The reduced effective Mueller matrices of forward scattering from birefringent turbid slab media were calculated using a Monte Carlo simulation and were factorized in two dimensions by the Lu–Chipman polar decomposition. For a slab medium with the birefringence axis parallel to the axis, the polarization parameters have second- or fourth-order rotational symmetry. Especially, the absolute value of linear retardance shows a characteristic variation; it becomes maximal at the azimuths of 0° and 180° but minimal at 90° and 270°. These features exactly agree with the measurement results. However, when the birefringence axis is inclined to the slab surfaces, the polarization parameters become non-symmetric with respect to the plane, though they are symmetric or anti-symmetric with respect to the plane. Moreover, as the inclination angle becomes larger than 45°, the fast-axis orientation exhibits new centers of the radial pattern whose position becomes closer to the preexisting center. The photon trajectory in the medium may be approximated by a double scattering model in which the photon penetrates forward into a depth, travels along the radial direction, and propagates forward to the front surface for exiting. The non-symmetry of the polarization parameters and the appearance of the second centers of the radial pattern suggest that the radial traveling of the photon may be oblique forward and that the obliqueness angle becomes smaller as the photon exits at distances farther away from the center.
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