Abstract

Monte Carlo techniques are the gold standard for studying light propagation in turbid media. Traditional Monte Carlo techniques are unable to include wave effects, such as diffraction; thus, these methods are unsuitable for exploring focusing geometries where a significant ballistic component remains at the focal plane. Here, a method is presented for accurately simulating photon propagation at the focal plane, in the context of a traditional Monte Carlo simulation. This is accomplished by propagating ballistic photons along trajectories predicted by Gaussian optics until they undergo an initial scattering event, after which, they are propagated through the medium by a traditional Monte Carlo technique. Solving a known problem by building upon an existing Monte Carlo implementation allows this method to be easily implemented in a wide variety of existing Monte Carlo simulations, greatly improving the accuracy of those models for studying dynamics in a focusing geometry.

© 2015 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  26. V P Kandidov, V O Militsin, A. V. Bykov, and A. V P., “Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media,” Quantum Electron. 36, 1003–1008 (2006).
    [Crossref]
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2014 (5)

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, and V. V. Yakovlev, “Higher order processes in random Raman lasing,” Appl. Phys. A 117, 681–685 (2014).
[Crossref]

B. H. Hokr, V. V. Yakovlev, and M. O. Scully, “Efficient time-dependent Monte Carlo simulations of stimulated raman scattering in a turbid medium,” ACS Photonics 1, 1322–1329 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

F. Cai and S. He, “Electric field Monte Carlo simulation of focused stimulated emission depletion beam, radially and azimuthally polarized beams for in vivo deep bioimaging.” J. Biomed. Opt. 19, 11022 (2014).
[Crossref]

2013 (2)

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

B. H. Hokr and V. V. Yakovlev, “Raman signal enhancement via elastic light scattering,” Opt. Express 21, 11757–11762 (2013).
[Crossref] [PubMed]

2011 (3)

2009 (1)

2007 (1)

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, 269–278 (2007).
[Crossref]

2006 (2)

V P Kandidov, V O Militsin, A. V. Bykov, and A. V P., “Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media,” Quantum Electron. 36, 1003–1008 (2006).
[Crossref]

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, 024013 (2006).
[Crossref]

2005 (1)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (2)

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, 3321–3329 (2003).
[Crossref] [PubMed]

Q. Liu, C. Zhu, and N. Ramanujam, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8, 223–236 (2003).
[Crossref] [PubMed]

2002 (1)

I V Meglinskii, A N Bashkatov, E A Genina, D Yu Churmakov, and V. V. Tuchin, “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quantum Electron. 32, 875–882 (2002).
[Crossref]

1999 (3)

1998 (1)

1996 (2)

J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A, Opt. Image Sci. 13, 952–961 (1996).
[Crossref]

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Physics-Uspekhi 39, 1243–1272 (1996).
[Crossref]

1995 (2)

J. Y. Qu, C. E. MacAulay, S. Lam, and B. Palcic, “Laser-induced fluorescence spectroscopy at endoscopy: tissue optics, Monte Carlo modeling, and in vivo measurements,” Opt. Eng. 34, 3334–3343 (1995).
[Crossref]

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

1983 (1)

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).
[Crossref] [PubMed]

Adam, G.

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).
[Crossref] [PubMed]

Amblard, F.

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, 269–278 (2007).
[Crossref]

Bashkatov, A N

I V Meglinskii, A N Bashkatov, E A Genina, D Yu Churmakov, and V. V. Tuchin, “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quantum Electron. 32, 875–882 (2002).
[Crossref]

Beier, H. T.

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Ben-Letaief, K.

J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A, Opt. Image Sci. 13, 952–961 (1996).
[Crossref]

Bixler, J. N.

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, and V. V. Yakovlev, “Higher order processes in random Raman lasing,” Appl. Phys. A 117, 681–685 (2014).
[Crossref]

Blanca, C. M.

Boas, D. A.

Burden, R. L.

R. L. Burden and J. D. Faires, Numerical Analysis (Brookes/Cole, Boston, MA, 2010), 9th ed.

Bykov, A. V.

V P Kandidov, V O Militsin, A. V. Bykov, and A. V P., “Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media,” Quantum Electron. 36, 1003–1008 (2006).
[Crossref]

Cai, F.

F. Cai and S. He, “Electric field Monte Carlo simulation of focused stimulated emission depletion beam, radially and azimuthally polarized beams for in vivo deep bioimaging.” J. Biomed. Opt. 19, 11022 (2014).
[Crossref]

Cao, H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Chang, R. P. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Clark, C. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Cone, M.

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Dai, H.

K. Welsher, S. P. Sherlock, and H. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. 108, 8943–8948 (2011).
[Crossref] [PubMed]

Deng, X.

