Skip to main content
SpringerLink
Log in

Optical Coherence Tomography: Advanced Modeling

  • Reference work entry
  • First Online:
Handbook of Coherent-Domain Optical Methods

  • 2600 Accesses

Abstract

Analytical and numerical models for describing and understanding the light propagation in samples imaged by optical coherence tomography (OCT) systems are presented. An analytical model for calculating the OCT signal based on the extended Huygens-Fresnel principle valid both for the single- and multiple-scattering regimes is derived. An advanced Monte Carlo model for calculating the OCT signal is also derived, and the validity of this model is shown through a mathematical proof based on the extended Huygens-Fresnel principle. From the analytical model, an algorithm for enhancing OCT images is developed, the so-called true-reflection algorithm in which the OCT signal may be corrected for the attenuation caused by scattering. The algorithm is verified experimentally and by using the Monte Carlo model as a numerical tissue phantom. Applications of extraction of optical properties from tissue are discussed. Finally, the Wigner phase-space distribution function is derived in a closed-form solution, which may have applications in OCT.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 699.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  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)

    Google Scholar 

  2. 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)

    Article  ADS  Google Scholar 

  3. J.M. Schmitt, A. Knüttel, A.S. Gandjbakhche, R.F. Bonner, Optical characterization of dense tissues using low-coherence interferometry. Proc. SPIE 1889, 197–211 (1993)

    Article  ADS  Google Scholar 

  4. M.J. Yadlowsky, J.M. Schmitt, R.F. Bonner, Multiple scattering in optical coherence microscopy. Appl. Opt. 34, 5699–5707 (1995)

    Article  ADS  Google Scholar 

  5. M.J. Yadlowsky, J.M. Schmitt, R.F. Bonner, Contrast and resolution in the optical coherence microscopy of dense biological tissue. Proc. SPIE 2387, 193–203 (1995)

    Article  ADS  Google Scholar 

  6. Y. Pan, R. Birngruber, R. Engelhardt, Contrast limits of coherence-gated imaging in scattering media. Appl. Opt. 36, 2979–2983 (1997)

    Article  ADS  Google Scholar 

  7. L.S. Dolin, A theory of optical coherence tomography. Radiophys. Quant. Electron. 41, 850–873 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  8. J.M. Schmitt, A. Knüttel, Model of optical coherence tomography of heterogeneous tissue. J. Opt. Soc. Am. A 14, 1231–1242 (1997)

    Article  ADS  Google Scholar 

  9. D.J. Smithies, T. Lindmo, Z. Chen, J.S. Nelson, T.E. Milner, Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation. Phys. Med. Biol. 43, 3025–3044 (1998)

    Article  Google Scholar 

  10. L. Thrane, H.T. Yura, P.E. Andersen, Analysis of optical coherence tomography systems based on the extended Huygens-Fresnel principle. J. Opt. Soc. Am. A 17, 484–490 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  11. I.V. Turchin, E.A. Sergeeva, L.S. Dolin, V.A. Kamensky, N.M. Shakhova, R. Richards-Kortum, Novel algorithm of processing optical coherence tomography images for differentiation of biological tissue pathologies. J. Biomed. Opt. 10, 064024 (2005)

    Article  ADS  Google Scholar 

  12. A. Tycho, T.M. Jørgensen, H.T. Yura, P.E. Andersen, Derivation of a Monte Carlo method for modeling heterodyne detection in optical coherence tomography systems. Appl. Opt. 41, 6676–6691 (2002)

    Article  ADS  Google Scholar 

  13. H. Kahn, T.E. Harris, Estimation of particle transmission by random sampling, in Monte Carlo Methods. National Bureau of Standards Applied Mathematics Series, vol. 12 (U. S. Government Printing Office, Washington, DC, 1951)

    Google Scholar 

  14. B.C. Wilson, G. Adam, A Monte Carlo model for the absorption and flux distributions of light in tissue. Med. Phys. 10, 824–830 (1983)

    Article  Google Scholar 

  15. 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)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Y. Feng, R. Wang, J. Elder, Theoretical model of optical coherence tomography for system optimization and characterization. J. Opt. Soc. Am. A 20, 1792–1803 (2003)

