A new feedback interferometer is developed with which not only the magnitude but also the sign of a phase change caused by a variation in the optical path can be measured. This is an important feature, for example, in plasma diagnostics. Phase quadrature is obtained by using two axial modes of a He-Ne laser. The two interference signals can be separately detected by virtue of the orthogonal polarisation of the two axial modes of the laser without Brewster windows. The result is a versatile, stable and accurate instrument. In the experimental test the sensitivity proved to be approximately 1/5 fringe at a laser wavelength of 632.8 nm, equivalent to 0.1 mu m. In plasma applications the instrument would have a sensitivity of neL approximately=2*1020 m-2, where ne is the electron density and L the length of the laser cavity.