  We study theoretically the polarization state of light in multiple scattering
media in the limit of weak gradients in refractive index. Linearly polarized
photons are randomly rotated due to the Berry phase associated with the
scattering path. For circularly polarized light independent speckle patterns
are found for the two helical states. The statistics of the geometric phase is
related to the writhe distribution of semiflexible polymers such as DNA.
