Quality of a Gaussian beam diffracted by a concave non-spherical grating

We examine the propagation of a complex-source-point spherical wave via a concave non-spherical grating. First we trace the paraxial paths of a chief ray propagating from a complex source point through the system to complex image points of different orders. Then we represent the wave function of the light in terms of Seidel-type aberrations, while the terms of up to fourth order in aperture variables are taken into account. Based on the derived formula, we also evaluate the quality of a Gaussian beam degraded by the system. We show how the beam qualities in the sagittal and tangential sections are influenced by the conic constant (or the aspheric coefficient of fourth order) and the positions of source and stop.