Izvestiya of Saratov University.


ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

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Zimnyakov D. A., Alonova M. V., Yuvchenko S. A., Ushakova E. V. Mathematical Modeling of Lihgt Transfer in Low-Coherence Reflectometry of Random Media. Izvestiya of Sarat. Univ. Physics. , 2018, vol. 18, iss. 1, pp. 4-15. DOI: 10.18500/1817-3020-2018-18-1-4-15

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Mathematical Modeling of Lihgt Transfer in Low-Coherence Reflectometry of Random Media

Zimnyakov Dmitrii Aleksandrovich, Saratov State Technical University named after Yuri Gagarin
Alonova Marina Vasil'evna, Saratov State Technical University named after Yuri Gagarin
Yuvchenko Sergei Alekseevich, Saratov State Technical University named after Yuri Gagarin
Ushakova Ekaterina Vladimirovna, Saratov State Technical University named after Yuri Gagarin

Background and Objectives: The mathematical model of stochastic interference of spectrally selected fluorescence radiation in multiple scattering random media is considered. The expressions for the normalized second- and third-order moments of spatial intensity fluctuations of detected probe light are derived. The developed model establishes the relationships between the normalized second- and third-order statistical moments of the intensity fluctuations of detected probe light and the probability density function of the pathlength differences of fluorescence radiation in probed media. The obtained theoretical results are compared with the experimental data on the reference-free low-coherence reflectometry of dye-saturated model random media pumped with a continuous-wave laser radiation. Materials and Methods: The discrete scattering model is applied to derive the basic relationships between the normalized statistical moments of intensity fluctuations and the probability density function of the pathlength differences. The Monte-Carlo technique is applied to obtain the pathlength distributions in probed media for used illumination and detection conditions. The experimental data used for verification of the developed model are obtained using model scattering systems on the base of densely packed silica grains, which are saturated by a water solution of Rhodamine 6G and pumped by continuous-wave laser radiation at the wavelength of 532 nm. Results: The adequacy of the developed mathematical model is confirmed by the obtained experimental data. The universal relationship is established between the integral parameters dependent on the probability density function of the pathlength differences and the coherence function of spectrally selected probe radiation is established. Conclusion: The obtained results can be used as the physical base for the development of novel low-coherence probes for applications in biomedical optics and material science.

