Ray tracing of mechanically ruled gratings

To evaluate the quality of grating, it is desirable to have a ray tracing map of the designed grating. A method of ray tracing for mechanically ruled gratings is developed. Based on Fermats principle and light path function, it gets the spectral distribution of the incident rays, and it can get the ray tracing map through a matrix method. The method is applicable to plane, spherical and aspheric gratings with variable spacing. The groove spacing can vary in arbitrary forms, and the image surface can be chosen as a plane or a conicoid. The ray tracing map of a concave grating ruled on toroidal surface proves the feasibility of the method.