Abstract

The method of Fourier optics is applied to the problem of time-gated imaging through scattering media. To adapt the problem to this treatment, appropriate alterations are made: The continuous medium is replaced by a cascade of thin scatterers, and a spatial filtering process is substituted for the conventional gating processes. Closed-form solutions are derived.

© 2002 Optical Society of America

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References

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  1. R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
    [CrossRef]
  2. H. J. Caulfield, Alabama A and M University Research Institute, P.O. Box 313, Normal, Alabama 35752-0313 (personal communication, May2001).
  3. E. Leith, B. Hoover, S. Grannell, K. Mills, H. Chen, D. Dilworth, “Realization of time gating by use of spatial filtering,” Appl. Opt. 38, 1370–1376 (1999).
    [CrossRef]
  4. K. D. Mills, L. Deslauriers, D. S. Dilworth, S. M. Grannell, B. G. Hoover, B. D. Athey, E. N. Leith, “Investigation of ultrafast time gating by spatial filtering,” Appl. Opt. 40, 2282–2289 (2001).
    [CrossRef]
  5. Y. Chen, H. Chen, D. Dilworth, E. Leith, J. Lopez, M. Shih, P.-C. Sun, G. Vossler, “Evaluation of holographic methods for imaging through biological tissue,” Appl. Opt. 32, 4330–4336 (1993).
    [CrossRef] [PubMed]
  6. J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
    [CrossRef]

2001

1999

1996

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

1993

1975

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

Alferness, R.

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

Athey, B. D.

Bashkanski, M.

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Battle, P. R.

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Caulfield, H. J.

H. J. Caulfield, Alabama A and M University Research Institute, P.O. Box 313, Normal, Alabama 35752-0313 (personal communication, May2001).

Chen, H.

Chen, Y.

Deslauriers, L.

Dilworth, D.

Dilworth, D. S.

Duncan, M. D.

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Grannell, S.

Grannell, S. M.

Hoover, B.

Hoover, B. G.

Leith, E.

Leith, E. N.

Lopez, J.

Mahon, R.

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Mills, K.

Mills, K. D.

Moon, J. A.

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Reintjes, J.

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Shih, M.

Sun, P.-C.

Vossler, G.

Appl. Opt.

Appl. Phys.

R. Alferness, “Analysis of optical propagation in thick holographic gratings,” Appl. Phys. 7, 29–33 (1975).
[CrossRef]

Phys. Rev. E

J. A. Moon, P. R. Battle, M. Bashkanski, R. Mahon, M. D. Duncan, J. Reintjes, “Achievable spatial resolution of time resolved imaging systems which utilize multiply scattered light,” Phys. Rev. E 53, 1142–1155 (1996).
[CrossRef]

Other

H. J. Caulfield, Alabama A and M University Research Institute, P.O. Box 313, Normal, Alabama 35752-0313 (personal communication, May2001).

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Figures (4)

Fig. 1
Fig. 1

Spatial-filter gating system with discrete scatter plates. (a) Three diffusing plates in tandem, (b) the same plates with 4-F spatial filtering systems between them.

Fig. 2
Fig. 2

Optical system for calculating PSF width.

Fig. 3
Fig. 3

Comparison of curves from Eq. (8) with data generated by computer simulation. Solid curves, simulated data; dashed curves, Eq. 8 plots. The horizontal axis is plotted both in gating time (fs) and in spatial filter aperture size (mm).

Fig. 4
Fig. 4

Comparison of the plot of Eq. (8) with experimental data that we obtained using chicken breast. The stem plots represent experimental data.

Equations (11)

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WT=g1(n)(Ad/F+λF/A),
WT=g1(n)(2 fcλd+1/2 fc).
τ=(x/F)2d/2c=(λfx)2d/2c.
τ=(λfc)2d/2c.
fc=(1/λ)(2cτ/d)1/2.
WT=g1(n)[2(2cτd)1/2+(λ/2)(d/2cτ)1/2].
fc=g2(n)-1/2(2τT/λd)1/2.
WT=g1g2-1/2(8cτTd)1/2+g1g21/2λ(d/8cτT)1/2.
WT=n0.37(8cτTd)1/2+0.17nλ(d/2cτT)1/2.
WT=2(λd)1/2n0.63.
A(x)H(fx)Δθτ,

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