Abstract

An electric field Monte Carlo (EMC) simulation directly traces the complex electric field vectors in multiple scattering and estimates the electric field in a preferred direction. The full vectorial nature of EMC makes it a powerful and flexible tool to simulate the coherence and polarization phenomena of light. As a numerical method, EMC needs to launch a large number of photons to achieve an accurate result, making it time-consuming. Previously, EMC did not account for the beam size. Because of the stochastic character of the instantaneous electric field in the simulation, the convolution method alone is unsuitable for the Monte Carlo simulation of photon energy for a beam with a finite size. It is necessary to launch photons from all possible locations to simulate a finite-size beam, which results in a significant increase in the computational burden. In order to accelerate the simulation, a parallel implementation of the electric field Monte Carlo simulation based on the compute unified device architecture (CUDA) running on a graphics processing unit (GPU) is presented in this paper. Our program, which is optimized for Fermi architecture, is able to simulate the coherence phenomenon of a finite-size beam normally incident on turbid media. A maximum speedup of over 370x is achieved with a GTX480 GPU, compared with that obtained using an Intel i3-2120 CPU.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1999), Vol.1.
  2. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser speckle and related phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.
  3. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, Englewood, Colorado, 2007).
  4. 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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
    [CrossRef] [PubMed]
  5. 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]
  6. L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biomed.47(2), 131–146 (1995).
    [CrossRef]
  7. 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]
  8. S. Bartel and A. H. Hielscher, “Monte Carlo simulations of the diffuse backscattering Mueller matrix for highly scattering media,” Appl. Opt.39(10), 1580–1588 (2000).
    [CrossRef] [PubMed]
  9. M. Xu, “Electric field Monte Carlo simulation of polarized light propagation in turbid media,” Opt. Express12(26), 6530–6539 (2004).
    [CrossRef] [PubMed]
  10. S. Moon, D. Kim, and E. Sim, “Monte Carlo study of coherent diffuse photon transport in a homogeneous turbid medium: a degree-of-coherence based approach,” Appl. Opt.47(3), 336–345 (2008).
    [CrossRef] [PubMed]
  11. 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. Express16(8), 5728–5738 (2008).
    [CrossRef] [PubMed]
  12. M. Xu and R. R. Alfano, “Random walk of polarized light in turbid media,” Phys. Rev. Lett.95(21), 213901 (2005).
    [CrossRef] [PubMed]
  13. M. Xu and R. R. Alfano, “Circular polarization memory of light,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(6), 065601 (2005).
    [CrossRef] [PubMed]
  14. K. G. Phillips, M. Xu, S. Gayen, and R. Alfano, “Time-resolved ring structure of circularly polarized beams backscattered from forward scattering media,” Opt. Express13(20), 7954–7969 (2005).
    [CrossRef] [PubMed]
  15. R. Liao, H. Zhu, Y. Huang, and J. Lv, “Monte Carlo modelling of OCT with finite-size-spot photon beam,” Chin. Opt. Lett.3, S346–S347 (2005).
  16. 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]
  17. M. Šormaz and P. Jenny, “Contrast improvement by selecting ballistic-photons using polarization gating,” Opt. Express18(23), 23746–23755 (2010).
    [CrossRef] [PubMed]
  18. C. K. Hayakawa, E. O. Potma, and V. Venugopalan, “Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues,” Biomed. Opt. Express2(2), 278–290 (2011).
    [CrossRef] [PubMed]
  19. J. Von Neumann, “Various techniques used in connection with random digits,” J. Res. Natl. Bur. Stand.5, 36–38 (1951).
  20. E. Alerstam, W. C. Y. Lo, T. D. Han, J. Rose, S. Andersson-Engels, and L. Lilge, “Next-generation acceleration and code optimization for light transport in turbid media using GPUs,” Biomed. Opt. Express1(2), 658–675 (2010).
    [CrossRef] [PubMed]
  21. G. Marsaglia and A. Zaman, “A new class of random number generators,” Ann. Appl. Probab.1(3), 462–480 (1991).
    [CrossRef]
  22. Nvidia Corporation, “CUDA programming guide 4.2,” (2012).
  23. G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun.282(18), 3693–3700 (2009).
    [CrossRef]
  24. D. D. Duncan and S. J. Kirkpatrick, “The copula: a tool for simulating speckle dynamics,” J. Opt. Soc. Am. A25(1), 231–237 (2008).
    [CrossRef] [PubMed]

