Abstract

An effective point-spread function (EPSF) for microscopic imaging through turbid media is proposed and calculated. The EPSF incorporates the property of a microscope system as well as the scattering property of a turbid medium. We prove that the image of a thin object embedded in a turbid medium can be expressed by the convolution of the EPSF with an object function. With the help of the convolution relation, image modeling for 5,000,000 incident photons can be approximately 15  times faster than the direct Monte Carlo simulation method for a one-dimensional object and can be at least 2  orders of magnitude faster for a two-dimensional object.

© 1999 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  2. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).
  3. C. F. Bohern and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).
  4. Y. Hasegawa, Y. Yamada, M. Tamura, and Y. Nomura, Appl. Opt. 30, 4515 (1991).
    [CrossRef] [PubMed]
  5. H. Key, E. R. Davis, P. C. Jackson, and P. N. T. Wells, Phys. Med. Biol. 36, 591 (1991).
    [CrossRef] [PubMed]
  6. J. M. Schmitt, A. Knuttel, and M. Yadlowsky, J. Opt. Soc. Am. A 11, 2226 (1994).
    [CrossRef]
  7. J. M. Schmitt and K. Ben-Letaief, J. Opt. Soc. Am. A 13, 952 (1996).
    [CrossRef]
  8. A. Dunn and C. DiMarzio, J. Opt. Soc. Am. A 13, 65 (1996).
    [CrossRef]
  9. X. Gan and M. Gu, Optik 108, 129 (1998).
  10. X. Gan, S. P. Schilders, and M. Gu, Microscopy Microanalysis 3, 494 (1997).
  11. X. Gan, S. P. Schilders, and M. Gu, J. Opt. Soc. Am. A 15, 2025 (1998).
    [CrossRef]
  12. M. Gu, T. Tannous, and C. J. R. Sheppard, Opt. Lett. 21, 312 (1996).
    [CrossRef] [PubMed]
  13. S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 4300 (1998).
    [CrossRef]
  14. S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 5320 (1998).
    [CrossRef]

1998 (4)

X. Gan and M. Gu, Optik 108, 129 (1998).

X. Gan, S. P. Schilders, and M. Gu, J. Opt. Soc. Am. A 15, 2025 (1998).
[CrossRef]

S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 4300 (1998).
[CrossRef]

S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 5320 (1998).
[CrossRef]

1997 (1)

X. Gan, S. P. Schilders, and M. Gu, Microscopy Microanalysis 3, 494 (1997).

1996 (3)

1994 (1)

1991 (2)

Y. Hasegawa, Y. Yamada, M. Tamura, and Y. Nomura, Appl. Opt. 30, 4515 (1991).
[CrossRef] [PubMed]

H. Key, E. R. Davis, P. C. Jackson, and P. N. T. Wells, Phys. Med. Biol. 36, 591 (1991).
[CrossRef] [PubMed]

Ben-Letaief, K.

Bohern, C. F.

C. F. Bohern and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Davis, E. R.

H. Key, E. R. Davis, P. C. Jackson, and P. N. T. Wells, Phys. Med. Biol. 36, 591 (1991).
[CrossRef] [PubMed]

DiMarzio, C.

Dunn, A.

Gan, X.

X. Gan and M. Gu, Optik 108, 129 (1998).

X. Gan, S. P. Schilders, and M. Gu, J. Opt. Soc. Am. A 15, 2025 (1998).
[CrossRef]

S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 4300 (1998).
[CrossRef]

S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 5320 (1998).
[CrossRef]

X. Gan, S. P. Schilders, and M. Gu, Microscopy Microanalysis 3, 494 (1997).

Gu, M.

X. Gan and M. Gu, Optik 108, 129 (1998).

S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 5320 (1998).
[CrossRef]

S. Schilders, X. Gan, and M. Gu, Appl. Opt. 37, 4300 (1998).
[CrossRef]

X. Gan, S. P. Schilders, and M. Gu, J. Opt. Soc. Am. A 15, 2025 (1998).
[CrossRef]

X. Gan, S. P. Schilders, and M. Gu, Microscopy Microanalysis 3, 494 (1997).

M. Gu, T. Tannous, and C. J. R. Sheppard, Opt. Lett. 21, 312 (1996).
[CrossRef] [PubMed]

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

Hasegawa, Y.

Huffman, D. R.

C. F. Bohern and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).

Jackson, P. C.

H. Key, E. R. Davis, P. C. Jackson, and P. N. T. Wells, Phys. Med. Biol. 36, 591 (1991).
[CrossRef] [PubMed]

Key, H.

H. Key, E. R. Davis, P. C. Jackson, and P. N. T. Wells, Phys. Med. Biol. 36, 591 (1991).
[CrossRef] [PubMed]

Knuttel, A.

Nomura, Y.

Schilders, S.

Schilders, S. P.

X. Gan, S. P. Schilders, and M. Gu, J. Opt. Soc. Am. A 15, 2025 (1998).
[CrossRef]

X. Gan, S. P. Schilders, and M. Gu, Microscopy Microanalysis 3, 494 (1997).

Schmitt, J. M.

Sheppard, C. J. R.

Tamura, M.

Tannous, T.

Wells, P. N. T.

H. Key, E. R. Davis, P. C. Jackson, and P. N. T. Wells, Phys. Med. Biol. 36, 591 (1991).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Yadlowsky, M.

Yamada, Y.

Appl. Opt. (3)

J. Opt. Soc. Am. A (4)

Microscopy Microanalysis (1)

X. Gan, S. P. Schilders, and M. Gu, Microscopy Microanalysis 3, 494 (1997).

Opt. Lett. (1)

Optik (1)

X. Gan and M. Gu, Optik 108, 129 (1998).

Phys. Med. Biol. (1)

H. Key, E. R. Davis, P. C. Jackson, and P. N. T. Wells, Phys. Med. Biol. 36, 591 (1991).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980).

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

C. F. Bohern and D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a scanning optical microscope. An EPSF in the focal plane is schematically illustrated. A sample includes a turbid medium and an object.

Fig. 2
Fig. 2

EPSF in the focal plane for (a) different sizes of the confocal pinhole, νd and (b) different values of the optical thickness nNA 0.25,νd=100 μm.

Fig. 3
Fig. 3

Images of a thin circular disk of 20μm diameter NA 0.25,νd: (a) n=0, (b) n=6, (c) n=9, (d) n=12.

Tables (1)

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Table 1 Comparison of Image Resolution and Computational Time in the Convolution Method Presented in this Letter With Those in the Direct Simulation Method (Ref.  2) a

Equations (1)

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Ix,y=-hx,yOx-x,y-ydxdy,

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