The propagation distance between interactions, $t$, given by Eq. (1), is also affected by the difference in interaction cross-sections. In Eq. (1), the interaction coefficient, $\mu t$, corresponds to the overall interaction cross-section of a material. A larger $\mu t$ corresponds to a larger interaction cross-section, and, in turn, a larger interaction volume. Similar to how Schmitt and Kumar rescaled the total scattering coefficient for the total scattering cross-section,^{18} and how Verkruysse et al. rescaled the absorption and scattering coefficients,^{17} we redefined $\mu t$ as a weighted average of the interaction strengths of the two materials. Thus, the new $\mu t$, $\mu t,total$, has the form Display Formula
$\mu t,total=x\mu t,1+y\mu t,2\mu t,total=x\mu t,1+(1\u2212x)\mu t,2,$(9)
and is used in place of $\mu t$ in Eq. (1).