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Light Transport in Tissue Variable stepsize method The second Monte Carlo method varies the distance $\Delta s$ that the photon is moved each propagation step. The stepsize $\Delta s$ is chosen in such a way that it is the distance at which the photon is either scattered or absorbed. If distances in the tissue have been non-dimensionalized (Section 4.5) so that the mean free path is unity, then the probability density function for $\Delta s$ is $e^{-\Delta s}$. Appendix A shows how a stepsize $\Delta s$ with this probability density function may be generated as a function of a random number $\xi$ uniformly distributed between zero and one $$\Delta s=-\ln\xi$$ (2.8) Figure 2.2: Flowchart for the variable stepsize Monte Carlo technique. Notice that each time through the inner (dashed) loop, the photon is either scattered or absorbed. When $\Delta s$ is chosen in this manner, the photon is forced either to scatter or be absorbed after each propagation step. Given that the photon is either absorbed or scattered, the probability that it is scattered is equal to the ratio of the scattering coefficient to the sum of the absorption and scattering coefficients (the albedo). If $\xi$ is a random number uniformly distributed between zero and one, then the photon is scattered if $$\xi<{\mu_a\over\mu_a+\mu_s}=a.$$ (2.9) Otherwise, the photon is absorbed. If a photon is scattered then a new photon direction is chosen based on the phase function, otherwise the photon is absorbed and a new photon is launched. This process is described in the flowchart in Figure 2.2.

S. A. Prahl."Light Transport in Tissue," PhD thesis, University of Texas at Austin, 1988.