We propose and demonstrate a new interferometric approach in which a uniform phase difference between the arms of the interferometer manifests itself as spatially varying intensity distribution. The approach is based on interfering two orthogonal spatially varying vector fields, the radially and azimuthally polarized beams, and measuring the projection of the obtained field on an analyzer. This method provides additional spatial information that can be used to improve the smallest detectable phase change as compared with a conventional Michelson interferometer.