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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 2 — Feb. 1, 2011
  • pp: 278–299

Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues

Carole K. Hayakawa, Eric O. Potma, and Vasan Venugopalan  »View Author Affiliations

Biomedical Optics Express, Vol. 2, Issue 2, pp. 278-299 (2011)

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The focal field distribution of tightly focused laser beams in turbid media is sensitive to optical scattering and therefore of direct relevance to image quality in confocal and nonlinear microscopy. A model that considers both the influence of scattering and diffraction on the amplitude and phase of the electric field in focused beam geometries is required to describe these distorted focal fields. We combine an electric field Monte Carlo approach that simulates the electric field propagation in turbid media with an angular-spectrum representation of diffraction theory to analyze the effect of tissue scattering properties on the focal field. In particular, we examine the impact of variations in the scattering coefficient (µs ), single-scattering anisotropy (g), of the turbid medium and the numerical aperture of the focusing lens on the focal volume at various depths. The model predicts a scattering-induced broadening, amplitude loss, and depolarization of the focal field that corroborates experimental results. We find that both the width and the amplitude of the focal field are dictated primarily by µs with little influence from g. In addition, our model confirms that the depolarization rate is small compared to the amplitude loss of the tightly focused field.

© 2011 OSA

OCIS Codes
(170.0180) Medical optics and biotechnology : Microscopy
(260.1960) Physical optics : Diffraction theory
(290.7050) Scattering : Turbid media

ToC Category:
Optics of Tissue and Turbid Media

Original Manuscript: October 11, 2010
Revised Manuscript: December 13, 2010
Manuscript Accepted: December 14, 2010
Published: January 6, 2011

Carole K. Hayakawa, Eric O. Potma, and Vasan Venugopalan, "Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues," Biomed. Opt. Express 2, 278-299 (2011)