    Article  ADS  Google Scholar 

  18. B. Karamata, M. Laubscher, M. Leutenegger, S. Bourquin, T. Lasser, P. Lambelet, Multiple scattering in optical coherence tomography. I. Investigation and modeling. J. Opt. Soc. Am. A 22, 1369–1379 (2005)

    Google Scholar 

  19. J.W. Goodman, Statistical Optics (Wiley, New York, 1985)

    Google Scholar 

  20. R.G. Frehlich, M.J. Kavaya, Coherent laser radar performance for general atmospheric refractive turbulence. Appl. Opt. 30, 5325–5352 (1991)

    Article  ADS  Google Scholar 

  21. D. Arnush, Underwater light-beam propagation in the small-angle-scattering approximation. J. Opt. Soc. Am. 62, 1109–1111 (1972)

    Article  ADS  Google Scholar 

  22. H.T. Yura, A multiple scattering analysis of the propagation of radiance through the atmosphere, in Proceedings of the Union Radio-Scientifique Internationale Open Symposium, La Baule, 1977, pp. 65–69

    Google Scholar 

  23. H.T. Yura, L. Thrane, P.E. Andersen, Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium. J. Opt. Soc. Am. A 17, 2464–2474 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  24. M.G. Raymer, C. Cheng, D.M. Toloudis, M. Anderson, M. Beck, Propagation of Wigner coherence functions in multiple scattering media, in Advances in Optical Imaging and Photon Migration, vol. 2 of OSA Trends in Optics and Photonics Series, eds. by R.R. Alfano, J.G. Fujimoto (Optical Society of America, Washington, DC, 1996), pp. 236–238; C.-C. Cheng, M.G. Raymer, Long-range saturation of spatial decoherence in wave-field transport in random multiple-scattering media. Phys. Rev. Lett. 82, 4807–4810 (1999); M.G. Raymer, C.-C. Cheng, Propagation of the optical Wigner function in random multiple-scattering media, in Laser-Tissue Interaction XI: Photochemical, Photothermal, and Photomechanical, eds. by D.D. Duncan, J.O. Hollinger, S.L. Jacques. Proc. SPIE 3914, 376–380 (2000)

    Google Scholar 

  25. P.E. Andersen, T.M. Jørgensen, L. Thrane, A. Tycho, H.T. Yura, Modeling light–tissue interaction in optical coherence tomography systems, in Optical Coherence Tomography: Technology and Applications, ed. by W. Drexler, J.G. Fujimoto (Springer, New York, 2008), pp. 73–113 (Chap. 3). ISBN 3540775498

    Google Scholar 

  26. L. Thrane, H.T. Yura, P.E. Andersen, Optical coherence tomography: new analytical model and the shower curtain effect. Proc. SPIE 4001, 202–208 (2000)

    Article  ADS  Google Scholar 

  27. L. Thrane, H.T. Yura, P.E. Andersen, Calculation of the maximum obtainable probing depth of optical coherence tomography in tissue. Proc. SPIE 3915, 2–11 (2000)

    Article  ADS  Google Scholar 

  28. P.E. Andersen, L. Thrane, H.T. Yura, A. Tycho, T.M. Jørgensen, Modeling the optical coherence tomography geometry using the extended Huygens-Fresnel principle and Monte Carlo simulations. Proc. SPIE 3914, 394–406 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. I. Dror, A. Sandrov, N.S. Kopeika, Experimental investigation of the influence of the relative position of the scattering layer on image quality: the shower curtain effect. Appl. Opt. 37, 6495–6499 (1998)

    Article  ADS  Google Scholar 

  31. V.I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961)

    Google Scholar 

  32. A. Ishimaru, Wave Propagation and Scatteringin Random Media (IEEE Press, Piscataway, 1997)

    MATH  Google Scholar 

  33. J. Strohbehn (ed.), Laser Beam Propagation in the Atmosphere (Springer, New York, 1978)

    Google Scholar 

  34. R.L. Fante, Wave propagation in random media: a systems approach, in Progress in Optics XXII, ed. by E. Wolf (Elsevier, New York, 1985)

    Google Scholar 

  35. J.M. Schmitt, G. Kumar, Turbulent nature of refractive-index variations in biological tissue. Opt. Lett. 21, 1310–1312 (1996)

    Article  ADS  Google Scholar 

  36. S.M. Rytov, Y.A. Kravtsov, V.I. Tatarskii, Principles of statistical radiophysics, in Wave Propagation Through Random Media, vol. 4 (Springer, Berlin, 1989)

