Abstract

We show how to efficiently calculate the signal in optical coherence tomography (OCT) systems due to the ballistic photons, the quasi-ballistic photons, and the photons that undergo multiple diffusive scattering using Monte Carlo simulations with importance sampling. This method enables the calculation of these three components of the OCT signal with less than one hundredth of the computational time required by the conventional Monte Carlo method. Therefore, it can be used as a design tool to characterize the performance of OCT systems, and can also be used in the development of novel signal processing techniques that can extend the imaging range of OCT systems. We investigate the parameter dependence of our importance sampling method and we validate it by comparison to an existing method.

© 2012 OSA

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References

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  1. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
    [CrossRef]
  2. C. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, and S. A. Boppart, “Spectroscopic spectral-domain optical coherence microscopy,” Opt. Lett.31(8), 1079–1081 (2006).
    [CrossRef] [PubMed]
  3. G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol.44(9), 2307–2320 (1999).
    [CrossRef] [PubMed]
  4. I. T. Lima, A. Kalra, and S. S. Sherif, “Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography,” Biomed. Opt. Express2(5), 1069–1081 (2011).
    [CrossRef] [PubMed]
  5. G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett.14(3), 310–312 (2002).
    [CrossRef]
  6. I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett.15(1), 45–47 (2003).
    [CrossRef]
  7. I. T. Lima, A. M. Oliveira, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol.22(4), 1023–1032 (2004).
    [CrossRef]
  8. J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A13(5), 952–961 (1996).
    [CrossRef] [PubMed]
  9. H. Iwabuchi, “Efficient Monte Carlo method for radiative transfer modeling,” J. Atmos. Sci.63(9), 2324–2339 (2006).
    [CrossRef]
  10. N. Chen, “Controlled Monte Carlo method for light propagation in tissue of semi-infinite geometry,” Appl. Opt.46(10), 1597–1603 (2007).
    [CrossRef] [PubMed]
  11. M. J. Yadlowsky, J. M. Schmitt, and R. F. Bonner, “Multiple scattering in optical coherence microscopy,” Appl. Opt.34(25), 5699–5707 (1995).
    [CrossRef] [PubMed]
  12. I. T. Lima, Jr., “Advanced Monte Carlo methods applied to optical coherence tomography” (invited), presented at the 2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, Belém, Brazil, 3–6 Nov. 2009.
  13. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun.1(4), 153–156 (1969).
    [CrossRef]
  14. L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed.47(2), 131–146 (1995).
    [CrossRef] [PubMed]
  15. “Monte Carlo simulations,” Oregon Medical Laser Center, accessed Jan. 1, 2009, http://omlc.ogi.edu/software/mc/ .
  16. The Gnu Project, “Gnu Scientific Library,” accessed June 15, 2011, http://www.gnu.org/s/gsl/ .
  17. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).

2011 (1)

2007 (1)

2006 (2)

2004 (1)

2003 (2)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett.15(1), 45–47 (2003).
[CrossRef]

2002 (1)

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett.14(3), 310–312 (2002).
[CrossRef]

1999 (1)

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol.44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

1996 (1)

1995 (2)

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

M. J. Yadlowsky, J. M. Schmitt, and R. F. Bonner, “Multiple scattering in optical coherence microscopy,” Appl. Opt.34(25), 5699–5707 (1995).
[CrossRef] [PubMed]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun.1(4), 153–156 (1969).
[CrossRef]

Ben-Letaief, K.

Biondini, G.

I. T. Lima, A. M. Oliveira, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol.22(4), 1023–1032 (2004).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett.14(3), 310–312 (2002).
[CrossRef]

Bonner, R. F.

Boppart, S. A.

Chen, N.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
[CrossRef]

Iwabuchi, H.

H. Iwabuchi, “Efficient Monte Carlo method for radiative transfer modeling,” J. Atmos. Sci.63(9), 2324–2339 (2006).
[CrossRef]

Jacques, S. L.

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

Kalra, A.

Kath, W. L.

I. T. Lima, A. M. Oliveira, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol.22(4), 1023–1032 (2004).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett.14(3), 310–312 (2002).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
[CrossRef]

Lima, A. O.

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett.15(1), 45–47 (2003).
[CrossRef]

Lima, I. T.

Luo, W.

Menyuk, C. R.

