In most of grating x-ray interferometry one needs an absorbing grating as the analyzer to measure high-resolution interference fringes. Dual phase grating interferometry is a technique to get rid of the absorbing grating for radiation dose reduction. The authors present a quantitative theory of dual grating x-ray interferometry. The theory elucidates the fringe formation mechanism. The derived formulas of fringe period and fringe visibility provide useful tools for design optimization of dual phase grating interferometers.