Babinet-Soleil compensators are routinely used in spectroscopy using Fourier TransformSpectroscopy principles to extract the spectral information of light sources. The Babinet-Soleilcompensator allows for precise control and adjustment of the phase difference between twopolarized light beams. It offers several advantages over other interferometer types such as excellentstability compactness and delay precision. However, the interference signal measured with thiscommon path interferometer is usually degraded by the presence of a displacement between thetwo polarization replicas at the output of the interferometer. This is due to a splitting between the twopolarization paths happening when the light passes through the air-gap of the wedge-shaped crystalsinside the Babinet-Soleil interferometer. This paper explores various modifications to the Babinet-Soleil scheme to mitigate birefringence-induced displacement effects between two interferingreplicas. The proposed schemes enhance the contrast of the interference signal, making itparticularly advantageous for high-precision metrology, optical coherence tomography, and otherinterferometric techniques requiring high visibility and stability.