Abstract

A method to distinguish a hidden object from a perturbing environment is to use an ultrashort femtosecond pulse of light and a time-resolved detection. To separate ballistic light containing information on a hidden object from multiscattered light coming from the surrounding environment that scrambles the signal, an optical Kerr gate can be used. It consists of a carbon disulfide (CS2) cell in which birefringence is optically induced. An imaging beam passes through the studied medium while a pump pulse is used to open the gate. The time-delayed scattered light is excluded from measurements by the gate, and the multiple-scattering scrambling effect is reduced. In previous works, the two beams had the same wavelength. We propose a new two-color experimental setup for ballistic imaging in which a second harmonic is generated and used for the image, while the fundamental is used for gate switching. This setup allows one to obtain better resolution by using a spectral filtering to eliminate noise from the pump pulse, instead of a spatial filtering. This new setup is suitable for use in ballistic imaging of dense sprays, multidiffusive, and large enough to show scattered light time delays greater than the gate duration (τ=1.3ps).

© 2009 Optical Society of America

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References

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  1. C. Dumouchel, “On the experimental investigation of primary atomization of liquid streams,” Exp. Fluids 45, 371-422 (2008).
    [CrossRef]
  2. P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).
  3. M. Paciaroni and M. Linne, “Single-shot two-dimensional ballistic imaging through scattering media,” Appl. Opt. 43, 5100-5109 (2004).
    [CrossRef] [PubMed]
  4. M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
    [CrossRef]
  5. M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40, 836-846 (2006).
    [CrossRef]
  6. C. Calba, L. Méès, C. Rozé, and T. Girasole, “Ultra-short pulse propagation through a strongly scattering medium: simulation and experiments,” J. Opt. Soc. Am. A 25, 1541-1550 (2008).
    [CrossRef]
  7. C. Calba, C. Rozé, T. Girasole, and L. Méès, “Monte Carlo simulation of the interaction between an ultra short pulse and a dense scattering medium: case of large size particles,” Opt. Commun. 265, 373-382 (2006).
    [CrossRef]
  8. L. Wang, P. P. Ho, F. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769-771 (1991).
    [CrossRef] [PubMed]
  9. M. A. Linne, M. Paciaroni, J. R. Gord, and T. R. Meyer, “Ballistic imaging of the liquid core for a steady jet in crossflow,” Appl. Opt. 44, 6627-6634 (2005).
    [CrossRef] [PubMed]
  10. D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443-454 (1988).
    [CrossRef]
  11. I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, “Time-resolved optical Kerr-effect investigation of CS2/polystyrene mixtures,” J. Chem. Phys. 123(054509), 1-6 (2005).
    [CrossRef]
  12. A. Gnoli, L. Razzani, and M. Righini, “Z-scan measurements using high repetition rate lasers: how to manage thermal effects,” Opt. Express 13, 7976-7981 (2005).
    [CrossRef] [PubMed]
  13. R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
    [CrossRef]
  14. A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167-6174 (2003).
    [CrossRef]

2008 (2)

2006 (3)

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

M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
[CrossRef]

M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40, 836-846 (2006).
[CrossRef]

2005 (3)

2004 (2)

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

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

2003 (1)

A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

1995 (1)

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

1991 (1)

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

1988 (1)

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

Alfano, R. R.

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

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

Baba, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Breisacher, K.

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

Buckup, T.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, “Time-resolved optical Kerr-effect investigation of CS2/polystyrene mixtures,” J. Chem. Phys. 123(054509), 1-6 (2005).
[CrossRef]

Calba, C.

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

Correia, R. R. B.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, “Time-resolved optical Kerr-effect investigation of CS2/polystyrene mixtures,” J. Chem. Phys. 123(054509), 1-6 (2005).
[CrossRef]

Cunha, S. L. S.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, “Time-resolved optical Kerr-effect investigation of CS2/polystyrene mixtures,” J. Chem. Phys. 123(054509), 1-6 (2005).
[CrossRef]

Delpanque, J. P.

