.

Zheng, L.

L. Wang, S. L. Jacques, L. Zheng, "MCML - Monte Carlo modelling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

Appl. Opt.

G. Zaccanti, "Monte Carlo study of light propagation in optically thick media: point source case," Appl. Opt. 30, 2031-2041 (1991)
[CrossRef] [PubMed]

G. Zaccanti, P. Bruscaglioni, A. Ismaelli, L. Carraresi, M. Gurioli, and Q. Wei, "Transmission of a pulsed thin light beam through thick turbid media: experimental results," Appl. Opt. 31, 2141-2147 (1992)
[CrossRef] [PubMed]

P. Bruscaglioni, P. Donelli, A. Ismaelli, and G. Zaccanti, "Monte Carlo calculations of the modulation transfer function of an optical system operating in a turbid medium," Appl. Opt. 32, 2813-2824 (1993)
[CrossRef] [PubMed]

L. R. Poole, D. D. Venable, and J. W. Campbell, "Semianalytic Monte Carlo radiative transfer model for oceanographic lidar systems," Appl. Opt. 20, 3653-3656 (1981)
[CrossRef] [PubMed]

M. Gai, M. Gurioli, P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Laboratory simulations of lidar returns from clouds," Appl. Opt. 35, 5435-5442 (1996)
[CrossRef] [PubMed]

V. Sankaran, K. Schnenberger, J. T. Walsh, and D. J. Maitland, "Polarization Discrimination of Coherently Propagating Light in Turbid Media," Appl. Opt. 38, 4252-4261 (1999)
[CrossRef]

E. Berrocal, D. Y. Churmakov, V. P. Romanov, M. C. Jermy, and I. V. Meglinski, "Crossed source/detector geometry for novel spray diagnostic: Monte Carlo and analytical results", Appl. Opt. 44, 2519-2529 (2005)
[CrossRef] [PubMed]

B. Kaldvee, A. Ehn, J. Bood, and M. Aldén, "Development of a picosecond lidar system for large-scale combustion diagnostics," Appl. Opt. 48, B65-B72 (2009)
[CrossRef] [PubMed]

Comput. Methods Programs Biomed.

L. Wang, S. L. Jacques, L. Zheng, "MCML - Monte Carlo modelling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995)
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D: Appl. Phys.

C. Dunsby and P. M. W. French, "Techniques for Depth-Resolved Imaging through Turbid Media including Coherence-gated Imaging," J. Phys. D: Appl. Phys. 36R207-R227 (2003)
[CrossRef]

Opt. Commun.

C. Rozé, T. Girasole, L. Méès, G. Gréhan, L. Hespel, A. Delfour, "Interaction between ultra short pulses and a dense scattering medium by Monte Carlo simulation: consideration of particle size effect," Opt. Commun. 220, 237-245, (2003)
[CrossRef]

C. Calba, C. Rozé, T. Girasole, 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, 373-382, (2006)
[CrossRef]

V. M. Podgaetsky, S. A. Tereshchenko, A. V. Smirnov, and N. S. Vorob'ev, "Bimodal temporal distribution of photons in ultrashort laser pulse passed through a turbid medium," Opt. Commun. 180, 217-223 (2000)
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectros.

V. P.  Romanov, D. Yu.  Churmakov, E.  Berrocal and I. V.  Meglinski, "Low-order light scattering in multiple scattering disperse media," Opt. Spectros. 97, 847-854 (2004)

Proc. Combust. Inst.

M. A. Linne M. Paciaroni, E. Berrocal and D. Sedarsky, "Ballistic imaging of liquid breakup processes in dense sprays," Proc. Combust. Inst. 32, 2147-2161 (2009)
[CrossRef]

Other

J. C. Hebden, R. A. Kruger, and K. S. Wong, " Time resolved imaging through a highly scattering medium," Appl. Opt. 30, 788- (1991)
[CrossRef] [PubMed]

H. C. van de Hulst, Light scattering by small particles (Dover, N.Y., 1981)

C. Bohren and D. Huffman, Absorption and scattering of light by small particles (Wiley, N.Y., 1983)

R. M. Measures, Laser Remote Sensing: Fundamentals and applications (Krieger, Florida, 1992)

I. M. Sobol, The Monte Carlo Method (University of Chicago, Chicago, Ill., 1974)

E. Berrocal, Multiple scattering of light in optical diagnostics of dense sprays and other complex turbid media (PhD Thesis, Cranfield University, 2006)

K. M. Yoo and R. R. Alfano, "Time-resolved coherent and incoherent components of forward light scattering in random media," Opt. Lett. 15, 320- (1990)
[CrossRef] [PubMed]

Supplementary Material (6)

» Media 1: AVI (1294 KB)     
» Media 2: AVI (1188 KB)     
» Media 3: AVI (2226 KB)     
» Media 4: AVI (1206 KB)     
» Media 5: AVI (1188 KB)     
» Media 6: AVI (2226 KB)     

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Figures (13)

Fig. 1.
Fig. 1.