    Book  Google Scholar 

  37. R.F. Lutomirski, H.T. Yura, Propagation of a finite optical beam in an inhomogeneous medium. Appl. Opt. 10, 1652–1658 (1971)

    Article  ADS  Google Scholar 

  38. Z.I. Feizulin, Y.A. Kravtsov, Expansion of a laser beam in a turbulent medium. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 24, 1351–1355 (1967)

    Google Scholar 

  39. J.W. Goodman, Introduction to Fourier Optics, 2nd edn. (McGraw-Hill, Singapore, 1996)

    Google Scholar 

  40. H.T. Yura, S.G. Hanson, Optical beam wave propagation through complex optical systems. J. Opt. Soc. Am. A 4, 1931–1948 (1987)

    Article  ADS  Google Scholar 

  41. H.T. Yura, S.G. Hanson, Second-order statistics for wave propagation through complex optical systems. J. Opt. Soc. Am. A 6, 564–575 (1989)

    Article  ADS  Google Scholar 

  42. A.E. Siegman, Lasers (University Science, Mill Valley, 1986), pp. 626–630

    Google Scholar 

  43. M.J.C. Van Gemert, S.L. Jacques, H.J.C.M. Sterenborg, W.M. Star, Skin optics. IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989)

    Article  Google Scholar 

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

    Google Scholar 

  45. H.T. Yura, S.G. Hanson, Effects of receiver optics contamination on the performance of laser velocimeter systems. J. Opt. Soc. Am. A 13, 1891–1902 (1996)

    Article  ADS  Google Scholar 

  46. L. Thrane, Optical coherence tomography: modeling and applications, PhD dissertation Risø National Laboratory, Denmark, 2000. ISBN 87-550-2771-7

    Google Scholar 

  47. L.G. Henyey, J.L. Greenstein, Diffuse radiation in the galaxy. Astro-Phys. J. 93, 70–83 (1941)

    Article  ADS  Google Scholar 

  48. S.L. Jacques, C.A. Alter, S.A. Prahl, Angular dependence of He-Ne laser light scattering by human dermis. Lasers Life Sci. 1, 309–333 (1987)

    Google Scholar 

  49. C.M. Sonnenschein, F.A. Horrigan, Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere. Appl. Opt. 10, 1600–1604 (1971)

    Article  ADS  Google Scholar 

  50. D.L. Fried, Optical heterodyne detection of an atmospherically distorted signal wave front. Proc. IEEE 55, 57–67 (1967)

    Article  Google Scholar 

  51. V.V. Tuchin, S.R. Utz, I.V. Yaroslavsky, Skin optics: modeling of light transport and measuring of optical parameters, in Medical Optical Tomography: Functional Imaging and Monitoring, ed. by G. Mueller, B. Chance, R. Alfano et al., vol. IS11 (SPIE Press, Bellingham, 1993), pp. 234–258

    Google Scholar 

  52. V.I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, 1971)

    Google Scholar 

  53. A. Tycho, T.M. Jørgensen, Comment on ‘Excitation with a focused, pulsed optical beam in scattering media: diffraction effects. Appl. Opt. 41, 4709–4711 (2002)

    Article  ADS  Google Scholar 

  54. V.R. Daria, C. Saloma, S. Kawata, Excitation with a focused, pulsed optical beam in scattering media: diffraction effects. Appl. Opt. 39, 5244–5255 (2000)

    Article  ADS  Google Scholar 

  55. J. Schmitt, A. Knüttel, M. Yadlowski, Confocal microscopy in turbid media. J. Opt. Soc. A 11, 2226–2235 (1994)

    Article  ADS  Google Scholar 

  56. J.M. Schmitt, K. Ben-Letaief, Efficient Monte Carlo simulation of confocal microscopy in biological tissue. J. Opt. Soc. Am. A 13, 952–961 (1996)

    Article  ADS  Google Scholar 

  57. C.M. Blanca, C. Saloma, Monte Carlo analysis of two-photon fluorescence imaging through a scattering medium. Appl. Opt. 37, 8092–8102 (1998)

    Article  ADS  Google Scholar 

  58. Y. Pan, R. Birngruber, J. Rosperich, R. Engelhardt, Low-coherence optical tomography in turbid tissue – theoretical analysis. Appl. Opt. 34, 6564–6574 (1995)

