Simulation of mechanically ruled concave diffraction gratings by use of an original geometric theory

A geometric theory is developed for a spherical concave diffraction grating that has variable line spacing and curved grooves and can be produced with existing technology. The aberration coefficients of this grating are determined. A comparison of these coefficients with the corresponding coefficients of holographic gratings and with CODE V polynomial coefficients gives a clearer understanding of the similarity and difference between mechanically ruled and holographically recorded concave gratings and allows the optimization of these gratings with standard computer programs.