Monte Carlo study of diffuse reflectance at source–detector separations close to one transport mean free path

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Abstract
The spatially resolved reflectance of turbid media is studied at short source–detector separations (approximately one transport mean free path) with Monte Carlo simulations. For such distances we found that the first and second moments of the phase function play a significant role in the reflectance curve, whereas the effect of higher-order moments is weak. Second-order similarity relations are tested and are found efficient at reducing the number of relevant parameters necessary to predict the reflectance. Indeed, only the four following parameters are necessary: the refractive index, the absorption coefficient, the reduced scattering coefficient, and a phase function parameter γ that depends on the first and second moments of the phase function. For media of known γ, the absorption and reduced scattering coefficients can be determined from the intensity and the slope of the log of the reflectance, measured at a single distance. Other empirical properties of the reflectance are derived from the simulations, using short-distance measurements, which provide clues for determining the scattering and absorption properties. In particular, the slope of the square root of the reflectance does not depend on the absorption coefficient but depends on both the reduced scattering coefficient and the phase function parameter γ.