A cw Mach Zehnder multichannel interferometer has been developed to measure time‐dependent fractional fringe shifts with an accuracy of one‐fortieth fringe. The design is quasi‐quadrature in that known phase shifts, introduced in the reference beam, are time multiplexed with the normal reference beam. This technique requires only one detector per interferometer channel as compared to two detectors for most quadrature designs. The quadrature information makes the sense of density changes unambiguous, it automatically calibrates the instrument during the plasma event, and it makes fringe shift measurements virtually independent of fringe contrast fluctuations caused by plasma refractive and/or absorptive effects. The interferometer optical design is novel in that the electro‐optic crystal used to introduce the 90° phase shifts is located in the common 2‐mm‐diam HeNe entrance beam to the interferometer, by exploiting polarization techniques, rather than in the expanded 1–2‐cm reference beam itself. This arrangement greatly reduces the size, cost, and high‐voltage requirements for the phase modulating crystal.