Virtual Photonics Technology Initiative

References

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Radiative Transport and the Standard Diffusion Approximation (SDA)

[1] M. S. Patterson, B. C. Wilson, D. R. Wyman. The propagation of optical radiation in tissue I. Models of radiation transport and their application. Lasers in Medical Science, 6(2):155-168, 1991. Clear description of the 'metrics' used in radiative transport and provides a clear derivation of the time-invariant standard diffusion/P1 approximation to the radiative transport equation.

[2] A. Kienle and M. S. Patterson. Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite medium. Journal of the Optical Society of America A, 14(1):246-254, 1997. Provides the solutions for steady-state and time-resolved diffuse reflectance within the SDA.

[3] A. Kienle and M. S. Patterson. Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source. Physics in Medicine and Biology, 42(9):1801-1819, 1997. Provides the solutions for the spatially-resolved diffuse reflectance within the SDA for the (temporal) frequency domain. Examines its use for the recovery of optical properties from measurements made a two source-detector separations.

[4] Kienle and M. S. Patterson. Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite medium. Journal Provides the solutions for the spatially-resolved diffuse reflectance within the SDA for the (temporal) frequency domain. Examines its use for the recovery of optical properties from measurements made at two source-detector separations.

[5] Kienle and T. Glanzmann, G. Wagnières, and H. van den Bergh. Investigation of two-layered turbid media with time-resolved reflectance. Applied Optics, 37(28):6852-6862, 1998. Provides the solutions for time-domain spatially-resolved diffuse reflectance within the SDA for a two-layer medium. Examines its use for the recovery of the optical properties of the two layers and the layer thickness.

Higher-Order Approximate Methods for Radiative Transport [6] E. L. Hull and T. H. Foster. Steady-state reflectance spectroscopy in the P3 approximation. Journal of the Optical Society of America A, 18(3):584-599, 2001. Provides a derivation for steady-state, spatially-resolved diffuse reflectance within the P3 approximation to the radiative transport equation.

[7] S. A. Carp, S. A. Prahl, and V. Venugopalan. Radiative transport in the delta-P1 approximation: Accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media. Journal of Biomedical Optics, 9(3):632-647, 2004. Provides derivation for internal fluence rate distributions established by planar and Gaussian beam irradiation of tissue within the delta-P1 approximation to the radiative transport equation.

Conventional Monte Carlo

[8] S. L. Jacques and L. Wang. "Monte Carlo Modeling of Light Transport in Tissues", In Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch and M. J. C van Gemert, Editors, Plenum Press, 1995. A very clear and approachable article describing the elements of a Monte Carlo simulation for radiative transport in tissues.

[9] J. Spanier and E. M. Gelbard. Monte Carlo Principles and Neutron Transport Problems. Addison Wesley Publishing Co., 1969. (Re-issued in 2008 by Dover Publications) Provides a rigorous mathematical framework for formulating stochastic solutions to the radiative transport equation. Although written with a focus on neutron transport, the basics apply equally well to photon transport.

Adaptive Monte Carlo

[10] R. Kong, M. Ambrose and J. Spanier. Efficient, Automated Monte Carlo Methods for Radiation Transport. Journal of Computational Physics, 227(22):9463-9476, 2008. Outlines a new adaptive Monte Carlo strategy that describes how conventional Monte Carlo simulations can be exponentially accelerated.

[11] R. Kong and J. Spanier. A new proof of geometric convergence for general transport problems based on sequential correlated sampling methods. Journal of Computational Physics, 227(23):9762-9777, 2008. Establishes rigorously the geometric convergence of adaptive Monte Carlo algorithms for very general radiative transport problems.

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