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, 024013 (2006).
[Crossref]

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, 3321–3329 (2003).
[Crossref] [PubMed]

Denk, W.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

Denton, M. L.

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

Dong, K.

Doronin, A.

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988), 1st ed.

Everall, N.

Faires, J. D.

R. L. Burden and J. D. Faires, Numerical Analysis (Brookes/Cole, Boston, MA, 2010), 9th ed.

Fang, Q.

Gan, X.

Genina, E A

I V Meglinskii, A N Bashkatov, E A Genina, D Yu Churmakov, and V. V. Tuchin, “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quantum Electron. 32, 875–882 (2002).
[Crossref]

Golovan, L. A.

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Gu, M.

Guo, Z.

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, 024013 (2006).
[Crossref]

Hahn, T.

Hayakawa, C. K.

He, S.

F. Cai and S. He, “Electric field Monte Carlo simulation of focused stimulated emission depletion beam, radially and azimuthally polarized beams for in vivo deep bioimaging.” J. Biomed. Opt. 19, 11022 (2014).
[Crossref]

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

Ho, S. T.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Hokr, B. H.

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

B. H. Hokr, J. N. Bixler, and V. V. Yakovlev, “Higher order processes in random Raman lasing,” Appl. Phys. A 117, 681–685 (2014).
[Crossref]

B. H. Hokr, V. V. Yakovlev, and M. O. Scully, “Efficient time-dependent Monte Carlo simulations of stimulated raman scattering in a turbid medium,” ACS Photonics 1, 1322–1329 (2014).
[Crossref]

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr and V. V. Yakovlev, “Raman signal enhancement via elastic light scattering,” Opt. Express 21, 11757–11762 (2013).
[Crossref] [PubMed]

Horton, N. G.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Hu, X. H.

Huguet, E.

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, 269–278 (2007).
[Crossref]

Jacques, S. L.

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

Kandidov, V P

V P Kandidov, V O Militsin, A. V. Bykov, and A. V P., “Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media,” Quantum Electron. 36, 1003–1008 (2006).
[Crossref]

Kandidov, V. P.

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Physics-Uspekhi 39, 1243–1272 (1996).
[Crossref]

Kobat, D.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Lam, S.

J. Y. Qu, C. E. MacAulay, S. Lam, and B. Palcic, “Laser-induced fluorescence spectroscopy at endoscopy: tissue optics, Monte Carlo modeling, and in vivo measurements,” Opt. Eng. 34, 3334–3343 (1995).
[Crossref]

Le Grand, Y.

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, 269–278 (2007).
[Crossref]

Leray, A.

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, 269–278 (2007).
[Crossref]

Liu, H.

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, 024013 (2006).
[Crossref]

Liu, Q.

Q. Liu, C. Zhu, and N. Ramanujam, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8, 223–236 (2003).
[Crossref] [PubMed]

Lu, J. Q.

MacAulay, C. E.

J. Y. Qu, C. E. MacAulay, S. Lam, and B. Palcic, “Laser-induced fluorescence spectroscopy at endoscopy: tissue optics, Monte Carlo modeling, and in vivo measurements,” Opt. Eng. 34, 3334–3343 (1995).
[Crossref]

Mason, J. D.

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Matousek, P.

Meglinski, I.

Meglinskii, I V

I V Meglinskii, A N Bashkatov, E A Genina, D Yu Churmakov, and V. V. Tuchin, “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quantum Electron. 32, 875–882 (2002).
[Crossref]

Militsin, V O

V P Kandidov, V O Militsin, A. V. Bykov, and A. V P., “Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media,” Quantum Electron. 36, 1003–1008 (2006).
[Crossref]

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988), 1st ed.

Noojin, G. D.

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Odin, C.

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, 269–278 (2007).
[Crossref]

P., A. V

V P Kandidov, V O Militsin, A. V. Bykov, and A. V P., “Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media,” Quantum Electron. 36, 1003–1008 (2006).
[Crossref]

Palcic, B.

J. Y. Qu, C. E. MacAulay, S. Lam, and B. Palcic, “Laser-induced fluorescence spectroscopy at endoscopy: tissue optics, Monte Carlo modeling, and in vivo measurements,” Opt. Eng. 34, 3334–3343 (1995).
[Crossref]

Parker, A. W.

Petrov, G. I.

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Potma, E. O.

Qu, J. Y.

J. Y. Qu, C. E. MacAulay, S. Lam, and B. Palcic, “Laser-induced fluorescence spectroscopy at endoscopy: tissue optics, Monte Carlo modeling, and in vivo measurements,” Opt. Eng. 34, 3334–3343 (1995).
[Crossref]

Ramanujam, N.