M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
[CrossRef]

Dumouchel, C.

C. Dumouchel, “On the experimental investigation of primary atomization of liquid streams,” Exp. Fluids 45, 371-422 (2008).
[CrossRef]

Galland, P. A.

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

Ganeev, R. A.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Girasole, T.

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

Gnoli, A.

Gord, J. R.

Hall, T.

M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40, 836-846 (2006).
[CrossRef]

M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
[CrossRef]

Heisler, I. A.

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, “Time-resolved optical Kerr-effect investigation of CS2/polystyrene mixtures,” J. Chem. Phys. 123(054509), 1-6 (2005).
[CrossRef]

Ho, P. P.

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

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

Ishizawa, N.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Kenney-Wallace, G. A.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

Kuroda, H.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Liang, X.

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

Linne, M.

M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
[CrossRef]

M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40, 836-846 (2006).
[CrossRef]

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

Linne, M. A.

Liou, L.

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

Liu, F.

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

Lotshaw, W. T.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

McMorrow, D.

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

Méès, L.

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

Meyer, T. R.

Paciaroni, M.

M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
[CrossRef]

M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40, 836-846 (2006).
[CrossRef]

M. A. Linne, M. Paciaroni, J. R. Gord, and T. R. Meyer, “Ballistic imaging of the liquid core for a steady jet in crossflow,” Appl. Opt. 44, 6627-6634 (2005).
[CrossRef] [PubMed]

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

Parker, T.

M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
[CrossRef]

M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40, 836-846 (2006).
[CrossRef]

Razzani, L.

Righini, M.

Rozé, C.

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

Ryasnyansky, A. I.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Sakakibara, S.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Samoc, A.

A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

Suzuki, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Turu, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Wang, L.

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

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

Zhang, G.

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

Appl. Opt. (2)

Appl. Phys. B: Photophys. Laser Chem. (1)

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B: Photophys. Laser Chem. 78, 433-438 (2004).
[CrossRef]

Atomization Sprays (1)

M. Paciaroni, T. Hall, J. P. Delpanque, T. Parker, and M. Linne, “Single-shot two-dimensional ballistic imaging of the liquid core in an atomizing spray,” Atomization Sprays 16, 51-59 (2006).
[CrossRef]

Exp. Fluids (2)

M. Linne, M. Paciaroni, T. Hall, and T. Parker, “Ballistic imaging of the near field in a diesel spray,” Exp. Fluids 40, 836-846 (2006).
[CrossRef]

C. Dumouchel, “On the experimental investigation of primary atomization of liquid streams,” Exp. Fluids 45, 371-422 (2008).
[CrossRef]

HTD (Am. Soc. Mech. Eng.) (1)

P. A. Galland, X. Liang, L. Wang, K. Breisacher, L. Liou, P. P. Ho, and R. R. Alfano, “Time-resolved optical imaging of jet sprays and droplets in highly scattering medium,” HTD (Am. Soc. Mech. Eng.) HTD-321, 585-588 (1995).

IEEE J. Quantum Electron. (1)

D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. 24, 443-454 (1988).
[CrossRef]

J. Appl. Phys. (1)

A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167-6174 (2003).
[CrossRef]

J. Chem. Phys. (1)

I. A. Heisler, R. R. B. Correia, T. Buckup, and S. L. S. Cunha, “Time-resolved optical Kerr-effect investigation of CS2/polystyrene mixtures,” J. Chem. Phys. 123(054509), 1-6 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

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

Opt. Express (1)

Science (1)

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

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Figures (15)

Fig. 1
Fig. 1

Time-resolved transmission of a 100 fs light pulse through a glass particle suspension; particle diameter is 1.8 μ m , optical depth is 18.16, collection solid angle = 0.024 ° .

