The orthogonal geometry of three-wave mixing in non-gyrotropic photorefractive crystal (PRC) with cubic symmetry is proposed and studied. In this geometry a single phase-modulated object wave and two elliptically polarized reference waves are mutually orthogonal and propagate in crystal along its principal axes ,  and , respectively. It is shown that each of two holograms recorded by pair of object and reference waves operates independently as a polarization-selective element and produces a demodulation signal which is related with one of two polarization components of the object wave. The resulting demodulation signal is a superposition of two demodulation signals originated from two holograms which are combined incoherently. It is shown that orthogonal geometry of three-wave mixing opens a possibility to design a completely polarization-independent adaptive interferometer.