2011 (1)

2010 (2)

2009 (2)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun.282(18), 3693–3700 (2009).
[CrossRef]

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]

2008 (3)

2005 (4)

2004 (1)

2000 (1)

1999 (1)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biomed.47(2), 131–146 (1995).
[CrossRef]

1991 (2)

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

G. Marsaglia and A. Zaman, “A new class of random number generators,” Ann. Appl. Probab.1(3), 462–480 (1991).
[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(6), 824–830 (1983).
[CrossRef] [PubMed]

1951 (1)

J. Von Neumann, “Various techniques used in connection with random digits,” J. Res. Natl. Bur. Stand.5, 36–38 (1951).

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(6), 824–830 (1983).
[CrossRef] [PubMed]

Alerstam, E.

Alfano, R.

Alfano, R. R.

M. Xu and R. R. Alfano, “Circular polarization memory of light,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(6), 065601 (2005).
[CrossRef] [PubMed]

M. Xu and R. R. Alfano, “Random walk of polarized light in turbid media,” Phys. Rev. Lett.95(21), 213901 (2005).
[CrossRef] [PubMed]

Andersson-Engels, S.

Arizaga, R.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun.282(18), 3693–3700 (2009).
[CrossRef]

Bartel, S.

Chang, W.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Drezek, R.

Duncan, D. D.

Dunn, A.

et,

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Flotte, T.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Gayen, S.

Gregory, K.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Han, T. D.

Hayakawa, C. K.

C. K. Hayakawa, E. O. Potma, and V. Venugopalan, “Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues,” Biomed. Opt. Express2(2), 278–290 (2011).
[CrossRef] [PubMed]

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]

Hee, M. R.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hielscher, A. H.

Huang, D.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, Y.

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. Biomed.47(2), 131–146 (1995).
[CrossRef]

Jenny, P.

Kastor, N.

Kim, D.

Kirkpatrick, S. J.

Krishnamachari, V. V.

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]

Liao, R.

Lilge, L.

Lin, C. P.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Lo, W. C. Y.

Lv, J.

Marsaglia, G.

G. Marsaglia and A. Zaman, “A new class of random number generators,” Ann. Appl. Probab.1(3), 462–480 (1991).
[CrossRef]

Moon, S.

Phillips, K. G.

Potma, E. O.

C. K. Hayakawa, E. O. Potma, and V. Venugopalan, “Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues,” Biomed. Opt. Express2(2), 278–290 (2011).
[CrossRef] [PubMed]

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]

Puliafito, C. A.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Rabal, H.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun.282(18), 3693–3700 (2009).
[CrossRef]

Richards-Kortum, R.

Rose, J.

Sawicki, J.

Schuman, J. S.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Sendra, G.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun.282(18), 3693–3700 (2009).
[CrossRef]

Sim, E.

Šormaz, M.

Stinson, W. G.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

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 et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Trivi, M.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun.282(18), 3693–3700 (2009).
[CrossRef]

Venugopalan, V.

C. K. Hayakawa, E. O. Potma, and V. Venugopalan, “Electric field Monte Carlo simulations of focal field distributions produced by tightly focused laser beams in tissues,” Biomed. Opt. Express2(2), 278–290 (2011).
[CrossRef] [PubMed]

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]

Von Neumann, J.

J. Von Neumann, “Various techniques used in connection with random digits,” J. Res. Natl. Bur. Stand.5, 36–38 (1951).

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biomed.47(2), 131–146 (1995).
[CrossRef]

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(6), 824–830 (1983).
[CrossRef] [PubMed]

Xu, M.

Zaman, A.

G. Marsaglia and A. Zaman, “A new class of random number generators,” Ann. Appl. Probab.1(3), 462–480 (1991).
[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. Biomed.47(2), 131–146 (1995).
[CrossRef]

Zhu, H.

