Abstract: Based on Chrisp's wave-front aberration theory of grating, the wave-front aberration coefficients are derived with a grating surface of polynomial expression, which can be used to design and analyze a grating of toroidal or conicoid surface figure. The transformation formula can be obtained from the wavefront aberration to transverse aberration on image plane even if the exit wave front is astigmatic and the image plane is out of focus. Finally, the numerical results are compared with the ray tracing results.

Key words: grating imaging, multi-element systems, wave-front aberration