Abstract

A comprehensive model of optical coherence tomography (OCT) is described that includes the interference effects that produce speckle in images of dense heterogeneous tissue. It is based on the extended Huygens–Fresnel formulation of beam propagation in a turbulent atmosphere, adapted to the analysis of OCT. Incorporated in the model is a fractal description of the size distribution of scatterers in tissue. We demonstrate its application in the simulation of images of tissue volumes containing high-contrast targets embedded in a mixture of two sizes of particles. The simulated images show the degradation of image quality caused by speckle noise, along with the benefits of employing a light source with a short coherence time and an objective lens with a high numerical aperture. Based on model results, an estimate of the maximum probing depth is given in terms of the design variables of an OCT scanner and the optical properties of the tissue.

© 1997 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. A. F. Fercher, K. Mengedoht, W. Werner, “Eye length measurement by interferometry with partially coherent light,” Opt. Lett. 13, 186–188 (1988).
    [CrossRef] [PubMed]
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  4. B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, J. G. Fujimoto, “High resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett. 20, 1486–1488 (1995).
    [CrossRef] [PubMed]
  5. J. M. Schmitt, M. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology 191, 93–98 (1995).
  6. J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
    [CrossRef] [PubMed]
  7. J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
    [CrossRef] [PubMed]
  8. M. J. Yadlowsky, J. M. Schmitt, R. F. Bonner, “Multiple scattering in optical coherence microscopy,” Appl. Opt. 34, 5699–5707 (1995).
    [CrossRef] [PubMed]
  9. Y. T. Pan, R. Birngruber, J. Rosperich, R. Engelhardt, “Low-coherence optical tomography in turbid tissue: theoretical analysis,” Appl. Opt. 34, 6564–6574 (1995).
    [CrossRef] [PubMed]
  10. J. M. Schmitt, A. Knüttel, A. S. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. SPIE1889, 197–211 (1993).
  11. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
    [CrossRef] [PubMed]
  12. A. Knüttel, R. Schork, D. Böcker, “Analytical modeling of spatial resolution curves in turbid media acquired with optical coherence tomography (OCT),” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 258–270 (1996).
  13. H. T. Yura, “Mutual coherence function of a finite cross section beam propagating in a turbulent medium,” Appl. Opt., 11, 1399–1406 (1972).
    [CrossRef] [PubMed]
  14. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
    [CrossRef]
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  17. J. M. Schmitt, G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21, 1310–1312 (1996).
    [CrossRef] [PubMed]
  18. G. Kumar, J. M. Schmitt, “Micro-optical properties of tissue,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. R. Alfano, ed., Proc. SPIE2679, 106–116 (1996).
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    [CrossRef] [PubMed]

1996 (1)

1995 (5)

1994 (2)

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

1993 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1988 (1)

1979 (1)

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

1978 (2)

1972 (1)

1971 (1)

Birngruber, R.

Böcker, D.

A. Knüttel, R. Schork, D. Böcker, “Analytical modeling of spatial resolution curves in turbid media acquired with optical coherence tomography (OCT),” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 258–270 (1996).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 121.

Bonner, R. F.

M. J. Yadlowsky, J. M. Schmitt, R. F. Bonner, “Multiple scattering in optical coherence microscopy,” Appl. Opt. 34, 5699–5707 (1995).
[CrossRef] [PubMed]

J. M. Schmitt, M. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology 191, 93–98 (1995).

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, A. S. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. SPIE1889, 197–211 (1993).

Boppart, S. A.

Bouma, B.

Brezinski, M. E.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Duker, J. S.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

Eckhaus, M. A.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

Engelhardt, R.

Fercher, A. F.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, J. G. Fujimoto, “High resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett. 20, 1486–1488 (1995).
[CrossRef] [PubMed]

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gandjbakhche, A. S.

J. M. Schmitt, A. Knüttel, A. S. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. SPIE1889, 197–211 (1993).

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

B. Bouma, G. J. Tearney, S. A. Boppart, M. R. Hee, M. E. Brezinski, J. G. Fujimoto, “High resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett. 20, 1486–1488 (1995).
[CrossRef] [PubMed]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Horrigan, F. A.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 121.

Ishimaru, A.

A. Ishimaru, “Limitation on image resolution imposed by a random medium,” Appl. Opt. 17, 348–352 (1978).
[CrossRef] [PubMed]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, pp. 448–454.

Izatt, J. A.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

Knüttel, A.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, A. S. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. SPIE1889, 197–211 (1993).

A. Knüttel, R. Schork, D. Böcker, “Analytical modeling of spatial resolution curves in turbid media acquired with optical coherence tomography (OCT),” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 258–270 (1996).

Kumar, G.

J. M. Schmitt, G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21, 1310–1312 (1996).
[CrossRef] [PubMed]

G. Kumar, J. M. Schmitt, “Micro-optical properties of tissue,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. R. Alfano, ed., Proc. SPIE2679, 106–116 (1996).

Lin, C. P.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Lutomirski, R. F.

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1977).

Mengedoht, K.

Owen, G. M.

Pan, Y. T.

Puliafito, C. A.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Reichel, E.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

Rosperich, J.

Schmitt, J. M.

J. M. Schmitt, G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21, 1310–1312 (1996).
[CrossRef] [PubMed]

M. J. Yadlowsky, J. M. Schmitt, R. F. Bonner, “Multiple scattering in optical coherence microscopy,” Appl. Opt. 34, 5699–5707 (1995).
[CrossRef] [PubMed]

J. M. Schmitt, M. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology 191, 93–98 (1995).

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, A. S. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. SPIE1889, 197–211 (1993).

G. Kumar, J. M. Schmitt, “Micro-optical properties of tissue,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. R. Alfano, ed., Proc. SPIE2679, 106–116 (1996).

Schork, R.

A. Knüttel, R. Schork, D. Böcker, “Analytical modeling of spatial resolution curves in turbid media acquired with optical coherence tomography (OCT),” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 258–270 (1996).

Schuman, J. S.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sonnenschein, C. M.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

Werner, W.

Yadlowsky, M.

J. M. Schmitt, M. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology 191, 93–98 (1995).

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

Yadlowsky, M. J.

Yura, H. T.

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

H. T. Yura, “Mutual coherence function of a finite cross section beam propagating in a turbulent medium,” Appl. Opt., 11, 1399–1406 (1972).
[CrossRef] [PubMed]

Appl. Opt. (7)

Dermatology (1)

J. M. Schmitt, M. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology 191, 93–98 (1995).

Opt. Acta (1)

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

Opt. Lett. (4)

Opthalmology (1)

C. A. Puliafito, M. R. Hee, C. P. Lin, E. Reichel, J. S. Schuman, J. S. Duker, J. A. Izatt, E. A. Swanson, J. G. Fujimoto, “Imaging of macular disease with optical coherence tomography,” Opthalmology 120, 217–229 (1995).

Phys. Med. Biol. (1)

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (7)

J. M. Schmitt, A. Knüttel, A. S. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. SPIE1889, 197–211 (1993).

A. Knüttel, R. Schork, D. Böcker, “Analytical modeling of spatial resolution curves in turbid media acquired with optical coherence tomography (OCT),” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 258–270 (1996).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, pp. 448–454.

G. Kumar, J. M. Schmitt, “Micro-optical properties of tissue,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases III: Optical Biopsy, R. R. Alfano, ed., Proc. SPIE2679, 106–116 (1996).

Ref. 16, p. 318.

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1977).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 121.

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