    Article  ADS  Google Scholar 

  59. G. Yao, L.V. Wang, Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media. Phys. Med. Biol. 44, 2307–2320 (1999)

    Article  Google Scholar 

  60. Z. Song, K. Dong, X.H. Hu, J.Q. Lu, Monte Carlo simulation of converging laser beams propagating in biological materials. Appl. Opt. 38, 2944–2949 (1999)

    Article  ADS  Google Scholar 

  61. C.M. Blanca, C. Saloma, Efficient analysis of temporal broadening of a pulsed focused Gaussian beam in scattering media. Appl. Opt. 38, 5433–5437 (1999)

    Article  ADS  Google Scholar 

  62. L.V. Wang, G. Liang, Absorption distribution of an optical beam focused into a turbid medium. Appl. Opt. 38, 4951–4958 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  63. A.K. Dunn, C. Smithpeter, A.J. Welch, R. Richards-Kortum, Sources of contrast in confocal reflectance imaging. Appl. Opt. 35, 3441–3446 (1996)

    Article  ADS  Google Scholar 

  64. L.-H. Wang, S.L. Jacques, L.-Q. Zheng, MCML – Monte Carlo modeling of photon transport in multi-layered tissues. Comput. Methods Programs Biomed. 47, 131–146 (1995)

    Article  Google Scholar 

  65. S.A. Prahl, M. Keijzer, S.L. Jacques, A.J. Welch, A Monte Carlo model for light propagation in tissue, in Dosimetry of Laser Radiation in Medicine and Biology, ed. by S.A. Prahl. SPIE Institute Series, vol. IS5 (SPIE Press, Bellingham, 1998)

    Google Scholar 

  66. D.I. Hughes, F.A. Duck, Automatic attenuation compensation for ultrasonic imaging. Ultrasound Med. Biol. 23, 651–664 (1997)

    Article  Google Scholar 

  67. L. Thrane, T.M. Jørgensen, P.E. Andersen, H.T. Yura, True-reflection OCT imaging. Proc. SPIE 4619, 36–42 (2002)

    ADS  Google Scholar 

  68. S.A. Prahl, M.J.C. van Gemert, A.J. Welch, Determining the optical properties of turbid media by using the adding-doubling method. Appl. Opt. 32, 559–568 (1993)

    Article  ADS  Google Scholar 

  69. J.M. Schmitt, S.H. Xiang, K.M. Yung, Speckle in optical coherence tomography. J. Biomed. Opt. 4, 95–105 (1999)

    Article  ADS  Google Scholar 

  70. L. Thrane, M.H. Frosz, A. Tycho, T.M. Jørgensen, H.T. Yura, P.E. Andersen, Extraction of optical scattering parameters and attenuation compensation in optical coherence tomography images of multi-layered tissue structures. Opt. Lett. 29, 1641–1643 (2004)

    Article  ADS  Google Scholar 

  71. G.J. Tearney, S.A. Boppart, B.E. Bouma, M.E. Brezinski, N.J. Weissman, J.F. Southern, J.G. Fujimoto, Scanning single-mode fiber optic catheter-endoscope for optical coherence tomography. Opt. Lett. 21, 543–545 (1996)

    Article  ADS  Google Scholar 

  72. R.O. Esenaliev, K.V. Larin, I.V. Larina, M. Motamedi, Noninvasive monitoring of glucose concentration with optical coherence tomography. Opt. Lett. 26, 992–994 (2001)

    Article  ADS  Google Scholar 

  73. K.V. Larin, T. Akkin, R.O. Esenaliev, M. Motamedi, T.E. Milner, Phase-sensitive optical low-coherence reflectometry for the detection of analyte concentrations. Appl. Opt. 43, 3408–3414 (2004)

    Article  ADS  Google Scholar 

  74. D.J. Faber, M.C.G. Aalders, E.G. Mik, B.A. Hooper, M.J.C. van Gemert, T.G. van Leeuwen, Oxygen saturation-dependent absorption and scattering of blood. Phys. Rev. Lett. 93, 028102-1–028102-4 (2004)

    Article  ADS  Google Scholar 

  75. D.J. Faber, E.G. Mik, M.C.G. Aalders, T.G. van Leeuwen, Toward assessment of blood oxygen saturation by spectroscopic optical coherence tomography. Opt. Lett. 30, 1015–1017 (2005)