Schematic presentation of ballistic I (0), single I (1), double I (2) and triple I (3) scattered photons. The black circles on the illustration represent the last scattering event before detection.

Fig. 2.
Fig. 2.

Simulation configuration: The laser source S is modeled from the experimental image matrix. Six billion photons are sent into a cubic scattering volume (10 mm side) containing polystyrene spheres suspended in distilled water. Two sources of light have been considered: In one case (section 3 and 4) the full laser beam profile is assumed whereas in another case (section 5) a modulated beam profile has been assumed to quantify effects by individual scattering orders on image contrast.

Fig. 3.
Fig. 3.

Movies showing the front face simulated images from the n successive scattering orders. The two-dimensional intensity contributions are presented in the range 0≤n≤12 with the related profile along the vertical central axis (white dashed line). Solutions of polystyrene spheres are considered at optical depth OD=2, OD=5 and OD=10. The detection acceptance angle is θa =8.5°. In (a) (Media 1) the particle diameter is 1 µm and in (b) (Media 2) D equals 5 µm.

Fig. 4.
Fig. 4.

Comparison between the 1 and 5 µm particles for the relative maximum light intensity transmitted per scattering order: (a), (b), and (c) correspond to the respective optical depths 2, 5 and 10. In (d), the increase of the Full Width at Half Maximum d/da (where da is the initial width of the laser beam) can be visualized as a function of the scattering order.

Fig. 5.
Fig. 5.

Photon time-of-arrival for individual scattering orders in the forward scattering direction. Results for polystyrene spheres of 1 µm (on the left side) and 5 µm (on the right side) are compared at optical depth OD=2, OD=5 and OD=10. The light intensity is normalized to the value of the sum of all scattering orders.

Fig. 6.
Fig. 6.

Normalized number density of scattering events occurring within the central plane P as defined in Fig. 2. Only the scattering order n=4 is considered. Effects due to particle size, optical depth and detection acceptance angle are investigated. It is observed here that no apparent changes occur for variations in optical depth.

Fig. 7.
Fig. 7.

(a). Movie (Media 3) showing the position of the final scattering events in P for 1≤n≤5. Here, the detection acceptance angle is θa =8.5°. Results for 1 µm, 5 µm, and isotropic scattering are presented. (b): Temporal position of the maximum peak as a function of scattering order (extracted from Fig.8). The earliest photon time-of-arrival equals 44.4 ps, corresponding to the time necessary for the photons to cross 10 mm of distilled water.

Fig. 8.
Fig. 8.

Temporal and spatial transmitted light intensity profiles of individual scattering orders. Theses normalized transmitted data are independent of particle concentration in the scattering medium.

Fig. 9.
Fig. 9.

Movies showing the side face simulated images from the n successive scattering orders. The two-dimensional intensity contributions are presented in the range 0≤n≤12 with the related intensity profile along the horizontal central axis (white dashed line). Solutions of polystyrene spheres are considered at optical depth OD=2, OD=5 and OD=10. The detection acceptance angle is θa =8.5°. In (a) (Media 4) the particles diameter is 1 µm whereas in (b) (Media 5) D=5 µm.

Fig. 10.
Fig. 10.

Light intensity contribution of the twelve first scattering orders along the vertical axis at X=5 mm for side-scattering. Results for polystyrene spheres of 1 µm (on the left side) and 5 µm (on the right side) are compared at optical depth OD=2, OD=5 and OD=10. The light intensity is normalized to the maximum value of the sum of all scattering orders.

Fig. 11.
Fig. 11.

Photon time-of-arrival for individual scattering orders in the forward scattering direction. Results for polystyrene spheres of 1 µm (on the left side) and 5 µm (on the right side) are compared at optical depth OD=2, OD=5 and OD=10. The light intensity is normalized, here, to the value of the sum of all scattering orders (black solid line).

Fig. 12.
Fig. 12.

Movies (Media 6) showing the front face simulated images from the successive scattering orders n. The two-dimensional intensity contributions are presented in the range 0≤n≤4. Here, the detection acceptance angle is θa =8.5°. Results for 1 µm, 5 µm, and isotropic scattering are presented.

Fig. 13.
Fig. 13.

Histograms showing the image contrast for individual scattering orders in (a) and for the total light intensity in (b). Results for both anisotropic scattering (particle size parameters x=3.9 and x=19.6) and isotropic scattering are investigated. The detection acceptance angle is θa =8.5°.

Equations (4)

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I(TOT)=I(0)+I(1)+I(2)+I(3)+Σn=4+I(n)
I(TOT)(N)=Σn=0+P(n)(N)·I(n)normalized
C=[ImaxImin][Imax+Imin]
C(TOT)(N)=Σn=0+P(n)(N)·C(n)

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