  1. Fujimoto J. G., Brezinski M. E., Tearney G. J., Boppart S. A., Bouma B., Hee M. R., Southern J. F., Swanson E. A. Optical biopsy and imaging using optical coherence tomography. Nature Medicine, 1995, vol. 1, no. 9, pp. 970–972. 
  2. Youngquist R. C., Carr S., Davies D. E. N. Optical coherence-domain refl ectometry: a new optical evaluation technique. Optics Letters, 1987, vol. 12, no. 3, pp. 158–160. 
  3. Schmitt J. M., Knüttel A., Bonner R. F. Measurement of optical properties of biological tissues by low-coherence reflectometry. Applied Optics, 1993, vol. 32, no. 30, pp. 6032–6042. 
  4. Webster P. J. L., Yu J. X. Z., Leung B. Y. C., Anderson M. D., Yang V.X.D., Fraser J. M. In situ 24 kHz coherent imaging of morphology change in laser percussion drilling. Optics Letters, 2010, vol. 35, pp. 646–648. 
  5. Walecki W., Wei F., Van P., Lai K., Lee T., Lau S. H., Koo A. Novel low coherence metrology for nondestructive characterization of high-aspect-ratio microfabricated and micromachined structures. Proc. SPIE, 2003, vol. 5343, pp. 55–63. DOI: https://doi.org/10.1117/12.530749
  6. Walecki W. J., Lai K., Souchkov V., Van P., Lau S., Koo A. Novel noncontact thickness metrology for backend manufacturing of wide bandgap light emitting devices. Physica status solidi (c), 2005, vol. 2, no. 3, pp. 984–989. DOI: https://doi.org/10.1002/pssc.200460606
  7. Walecki W., Pravdivtsev A., Santos M., Koo A. Highspeed high-accuracy fi ber optic low-coherence interferometry for in situ grinding and etching process monitoring. Proc. SPIE, 2006, vol. 6293, pp. 62930D. DOI: https://doi.org/10.1117/12.675592 
  8. Wang J., Gao X., Huang W., Wang W., Chen S., Du Sh., Li X., Zhang X. Swept-source optical coherence tomography imaging of macular retinal and choroidal structures in healthy eyes. BMC Ophthalmology, 2015, vol. 15, no. 1, pp. 122. 
  9. Fathipour V., Schmoll T., Bonakdar A., Wheaton S., Mohseni H. Demonstration of Shot-noise-limited Swept Source OCT Without Balanced Detection. Scientifi c Reports, 2017, vol. 7, pp. 1183. 
  10. Ozcan A., Bilenca A., Desjardins A. E., Bouma B. E., Tearney G. J. Speckle reduction in optical coherence tomography images using digital fi ltering. JOSA A, 2007, vol. 24, no. 7, pp. 1901–1910. 
  11. Puvanathasan P., Bizheva K. Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set. Optics Express, 2007, vol. 15, no. 24, pp. 15747–15758. 
  12. Bouma B. E., Iftimia N., Tearney G. J. Speckle reduction in optical coherence tomography by path length encoded angular compounding. Journal of Biomedical Optics, 2003, vol. 8, pp. 260–263. 
  13. Zymnyakov D. A., Sina J. S., Yuvchenko S. A., Isaeva E. A., Chekmasov S. P. Measurement of the transportscattering coeffi cient in random inhomogeneous media using the method of low-coherence refl ectometry. Technical Physics Letters, 2014, vol. 40, iss. 2, pp. 132–134 (in Russian). 
  14. Zimnyakov D. A., Yuvchenko S. A., Asharchuk I. A., Sviridov A. P. Stochastic interference of fl uorescence radiation in random media with large inhomogeneities. Optics Communications, 2017, vol. 387, pp. 121–127. 
  15. Zimnyakov D. A., Yuvchenko S. A., Pavlova M. V., Alonova M. V. Reference-free path length interferometry of random media with the intensity moments analysis. Optics Express, 2017, vol. 25, no. 13, pp. 13953–13972. 
  16. Zimnyakov D. A., Asharchuk I. A., Yuvchenko S. A., Sviridov A. P. Speckle spectroscopy of fl uorescent randomly inhomogeneous media. Quantum Electronics, 2016, vol. 46, no. 11, pp. 1047–1054 (in Russian).
  17. Johnson P. M., Imhof A., Bret B. P., Rivas J. G., Lagendijk A. Time-resolved pulse propagation in a strongly scattering material. Physical Review E., 2003, vol. 68, no. 1, pp. 016604. 
  18. Ishimaru A. Wave propagation and scattering in random media. New York, Academic Press, 1978, vol. 2, pp. 349–351. 
  19. Zimnyakov D. A., Chekmasov S. P., Ushakova O. V., Sviridov A. P., Bagratashvili V. N. Optical clearing and laser light dynamic scattering near the critical point of fl uid in mesoporous materials. Laser Physics Letters, 2013, vol. 10, no. 4, pp. 045601. 
  20. Zimnyakov D. A., Chekmasov S. P., Ushakova O. V., Isaeva E. A., Bagratashvili V. N., Yermolenko S. B. Laser speckle probes of relaxation dynamics in soft porous media saturated by near-critical fl uids. Applied Optics, 2014, vol. 53, no. 10, pp. B12–B21. 
  21. Zimnyakov D. A. On some manifestations of similarity in multiple scattering of coherent light. Waves in Random Media, 2000, vol. 10, no. 4, pp. 417–434. 
  22. Zimnyakov D. A. Similarity effects in multiple scattering of coherent radiation: phenomenology and experiments. Optics and Spectroscopy, 2000, vol. 89, no. 3, pp. 453–462. 
  23. Levenberg K. A method for the solution of certain nonlinear problems in least squares. Quarterly of applied mathematics, 1944, vol. 2, no. 2, pp. 164–168. 
  24. Mandel L., Wolf E. Optical Coherence and Quantum Optics. Cambridge University Press, 1995. 1192 p. 
  25. Novickij P. V., Zograf I. A. Ocenka pogreshnostej rezul’tatov izmerenij [An estimate of measurement data errors]. Leningrad, Jenergoatomizdat, 1991. 304 p. (in Russian). 
  26. Henyey L. G., Greenstein J. L. Diffuse radiation in the galaxy. Astrophysical Journal, 1941, vol. 93, pp. 70–83. 
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