    Article  ADS  Google Scholar 

  76. D.J. Faber, T.G. van Leeuwen, Are quantitative attenuation measurements of blood by optical coherence tomography feasible? Opt. Lett. 34, 1435–1437 (2009)

    Article  ADS  Google Scholar 

  77. V.M. Kodach, D.J. Faber, J. van Marle, T.G. van Leeuwen, J. Kalkman, Determination of the scattering anisotropy with optical coherence tomography. Opt. Express 19, 6131–6140 (2011)

    Article  ADS  Google Scholar 

  78. F.J. van der Meer, D.J. Faber, D.M.B. Sassoon, M.C. Aalders, G. Pasterkamp, T.G. van Leeuwen, Localized measurement of optical attenuation coefficients of atherosclerotic plaque constituents by quantitative optical coherence tomography. IEEE Trans. Med. Imaging 24, 1369–1376 (2005)

    Article  Google Scholar 

  79. N.M. Shakhova, V.M. Gelikonov, V.A. Kamensky, R.V. Kuranov, I.V. Turchin, Clinical aspects of the endoscopic optical coherence tomography: a method for improving the diagnostic efficiency. Laser Phys. 12, 617–626 (2002)

    Google Scholar 

  80. D. Levitz, L. Thrane, M.H. Frosz, P.E. Andersen, C.B. Andersen, J. Valanciunaite, J. Swartling, S. Andersson-Engels, P.R. Hansen, Determination of optical scattering properties of highly-scattering media in optical coherence tomography images. Opt. Express 12, 249–259 (2004)

    Article  ADS  Google Scholar 

  81. R. Samatham, S.L. Jacques, P. Campagnola, Optical properties of mutant versus wild-type mouse skin measured by reflectance-mode confocal scanning laser microscopy (rCSLM). J. Biomed. Opt. 13, 041309 (2008)

    Article  ADS  Google Scholar 

  82. A. Knüttel, S. Bonev, W. Knaak, New method for evaluation of in vivo scattering and refractive index properties obtained with optical coherence tomography. J. Biomed. Opt. 9, 265–273 (2004)

    Article  ADS  Google Scholar 

  83. E.P. Wigner, On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)

    Article  ADS  Google Scholar 

  84. S. John, G. Pang, Y. Yang, Optical coherence propagation and imaging in a multiple scattering medium. J. Biomed. Opt. 1, 180–191 (1996)

    Article  ADS  Google Scholar 

  85. A. Wax, J.E. Thomas, Measurement of smoothed Wigner phase-space distributions for small-angle scattering in a turbid medium. J. Opt. Soc. Am. A 15, 1896–1908 (1998)

    Article  ADS  Google Scholar 

  86. C.-C. Cheng, M.G. Raymer, Propagation of transverse optical coherence in random multiple-scattering media. Phys. Rev. A 62, 023811-1–023811-12 (2000)

    ADS  Google Scholar 

  87. M. Hillery, R.F. O’Connel, M.O. Scully, E.P. Wigner, Distribution functions in physics: fundamentals. Phys. Rep. 106, 121–167 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  88. V.A. Banakh, V.L. Mironov, LIDAR in a Turbulent Atmosphere (Artech House, Boston, 1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Photonics Engineering, Technical University of Denmark, Kongens Lyngby, Denmark

    Peter E. Andersen, Lars Thrane, Andreas Tycho & Thomas M. Jørgensen

  2. Electronics and Photonics Laboratory, The Aerospace Corporation, 92957, Los Angeles, CA, 90009, USA

    Harold T. Yura

Authors
  1. Peter E. Andersen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lars Thrane
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Harold T. Yura
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andreas Tycho
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Thomas M. Jørgensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter E. Andersen .

Editor information

Editors and Affiliations

  1. , Chair of Optics and Biophotonics, Saratov State University, Astrakhanskaya str. 83, Saratov, 410012, Russia

    Valery V. Tuchin

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this entry

Cite this entry

Andersen, P.E., Thrane, L., Yura, H.T., Tycho, A., Jørgensen, T.M. (2013). Optical Coherence Tomography: Advanced Modeling. In: Tuchin, V. (eds) Handbook of Coherent-Domain Optical Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5176-1_17

Download citation

Publish with us

Policies and ethics

Search

Navigation