Fig. 2
Fig. 2

Principle of OKE time gating: (a) gate is closed, (b) gate is opened by pump pulse.

Fig. 3
Fig. 3

Schematic diagram of single-color OKE time gate experiment. M1, M2, M3, M4, M5. mirrors; P0, P1, P2: polarizers; ND: neutral density filter; PC: Pockels cell; L1, L2. lenses.

Fig. 4
Fig. 4

Optical Kerr gate time profile (single-color setup at 800 nm ). Symbols correspond to experimental points.

Fig. 5
Fig. 5

Imaging pulse polarization analysis after time gate.

Fig. 6
Fig. 6

Gate efficiency as a function of the pump power.

Fig. 7
Fig. 7

Image field recorded on the camera for different optical system magnification: (a) without the gate, (b) with the gate, for single-color configuration.

Fig. 8
Fig. 8

Spatio-temporal profile of the gate in the single-color configuration. The vertical line at t = 0 corresponds to a Dirac pulse image. The result on the sensor is shown on the right.

Fig. 9
Fig. 9

Temporal profile of the gate. Theoretical curve is computed with an image beam diameter of 40 μ m .

Fig. 10
Fig. 10

(a) Image through crossed polarizers, (b) image through parallel polarizers, (c) radially averaged power spectrum of the 2D Fourier transform of images (a) and (b) normalized to 1 at spatial frequency equal to .

Fig. 11
Fig. 11

MTF (a) and PSF (b) of single-color and two-color configuration.

Fig. 12
Fig. 12

Space-time diagram showing the propagation of pump and image pulses inside the C S 2 cell. Δ t is the delay between the two pulses.

Fig. 13
Fig. 13

Time-gate profile in two-color configuration for cell thickness L = 1 mm . All the curves are normalized to 1.

Fig. 14
Fig. 14

Space–time diagram showing the propagation of pump and image pulses inside the cell. Δ t is the delay between the two pulses.

Fig. 15
Fig. 15

Comparison of noise due to pump scattering of liquid C S 2 toward the camera.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Δ n ( r , t ) = n 2 t I p ( r , t ) exp [ t τ τ 0 ] { 1 exp [ t τ τ r ] } d τ ,
I p ( r , t ) = I p 0 exp [ r 2 r p 2 ] exp [ t 2 τ p 2 ] ,
Δ n ( r , t ) = π n 2 I p 0 τ p 2 exp [ x 2 + y 2 r p 2 ] exp [ τ p 2 4 τ 0 2 t z v p τ 0 ] { erfc [ τ p 2 τ 0 t z v p τ p ] exp [ τ p 2 4 τ r 2 + τ p 2 2 τ 0 τ r t z v p τ r ] erfc [ τ p 2 τ r + τ p 2 τ 0 t z v p τ p ] } ,
v p = c n ( λ 1 ) λ 1 ( d n d λ ) λ 1 = c n g ( λ 1 ) ,
S ( x , y , Δ t ) = t 1 t 2 I i ( x , y , t z e v i ) sin 2 [ Δ Φ ( x , y , z e , t , Δ t ) 2 ] d t ,
Δ Φ ( x , y , z , t , Δ t ) = 2 π λ 1 t v i d t Δ n ( r , t + Δ t ) ,
G ( x , y , t ) = sin 2 [ Δ Φ ( x , y , z e , t , Δ t ) 2 ] ,
I i ( x , y , t z v i ) = I i 0 exp [ r 2 r i 2 ] exp [ ( t z v i ) 2 τ i 2 ] π 2 τ i I i 0 exp [ r 2 r i 2 ] δ ( t z v i ) ,
S ( Δ t ) = π 2 τ i I i 0 A exp [ x 2 + y 2 r i 2 ] sin 2 [ Δ Φ ( x , y , z e , z e v i , Δ t ) 2 ] d A ,
Δ t z = ( 1 v i 1 v p cos θ ) .

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