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Optical Coherence Tomography: Advanced Modeling

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Handbook of Coherent Domain Optical Methods

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. It is argued that the algorithm may improve interpretation of OCT images. Finally, the Wigner phase-space distribution function is derived in a closed-form solution, and on this basis a novel method of OCT imaging is proposed.

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References to Optical Coherence Tomography: Advanced Modeling

  • 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, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • M. J. Yadlowsky, J. M. Schmitt, and 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 

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

    Article  ADS  Google Scholar 

  • L. S. Dolin, “A theory of optical coherence tomography,” Radiophys. and Quant. Electr. 41, 850–873 (1998).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  • D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and 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 

  • L. Thrane, H. T. Yura, and 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  ADS  Google Scholar 

  • A. Tycho, T. M. Jørgensen, H. T. Yura, and 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 

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

    Google Scholar 

  • B. C. Wilson and 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 

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

    Article  ADS  Google Scholar 

  • L. Thrane, H. T. Yura, and 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 

  • P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, and 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 

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

    Article  ADS  Google Scholar 

  • I. Dror, A. Sandrov, and 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 

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

    Book  Google Scholar 

  • A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE Press, Piscataway, New Jersey, 1997).

    MATH  Google Scholar 

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

    Google Scholar 

  • R. L. Fante, “Wave propagation in random media: A systems approach,” in Progress in Optics XXII, E. Wolf ed. (Elsevier, New York, 1985).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  • S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, “Principles of statistical radiophysics” in Wave Propagation Through Random Media Vol. 4 (Springer, Berlin, 1989).

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  • J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, Singapore, second ed., 1996).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  • H. T. Yura and 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 

  • A. E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986), 626–630.

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • H. T. Yura and 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 

  • L. Thrane, Optical coherence tomography: Modeling and applications (Risø National Laboratory, Denmark; PhD dissertation (2000), ISBN 87-550-2771-7).

    Google Scholar 

  • J. W. Goodman, Statistical Optics (J. Wiley & Sons, New York, 1985).

    Google Scholar 

  • L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astro-Physical J., 93, 70–83 (1941).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  • C. M. Sonnenschein and 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 

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

    Article  Google Scholar 

  • V. V. Tuchin, S. R. Utz, and I. V. Yaroslavsky, “Skin optics: Modeling of light transport and measuring of optical parameters,” in Medical Optical Tomography: Functional Imaging and Monitoring, IS11, G. Mueller, B. Chance, R. Alfano et al. eds. (SPIE Press, Bellingham, Washington, 1993), 234–258.

    Google Scholar 

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

    Google Scholar 

  • A. Tycho and 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • J. M. Schmitt and 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • G. Yao and 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 

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

    Article  ADS  Google Scholar 

  • C. M. Blanca and 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Meth. Prog. Bio. 47, 131–146 (1995).

    Article  Google Scholar 

  • S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model for light propagation in tissue” in Dosimetry of Laser Radiation in Medicine and Biology, PIE Institute Series IS 5 (SPIE Press, Bellingham, Washington, 1998).

    Google Scholar 

  • D. I. Hughes and F. A. Duck, “Automatic attenuation compensation for ultrasonic imaging,” Ultrasound in Med. & Biol. 23, 651–664 (1997).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  • S. A. Prahl, M. J. C. van Gemert, and 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • M. G. Raymer, C. Cheng, D. M. Toloudis, M. Anderson, and M. Beck, “Propagation of Wigner coherence functions in multiple scattering media” in Advances in Optical Imaging and Photon Migration, R. R. Alfano and J. G. Fujimoto eds. (Optical Society of America, Washington, D.C., 1996), 236–238.

    Google Scholar 

  • C.-C. Cheng and 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • A. Wax and 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 

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

    Article  ADS  Google Scholar 

  • H. T. Yura, L. Thrane, and 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  ADS  MathSciNet  Google Scholar 

  • M. Hillery, R. F. O'Connel, M. O. Scully, and E. P. Wigner, “Distribution functions in physics: fundamentals,” Phys. Rep. 106, 121–167 (1984).

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  • M. G. Raymer and C.-C. Cheng, “Propagation of the optical Wigner function in random multiple-scattering media,” Proc. SPIE 3914, 372–380 (2000).

    Article  ADS  Google Scholar 

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Andersen, P.E., Thrane, L., Yura, H.T., Tycho, A., Jørgensen, T.M. (2004). Optical Coherence Tomography: Advanced Modeling. In: Tuchin, V.V. (eds) Handbook of Coherent Domain Optical Methods. Springer, New York, NY. https://doi.org/10.1007/0-387-29989-0_14

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  • DOI: https://doi.org/10.1007/0-387-29989-0_14

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