**2. Optical properties of the scatterer that influence polarization**

The scattering through soybean oil is the principle mechanism that modifies the initial polarization state of the incident light. The polarization state of light after a single scattering event depends on the direction of scattering and incident polarization state. [26-27] In many turbid media such as tissue, scattering structures have a large variance in size and are distributed or oriented in a complex and sometimes apparently random manner. Because each scattering event can modify the incident polarization state differently, until finally the polarization state is completely randomized. An important exception is when the media consists of organized linear structures, such as birefrengent soybean oil, and then the phase retardation between orthogonal polarization components is proportional to the distance traveled through the birefrengent medium. The phase retardation of the scattering medium is given as.

$$\delta = \frac{2\pi\Delta n\chi}{\lambda} \tag{1}$$

The phase retardation measurement through turbid media is aimed at retrieving useful information from such multiply scattered light. The behavior of light in random media is well-known from the extensive study of wave propagation. Light traveling in a random medium can be classified into three categories, the ballistic, the snake and the diffuse light. The ballistic light either remains unscattered, or undergoes coherent forward scattering in the medium. This light travels undeviated and has the shortest path length in the medium. The snake light is that which undergoes near-forward scattering, and follows path that undulate about the ballistic path.[28] The diffuse photons largely exceed the other two categories in number and undergoes multiple scattering. We considered all three kinds of photons in our study.

A large number of different experiments are possible if one wants to study the polarization dependent scattering properties of turbid media. The probing light may be linearly polarized at various angles, right and left-hand circularly, or elliptically polarized. Light coming from the scattering medium can be analyzed in the same numerous ways. However, only a few measurements are needed to completely characterize the optical properties of any material. The necessary procedure is elegantly demonstrated by the Stokes-vector Mueller matrix approach to polarization and light scattering.
