Approximate analytical effective phase function obtained for a thin slab geometry

- Analytical approaches of effective phase function for turbid media are considered.
- An approximate effective phase function is proposed for a thin slab.
- The approximate function has been validated against Monte Carlo simulations.
- The optical anisotropy can be retrieved for an optical thickness smaller than 2.
- Application on experimental phase functions for diffusing and biological tissues.

The reflection and transmission of light from a slab containing a turbid medium provide a scattering effective phase function from which the true optical anisotropy factor may not be always easily retrieved. From the statistical Poissonian theory and thanks to approximations about the optical path related to the first scattering events, a simplified relationship is established between angular phase function and effective phase function. Therefore, with a modified Gegenbauer or a Two-Terms Henyey-Greenstein phase function, some adjustable analytic functions are proposed in order to fit the measurements linked to the true effective phase function. An efficiency of the approximate analytical function is proved, thanks to the light modelling by Monte Carlo method, for optical thickness lower or equal to 2. This is confirmed by comparisons of the anisotropy retrieval with other methods. Concerning applications, several fits were made on experimental effective phase functions corresponding to goniometric measurements from usual diffusing materials and biological tissues.