E.2      Interference intensity

To explain the polarization effects, the scalar description of the signal amplitudes is not adequate as it assume a single stationary polarization state that cannot be modified by the travel in the interferometer. We assume a stationary non-polarized light. For convenience, we define two orthogonal directions x and y which form with z a complete orthogonal reference system. The propagating light in the all-fiber interferometer is assumed to be a transverse electromagnetic (TEM) plane wave orthogonal to the traveling direction z. A vectorial amplitude signal E is then written in terms of its projection E_x and E_y on the directions x and y respectively

If q is the polarization angle difference between the reference and the test light arriving at the detector, the signal amplitudes E_r and E_t are given by

where b includes the complete reflection response of the test sample. The signal amplitude E_d and intensity I_d at the detector are given by

After some algebric manipulations we obtain

The spectral distribution is identical for all polarizations (same complex degree of coherence g) and for non-polarized light, both orthogonal components have half the total source intensity I_s. This allows a reformulation of I_d

For q = 0, the intensity I_d corresponds to the case where the polarization effects are neglected and the interferences are not perturbed. For other values of q, the cosinus factor reduce the fringe visibility and in the worst case for q = p/2, no interference at all will be detected.