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  1. V. Tuchin, Tissue Optics (SPIE Press, 2007).
  2. P. Theer, M. T. Hasan, and W. Denk, “Two-photon imaging to a depth of 1000 µm in living brains by use of a Ti:Al2O3 regenerative amplifier,” Opt. Lett. 28(12), 1022–1024 (2003). [CrossRef] [PubMed]
  3. M. Balu, T. Baldacchini, J. Carter, T. B. Krasieva, R. Zadoyan, and B. J. Tromberg, “Effect of excitation wavelength on penetration depth in nonlinear optical microscopy of turbid media,” J. Biomed. Opt. 14(1), 010508 (2009). [CrossRef] [PubMed]
  4. M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002). [CrossRef] [PubMed]
  5. L. Sherman, J. Y. Ye, O. Albert, and T. B. Norris, “Adaptive correction of depth-induced aberrations in multiphoton scanning microscopy using a deformable mirror,” J. Microsc. 206(1), 65–71 (2002). [CrossRef] [PubMed]
  6. T. M. Nieuwenhuizen, A. Lagendijk, and B. A. van Tiggelen, “Resonant point scatterers in multiple scattering of classical waves,” Phys. Lett. A 169(3), 191–194 (1992). [CrossRef]
  7. A. K. Dunn and R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2(4), 898–905 (1996). [CrossRef]
  8. R. Drezek, A. Dunn, and R. Richards-Kortum, “Light scattering from cells: finite-difference time-domain simulations and goniometric measurements,” Appl. Opt. 38(16), 3651–3661 (1999). [CrossRef] [PubMed]
  9. C. Liu, C. Capjack, and W. Rozmus, “3-D simulation of light scattering from biological cells and cell differentiation,” J. Biomed. Opt. 10(1), 014007 (2005). [CrossRef] [PubMed]
  10. I. R. Çapoglu, A. Taflove, and V. Backman, “Generation of an incident focused light pulse in FDTD,” Opt. Express 16(23), 19208–19220 (2008). [CrossRef] [PubMed]
  11. M. S. Starosta and A. K. Dunn, “Three-dimensional computation of focused beam propagation through multiple biological cells,” Opt. Express 17(15), 12455–12469 (2009). [CrossRef] [PubMed]
  12. A. Ishimaru, Wave Propagation and Scattering in Random Media, Vols. I and II (Academic Press, 1978).
  13. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
  14. A. D. Kim and J. B. Keller, “Light propagation in biological tissue,” J. Opt. Soc. Am. A 20(1), 92–98 (2003). [CrossRef] [PubMed]
  15. G. W. Kattawar and G. N. Plass, “Radiance and polarization of multiple scattered light from haze and clouds,” Appl. Opt. 7(8), 1519–1527 (1968). [CrossRef] [PubMed]
  16. B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983). [CrossRef] [PubMed]
  17. I. Lux, and L. Koblinger, Monte Carlo Particle Transport Methods: Neutron and Photon Calculations (CRC Press, 1991).
  18. X. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: a Monte Carlo study,” J. Biomed. Opt. 7(3), 279–290 (2002). [CrossRef] [PubMed]
  19. J. S. You, C. K. Hayakawa, and V. Venugopalan, “Frequency domain photon migration in the δ- P1 approximation: analysis of ballistic, transport, and diffuse regimes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(2), 021903 (2005). [CrossRef] [PubMed]
  20. J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A 13(5), 952–961 (1996). [CrossRef]
  21. C. M. Blanca and C. Saloma, “Monte carlo analysis of two-photon fluorescence imaging through a scattering medium,” Appl. Opt. 37(34), 8092–8102 (1998). [CrossRef] [PubMed]
  22. 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(13), 2944–2949 (1999). [CrossRef] [PubMed]
  23. L. V. Wang and G. Liang, “Absorption distribution of an optical beam focused into a turbid medium,” Appl. Opt. 38(22), 4951–4958 (1999). [CrossRef] [PubMed]
  24. X. S. Gan and M. Gu, “Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media,” Opt. Lett. 24(11), 741–743 (1999). [CrossRef] [PubMed]
  25. A. K. Dunn, V. P. Wallace, M. Coleno, M. W. Berns, and B. J. Tromberg, “Influence of optical properties on two-photon fluorescence imaging in turbid samples,” Appl. Opt. 39(7), 1194–1201 (2000). [CrossRef] [PubMed]
  26. X. Deng, X. Gan, and M. Gu, “Monte Carlo simulation of multiphoton fluorescence microscopic imaging through inhomogeneous tissuelike turbid media,” J. Biomed. Opt. 8(3), 440–449 (2003). [CrossRef] [PubMed]
  27. X. Deng and M. Gu, “Penetration depth of single-, two-, and three-photon fluorescence microscopic imaging through human cortex structures: Monte Carlo simulation,” Appl. Opt. 42(16), 3321–3329 (2003). [CrossRef] [PubMed]
  28. X. Deng, X. Wang, H. Liu, Z. Zhuang, and Z. Guo, “Simulation study of second-harmonic microscopic imaging signals through tissue-like turbid media,” J. Biomed. Opt. 11(2), 024013 (2006). [CrossRef] [PubMed]
  29. A. Leray, C. Odin, E. Huguet, F. Amblard, and Y. Le Grand, “Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations,” Opt. Commun. 272(1), 269–278 (2007). [CrossRef]
  30. J. M. Schmitt and A. Knuttel, “Model of optical coherence tomography of heterogeneous tissue,” J. Opt. Soc. Am. A 14(6), 1231–1242 (1997). [CrossRef]
  31. 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(10), 3025–3044 (1998). [CrossRef] [PubMed]
  32. 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(31), 6676–6691 (2002). [CrossRef] [PubMed]
  33. G. Xiong, P. Xue, J. Wu, Q. Miao, R. Wang, and L. Ji, “Particle-fixed Monte Carlo model for optical coherence tomography,” Opt. Express 13(6), 2182–2195 (2005). [CrossRef] [PubMed]
  34. D. G. Fischer, S. A. Prahl, and D. D. Duncan, “Monte Carlo modeling of spatial coherence: free space diffraction,” J. Opt. Soc. Am. A 25(10), 2571–2581 (2008). [CrossRef]
  35. V. R. Daria, C. Saloma, and S. Kawata, “Excitation with a focused, pulsed optical beam in scattering media: diffraction effects,” Appl. Opt. 39(28), 5244–5255 (2000). [CrossRef] [PubMed]
  36. M. Xu, “Electric field Monte Carlo simulation of polarized light propagation in turbid media,” Opt. Express 12(26), 6530–6539 (2004). [CrossRef] [PubMed]
  37. K. Phillips, M. Xu, S. K. Gayen, and R. R. Alfano, “Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media,” Opt. Express 13(20), 7954–7969 (2005). [CrossRef] [PubMed]
  38. J. Sawicki, N. Kastor, and M. Xu, “Electric field Monte Carlo simulation of coherent backscattering of polarized light by a turbid medium containing Mie scatterers,” Opt. Express 16(8), 5728–5738 (2008). [CrossRef] [PubMed]
  39. C. K. Hayakawa, V. Venugopalan, V. V. Krishnamachari, and E. O. Potma, “Amplitude and phase of tightly focused laser beams in turbid media,” Phys. Rev. Lett. 103(4), 043903 (2009). [CrossRef] [PubMed]
  40. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems 2: structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A 253(1274), 358–379 (1959). [CrossRef]
  41. L. Novotny, and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006).
  42. C. K. Hayakawa, J. Spanier, F. Bevilacqua, A. K. Dunn, J. S. You, B. J. Tromberg, and V. Venugopalan, “Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues,” Opt. Lett. 26(17), 1335–1337 (2001). [CrossRef] [PubMed]
  43. C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, 1983).
  44. T. L. Troy and S. N. Thennadil, “Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm,” J. Biomed. Opt. 6(2), 167–176 (2001). [CrossRef] [PubMed]
  45. S. L. Jacques, “Skin Optics,” http://omlc.ogi.edu/news/jan98/skinoptics.html .
  46. B. R. A. Nijboer, “The diffraction theory of optical aberrations. Part I: General discussion of the geometrical aberrations,” Physica 10(8), 679–692 (1943). [CrossRef]
  47. T. Wilson and A. R. Carlini, “Aberrations in confocal imaging systems,” J. Microsc. 154, 243–256 (1998).
  48. C. K. Tung, Y. Sun, W. Lo, S. J. Lin, S. H. Jee, and C. Y. Dong, “Effects of objective numerical apertures on achievable imaging depths in multiphoton microscopy,” Microsc. Res. Tech. 65(6), 308–314 (2004). [CrossRef] [PubMed]
  49. C. Y. Dong, K. Koenig, and P. So, “Characterizing point spread functions of two-photon fluorescence microscopy in turbid medium,” J. Biomed. Opt. 8(3), 450–459 (2003). [CrossRef] [PubMed]
  50. N. Ghosh, H. S. Patel, and P. K. Gupta, “Depolarization of light in tissue phantoms - effect of a distribution in the size of scatterers,” Opt. Express 11(18), 2198–2205 (2003). [CrossRef] [PubMed]

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