I. T. Lima, A. M. Oliveira, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol.22(4), 1023–1032 (2004).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett.15(1), 45–47 (2003).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett.14(3), 310–312 (2002).
[CrossRef]

Oliveira, A. M.

Ralston, T. S.

Schmitt, J. M.

Sherif, S. S.

Tan, W.

Vinegoni, C.

Wang, L.

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

Wang, L. V.

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol.44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun.1(4), 153–156 (1969).
[CrossRef]

Xu, C.

Yadlowsky, M. J.

Yao, G.

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol.44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

Zheng, L.

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

Zweck, J.

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett.15(1), 45–47 (2003).
[CrossRef]

Appl. Opt. (2)

Biomed. Opt. Express (1)

Comput. Methods Programs Biomed. (1)

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

IEEE Photon. Technol. Lett. (2)

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett.14(3), 310–312 (2002).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett.15(1), 45–47 (2003).
[CrossRef]

J. Atmos. Sci. (1)

H. Iwabuchi, “Efficient Monte Carlo method for radiative transfer modeling,” J. Atmos. Sci.63(9), 2324–2339 (2006).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun.1(4), 153–156 (1969).
[CrossRef]

Opt. Lett. (1)

Phys. Med. Biol. (1)

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol.44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003).
[CrossRef]

Other (4)

I. T. Lima, Jr., “Advanced Monte Carlo methods applied to optical coherence tomography” (invited), presented at the 2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, Belém, Brazil, 3–6 Nov. 2009.

“Monte Carlo simulations,” Oregon Medical Laser Center, accessed Jan. 1, 2009, http://omlc.ogi.edu/software/mc/ .

The Gnu Project, “Gnu Scientific Library,” accessed June 15, 2011, http://www.gnu.org/s/gsl/ .

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1984).

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of a simulation setup similar to [5].

Fig. 2
Fig. 2

The Class I reflectance, shown with thick solid black curve, and the Class II reflectance, shown with thin solid red curve, as a function of the depth for the importance sampling implementation described in Sec. 2 with 108 samples. The pink short dashed curve and the blue long dashed curve are results of 1011 standard Monte Carlo simulations of the Class I reflectance and the Class II reflectance, respectively.

Fig. 3
Fig. 3

The reflectance results shown in Fig. 2 for the depth interval from 640 µm to 680 µm. The error bars shown for every other point were estimated in the same ensemble of simulations.

Fig. 4
Fig. 4

The relative error in the calculation of the reflectance using importance sampling as a function of the bias coefficient a at 400 µm and at 670 µm of depth for p = 0.5.

Fig. 5
Fig. 5

The relative error in the calculation of the reflectance using importance sampling as a function of the probability of additional bias p at 400 µm and at 670 µm of depth for a = 0.9.

Equations (9)

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f HG ( cos θ s )= 1 g 2 2 ( 1+ g 2 2gcos θ s ) 3/2 ,
f B ( cos θ B )={ ( 1 1a a 2 +1 ) 1 a( 1a ) ( 1+ a 2 2acos θ B ) 3/2 ,  cos θ B [0, 1] 0,  otherwise ,
L( cos θ B )= f HG ( cos θ S ) f B ( cos θ B ) = 1 g 2 2a( 1a ) ( 1 1a a 2 +1 ) ( 1+ a 2 2acos θ B 1+ g 2 2gcos θ S ) 3/2 ,
L( cos θ B )= f HG ( cos θ S ) p f B ( cos θ B )+(1p) f HG ( cos θ S ) .
I 1 (z,i)={ 1,    l c >| Δ s i 2 z max |,  r i < d max ,   θ z,i < θ max ,   | Δ s i 2z |<  l c 0,  otherwise
I 2 (z,i)={ 1,   l c <| Δ s i 2 z max |,  r i < d max ,   θ z,i < θ max ,   | Δ s i 2z |< l c    0,  otherwise ,
R 1,2 (z)= 1 N i=1 N I 1 (z,i)L(i)W(i)
σ 1,2 2 (z)= 1 N( N1 ) i=1 N [ I 1 (z,i)L(i)W(i) R 1,2 (z) ] 2 ,
cos θ B,i = 1 2a { a 2 +1 [ u i ( 1 1a 1 a 2 +1 )+ 1 a 2 +1 ] 2 },

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