We present a novel configuration of an interferometer which is implemented by using vectorial wave mixing in the orthogonal geometry of wave interaction in a cubic photorefractive crystal, for the detection of small phase transients. The orthogonal geometry of wave interaction allows the linear regime of the phase-to-intensity transformation even when phase transients are encrypted in a depolarized wave without using any polarizing element. The use of a depolarized beam without a polarizing element strongly diminishes the noise level, thus increasing the sensitivity to phase transients.