Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling

Lima, Ivan T.; Lima, A.O.; Zweck, J.; Menyuk, Curtis R.

doi:10.1109/lpt.2002.805863

Cited by 14 publications

(9 citation statements)

References 10 publications

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“…This procedure produces the new propagation direction ˆ' u of the photon packet after the first biased scattering. Then the scattered photon packet is associated with a quantity that is defined as the likelihood ratio in the importance sampling formalism [13][14][15][16]. The likelihood ratio of the photon packet using our probability density function of the biased angle, Eq.…”

Section: Calculation Of Scattering Angle Of the First Backscattering mentioning

confidence: 99%

“…This very low probability of events of interest would require an unacceptably large computational time if standard Monte Carlo simulation were used. Importance Sampling is an advanced statistical method [12] that consists of biasing random events in such a way that the events of interest, which are often rare, appear more often in Monte Carlo simulations [13][14][15][16][17][18][19]. To produce the correct statistical result in Monte Carlo simulation with importance sampling, each biased sample is weighted by the likelihood in which this sample would have been observed in the unbiased simulation.…”

Section: Introductionmentioning

confidence: 99%

“…Importance sampling, tailored to each particular application, has been applied in optical communications [13][14][15][16], confocal microscopy [17], atmospheric optics [18] diffuse optical tomography (DOT) [11] and TD-OCT [5]. In the applications involving Monte Carlo simulation of light transport in three-dimensional space, one limitation that we addressed is the statistical bias that increases with depth as the photons are preferentially scattered in the backward direction by importance sampling based implementations.…”

Section: Introductionmentioning

confidence: 99%

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Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography

Lima¹,

Kalra²,

Sherif³

2011

Biomed. Opt. Express

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Abstract:We developed an importance sampling based method that significantly speeds up the calculation of the diffusive reflectance due to ballistic and to quasi-ballistic components of photons scattered in turbid media: Class I diffusive reflectance. These components of scattered photons make up the signal in optical coherence tomography (OCT) imaging. We show that the use of this method reduces the computation time of this diffusive reflectance in time-domain OCT by up to three orders of magnitude when compared with standard Monte Carlo simulation. Our method does not produce a systematic bias in the statistical result that is typically observed in existing methods to speed up Monte Carlo simulations of light transport in tissue. This fast Monte Carlo calculation of the Class I diffusive reflectance can be used as a tool to further study the physical process governing OCT signals, e.g., obtain the statistics of the depth-scan, including the effects of multiple scattering of light, in OCT. This is an important prerequisite to future research to increase penetration depth and to improve image extraction in OCT. Med. Phys. 10(6), 824-830 (1983). 9. 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). 10. N. G. Chen and J. Bai, "Estimation of quasi-straightforward propagating light in tissues," Phys. Med. Biol. 44(7), 1669-1676 (1999). 11. N. Chen, "Controlled Monte Carlo method for light propagation in tissue of semi-infinite geometry," Appl. Opt.46(10), 1597-1603 (2007

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Section: Calculation Of Scattering Angle Of the First Backscattering mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography

Lima¹,

Kalra²,

Sherif³

2011

Biomed. Opt. Express

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“…Thus, the values of play the role of the components of the random vector in (12). Specifically, we pick from the following pdf [24]: (17) which biases toward 1 when is positive, and corresponds to standard Monte Carlo simulations in the limit . The likelihood ratio for each value of that is obtained from the biasing pdf in (17) is given by (18) Since the values of are independent random variables, the likelihood ratio for a biased realization of the fiber PMD is equal to the product of the likelihood ratios for each of its biased angles (19) where is the amount of bias used in the th distribution, and is for the th section of the th sample obtained from the th distribution.…”

Section: Importance Sampling Biasing the Dgdmentioning

confidence: 99%

A Comparative Study of Single-Section Polarization-Mode Dispersion Compensators

Lima

Biondini

et al. 2004

J. Lightwave Technol.

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Abstract-This paper shows how to use multiple importance sampling to study the performance of polarization-mode dispersion (PMD) compensators with a single differential group delay (DGD) element. We compute the eye opening penalty margin for compensated and uncompensated systems with outage probabilities of 10 5 or less with a fraction of the computational cost required by standard Monte Carlo methods. This paper shows that the performance of an optimized compensator with a fixed DGD element is comparable to that of a compensator with a variable DGD element. It also shows that the optimal value of the DGD compensator is two to three times larger than the mean DGD of the transmission line averaged over fiber realizations. This technique can be applied to the optimization of any PMD compensator whose dominant sources of residual penalty are both the DGD and the length of the frequency derivative of the polarization-dispersion vector.

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“…Therefore, although there are important situations in which both the signal and the noise may become depolarized, the assumption used in this paper that the signal is polarized is reasonable, since it holds for an important class of experimental systems. The formula for the factor presented here can be used in combination with reduced models of the transmission line to quantify how the performance of a system depends on the combined effects of PMD, PDL, PDG and the gain saturation of optical amplifiers [15], [18]. In particular, in [17], the expression for the factor that was derived in this paper was used, together with the reduced Stokes' model of the polarization effects [15], to model the performance of a dispersion-managed soliton optical fiber recirculating loop.…”

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confidence: 99%

A receiver model for optical fiber communication systems with arbitrarily polarized noise

Lima

Sun³

et al. 2005

J. Lightwave Technol.

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Abstract-The authors have derived a receiver model that provides an explicit relationship between the factor and the optical signal-to-noise ratio (OSNR) in optical fiber communication systems for arbitrary pulse shapes, realistic receiver filters, and arbitrarily polarized noise. It is shown how the system performance depends on both the degree of polarization of the noise and the angle between the Stokes' vectors of the signal and the noise. The results demonstrate that the relationship between the OSNR and the factor is not unique when the noise is partially polarized. This paper defines the enhancement factor and three other parameters that explicitly quantify the relative performance of different modulation formats in a receiver. The theoretical and experimental results show that the performance of the return-to-zero format is less sensitive to variations in the receiver characteristics than is the performance of the nonreturn-to-zero format. Finally, a validation of the formula is presented for computing the factor from the OSNR and the Stokes vectors of the signal and the noise by comparison with both experiments and Monte Carlo simulations.

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Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling

Cited by 14 publications

References 10 publications

Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography

Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography

A Comparative Study of Single-Section Polarization-Mode Dispersion Compensators

A receiver model for optical fiber communication systems with arbitrarily polarized noise

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