Ms. Nathalie van Sterkenburg Profile

Nathalie van Sterkenburg

at Amsterdam UMC

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Proceedings Article | 4 March 2019 Presentation

Pathlength distribution of (sub)diffusively reflected light (Conference Presentation)

Dirk Faber, Nathalie van Sterkenburg, Anouk Post, Ton van Leeuwen

Proceedings Volume 10876, 1087608 (2019) https://doi.org/10.1117/12.2507402

KEYWORDS: Reflectivity, Photons, Absorption, Diffusion, Monte Carlo methods, Algorithms, Reflectance spectroscopy, Diagnostics

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The pathlength distribution of reflected photons can be determined from reflectance as a function of absorption coefficient through inverse Laplace transform (LT). We numerically evaluate a method based on Stehfest’s algorithm for inverse LT using exact solutions from diffusion theory. Inverse LT of the steady state reflectance equation matches the time(~pathlength) resolved reflectance equation for the same geometry, provided that the absorption coefficient is excluded from the definition of the diffusion coefficient. Different boundary conditions applied to the same measurement geometry lead to different solutions for steady state reflectance, and we investigate the effect of these changes on the extracted path length distribution. We proceed to validate the method using Monte Carlo simulations in which the reflectance as well as the pathlength of all simulated photons is stored. We confirm that the Stehfest algorithm is susceptible to noise, and introduce modifications to mitigate these effects. Knowledge of the path length distribution may be helpful in drafting models for sub-diffuse reflectance measurements such as Single Fiber Reflectance Spectroscopy, whereas moments of the pathlength distribution (mean and variance) may provide diagnostic information by themselves.

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