A new type of interferometry based on Fourier-transformation diffraction of coded gratings with an extended polychromatic illumination is proposed. In the system two coded gratings are inversely imaged to each other by a lens, and the tested phase object is placed between and imaged onto an observation screen. The intensity of a certain imago point is related to the phase variations in the corresponding part of the objective Fourier-spectrum of the coded grating encounters. Because of dispersion the resulted intorforogram is colored. Thus, various forms of interference can be easily obtained by using different coded gratings. The system is analysed in detail by the Frosnel first-order diffraction theory, consequently, a generalized conclusion is come to. The relation among the patterns of coded gratiags, their Fourier-transformations and tho possible forms of interference is discussed. The experiments are given, too.