Abstract: Based on the wave-front aberration theory of grating proposed by M.Chrisp, the wave-front aberration coefficients are derived with a grating surface of a polynomial shape. The groove pattern function is used to express the curvature and groove space of aberration reducing gratings. From the wave-front aberration coefficients, the effect of grating surface and groove pattern is discussed. These coefficients can be used to design and analyze a grating of conicoid surface figure.

Key words: aberration reducing gratings, groove pattern function, wave-front aberration