Q. Liu, C. Zhu, and N. Ramanujam, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8, 223–236 (2003).
[Crossref] [PubMed]

Rockwell, B. A.

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Saloma, C.

Schaffer, C. B.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Schmitt, J. M.

J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A, Opt. Image Sci. 13, 952–961 (1996).
[Crossref]

Scully, M. O.

B. H. Hokr, V. V. Yakovlev, and M. O. Scully, “Efficient time-dependent Monte Carlo simulations of stimulated raman scattering in a turbid medium,” ACS Photonics 1, 1322–1329 (2014).
[Crossref]

Seelig, E. W.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Sherlock, S. P.

K. Welsher, S. P. Sherlock, and H. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. 108, 8943–8948 (2011).
[Crossref] [PubMed]

Shingledecker, A. D.

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

Song, Z.

Thomas, R. J.

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Towrie, M.

Tuchin, V. V.

I V Meglinskii, A N Bashkatov, E A Genina, D Yu Churmakov, and V. V. Tuchin, “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quantum Electron. 32, 875–882 (2002).
[Crossref]

Venugopalan, V.

Wang, K.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Wang, L.

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

Wang, Q. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Wang, X.

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, 024013 (2006).
[Crossref]

Welsher, K.

K. Welsher, S. P. Sherlock, and H. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. 108, 8943–8948 (2011).
[Crossref] [PubMed]

Wilson, B. C.

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).
[Crossref] [PubMed]

Wise, F. W.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Xu, C.

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Yakovlev, V. V.

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

B. H. Hokr, V. V. Yakovlev, and M. O. Scully, “Efficient time-dependent Monte Carlo simulations of stimulated raman scattering in a turbid medium,” ACS Photonics 1, 1322–1329 (2014).
[Crossref]

B. H. Hokr, J. N. Bixler, and V. V. Yakovlev, “Higher order processes in random Raman lasing,” Appl. Phys. A 117, 681–685 (2014).
[Crossref]

B. H. Hokr and V. V. Yakovlev, “Raman signal enhancement via elastic light scattering,” Opt. Express 21, 11757–11762 (2013).
[Crossref] [PubMed]

Yu Churmakov, D

I V Meglinskii, A N Bashkatov, E A Genina, D Yu Churmakov, and V. V. Tuchin, “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quantum Electron. 32, 875–882 (2002).
[Crossref]

Zhao, Y. G.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Zheng, L.

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

Zhu, C.

Q. Liu, C. Zhu, and N. Ramanujam, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8, 223–236 (2003).
[Crossref] [PubMed]

Zhuang, Z.

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, 024013 (2006).
[Crossref]

ACS Photonics (1)

B. H. Hokr, V. V. Yakovlev, and M. O. Scully, “Efficient time-dependent Monte Carlo simulations of stimulated raman scattering in a turbid medium,” ACS Photonics 1, 1322–1329 (2014).
[Crossref]

Appl. Opt. (3)

Appl. Phys. A (1)

B. H. Hokr, J. N. Bixler, and V. V. Yakovlev, “Higher order processes in random Raman lasing,” Appl. Phys. A 117, 681–685 (2014).
[Crossref]

Appl. Spectrosc. (1)

Biomed. Opt. Express (2)

Comput. Meth. Prog. Bio. (1)

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

J. Biomed. Opt. (4)

J. N. Bixler, B. H. Hokr, M. L. Denton, G. D. Noojin, A. D. Shingledecker, H. T. Beier, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Assessment of tissue heating under tunable near-infrared radiation.” J. Biomed. Opt. 19, 070501 (2014).
[Crossref]

Q. Liu, C. Zhu, and N. Ramanujam, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8, 223–236 (2003).
[Crossref] [PubMed]

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, 024013 (2006).
[Crossref]

F. Cai and S. He, “Electric field Monte Carlo simulation of focused stimulated emission depletion beam, radially and azimuthally polarized beams for in vivo deep bioimaging.” J. Biomed. Opt. 19, 11022 (2014).
[Crossref]

J. Opt. Soc. Am. A, Opt. Image Sci. (1)

J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A, Opt. Image Sci. 13, 952–961 (1996).
[Crossref]

Med. Phys. (1)

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).
[Crossref] [PubMed]

Nat. Commun. (1)

B. H. Hokr, J. N. Bixler, M. Cone, J. D. Mason, H. T. Beier, G. D. Noojin, G. I. Petrov, L. A. Golovan, R. J. Thomas, B. A. Rockwell, and V. V. Yakovlev, “Bright emission from a random Raman laser,” Nat. Commun. 5, 4356 (2014).
[Crossref] [PubMed]