Ann. Appl. Probab. (1)

G. Marsaglia and A. Zaman, “A new class of random number generators,” Ann. Appl. Probab.1(3), 462–480 (1991).
[CrossRef]

Appl. Opt. (3)

Biomed. Opt. Express (2)

Chin. Opt. Lett. (1)

Comput. Meth. Prog. Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML–Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Meth. Prog. Biomed.47(2), 131–146 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Res. Natl. Bur. Stand. (1)

J. Von Neumann, “Various techniques used in connection with random digits,” J. Res. Natl. Bur. Stand.5, 36–38 (1951).

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(6), 824–830 (1983).
[CrossRef] [PubMed]

Opt. Commun. (1)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun.282(18), 3693–3700 (2009).
[CrossRef]

Opt. Express (4)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Xu and R. R. Alfano, “Circular polarization memory of light,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(6), 065601 (2005).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

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]

M. Xu and R. R. Alfano, “Random walk of polarized light in turbid media,” Phys. Rev. Lett.95(21), 213901 (2005).
[CrossRef] [PubMed]

Science (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, and et, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Other (4)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1999), Vol.1.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser speckle and related phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, Englewood, Colorado, 2007).

Nvidia Corporation, “CUDA programming guide 4.2,” (2012).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Block diagram of the simulation process.

Fig. 2
Fig. 2

Schematic diagram of memory access. The eight adjacent SPs access the contiguous global memory. Note that the 64 byte gaps in global memory are filled.

Fig. 3
Fig. 3

(a) The exact backscattering light intensity in the x-axis direction spatial distribution is recorded with an infinitely narrow beam incident on the turbid medium. 100,000 simulations are executed to obtain 100,000 images. (b) The probability density function of the real part of the normalized Ex calculated by CUDAEMC, which obeys the Gaussian distribution. (c)(d) The probability density functions of the normalized light intensity in the x-direction at different points of the images calculated from the results of EMC and CUDAEMC, which obey a negative exponent distribution. The parameters of the slab are given in the text

Fig. 4
Fig. 4

(a) (d) The means and standard error of light intensity in the x-direction Ix calculated by CUDAEMC. (b)(e) Relative error of mean and standard deviation of light intensity between CUDAEMC and EMC. (c)(f) Relative error of mean and standard deviation of light intensity between two runs of EMC. The side length of each figure is 20 l s with a resolution of 100 × 100

Fig. 5
Fig. 5

(a) (b) The instantaneous and average light intensity in x-axis direction. (c) The probability density functions of normalized light intensity in x-direction. (d) The average light intensity approximately follows two-dimensional Gaussian distribution. (e)(f) The cross section of the distribution of light intensity. The side lengths of (a) and (b) are both 20 l s with a resolution of 1000 × 1000

Fig. 6
Fig. 6

(a) Mueller matrix obtained by CUDAEMC. (b) The relative error of the Mueller matrix M11 between CUDAEMC and EMC. (c) The relative error of Mueller matrix M11 between two EMC results. The parameters of the slab are given in the text. The side length of each figure is 20 l s with a resolution of 200 × 200

Fig. 7
Fig. 7

Simulation time with and without memory copying for different detection grid side lengths.

Tables (1)

Tables Icon

Table 1 Performance Comparison of Programs

Equations (6)

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

( E n E n )=L(θ,φ)( E n1 E n1 )
L(θ,φ)= [ F(θ,φ) ] 1/2 ( S 2 cosφ S 2 sinφ S 1 sinφ S 1 cosφ )
F(θ,φ)=(| S 2 | 2 cos 2 φ+| S 1 | 2 sin 2 φ)| E | 2 +(| S 2 | 2 sin 2 φ+| S 1 | 2 cos 2 φ)| E | 2 +2(| S 2 | 2 | S 1 | 2 )cosφsinφRe[ E ( E )*]
p(θ,φ)= F(θ.φ) π x 2 Q sca
p(θ)= 0 2π p(θ,φ) dφ= | S 1 (θ) | 2 +| S 2 (θ) | 2 x 2 Q sca
p(φ|θ)= p(θ,φ) p(θ)

Metrics