Nat. Methods (1)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

Nat. Photonics (1)

N. G. Horton, K. Wang, D. Kobat, C. G. Clark, F. W. Wise, C. B. Schaffer, and C. Xu, “In vivo three-photon microscopy of subcortical structures within an intact mouse brain,” Nat. Photonics 7, 205–209 (2013).
[Crossref]

Opt. Commun. (1)

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, 269–278 (2007).
[Crossref]

Opt. Eng. (1)

J. Y. Qu, C. E. MacAulay, S. Lam, and B. Palcic, “Laser-induced fluorescence spectroscopy at endoscopy: tissue optics, Monte Carlo modeling, and in vivo measurements,” Opt. Eng. 34, 3334–3343 (1995).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999).
[Crossref]

Physics-Uspekhi (1)

V. P. Kandidov, “Monte Carlo method in nonlinear statistical optics,” Physics-Uspekhi 39, 1243–1272 (1996).
[Crossref]

Proc. Natl. Acad. Sci. (1)

K. Welsher, S. P. Sherlock, and H. Dai, “Deep-tissue anatomical imaging of mice using carbon nanotube fluorophores in the second near-infrared window,” Proc. Natl. Acad. Sci. 108, 8943–8948 (2011).
[Crossref] [PubMed]

Quantum Electron. (2)

I V Meglinskii, A N Bashkatov, E A Genina, D Yu Churmakov, and V. V. Tuchin, “Study of the possibility of increasing the probing depth by the method of reflection confocal microscopy upon immersion clearing of near-surface human skin layers,” Quantum Electron. 32, 875–882 (2002).
[Crossref]

V P Kandidov, V O Militsin, A. V. Bykov, and A. V P., “Application of corpuscular and wave Monte-Carlo methods in optics of dispersive media,” Quantum Electron. 36, 1003–1008 (2006).
[Crossref]

Other (2)

R. L. Burden and J. D. Faires, Numerical Analysis (Brookes/Cole, Boston, MA, 2010), 9th ed.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1988), 1st ed.

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Figures (3)

Fig. 1
Fig. 1 (A) Conceptual diagram of the transformation from collimated space to focusing space. (B) Schematic illustrating the interplay between the wavefront and the direction vector of the photon. The dashed lines represent the trajectories that would occur in a traditional Monte Carlo.
Fig. 2
Fig. 2 Spatial, (A), and temporal, (B), profile at the focus of a 1-ps, 1-μm beam focused with a 25.4-mm focal length lens with scattering turned off in the Monte Carlo simulation. The incident beam was 10.0-mm 1/e2-diameter at the lens. The green lines are Gaussian fits to the data.
Fig. 3
Fig. 3 Spatial, (A) and (C), and temporal, (B) and (D), profiles at the focus of 1 ps, 1 μm beams focused with a 25.4 mm focal length lens through a 1 mm thick index matched sample with the scattering coefficient given. In each case, g = 0.9 and the medium is assumed to have zero absorption. The focal plane coincides with the back plane of the medium in the Monte Carlo simulation. (A) and (B) track the Gaussian trajectories while (C) and (D) use a traditional Monte Carlo approach. Note that the tiny spec in the middle of each panel of (C) is the distribution. The spatial profiles in (A) have been normalized so that the average value of each plot is equal. (C) is scaled by the same factor as those in (A) to illustrate that traditional Monte Carlo dramatically over predicts the focal plane intensity. The scale of the inset in (C) goes from −0.2 μm to 0.2 μm.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

E ( x , y , z ) = E 0 w 0 w ( z ) exp { x 2 + y 2 w ( z ) 2 i [ k ( x 2 + y 2 2 R ( z ) + ( z z f ) ) ζ ( z ) ] } ,
R ( z ) = ( z z f ) [ 1 + ( z R z z f ) 2 ] .
w ( z ) = w 0 1 + ( z z f z R ) 2 ,
r = x , y , z = x z z f x 2 + y 2 + f 2 , y z z f x 2 + y 2 + f 2 , z f + f z z f x 2 + y 2 + f 2 .
v ^ = 1 1 + x 2 + y 2 R ( z ) 2 x R ( z ) , y R ( z ) , 1 .
Δ t = ε ( c n ) min ( 1 | x ¨ | , 1 | y ¨ | , 1 | z ¨ | )
r ¨ = x ¨ , y ¨ , z ¨ = ( c n ) 2 1 [ 1 + T ( z ) 2 ( x 2 + y 2 ) ] 2 z R 2 [ ( z z f ) 2 + z R 2 ] 2 x , y , T ( x ) ( x 2 + y 2 ) .

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