Phase space description of vignetting in optical systems

A general theory of vignetting in real optical systems has been developed. Considered a beam of light rays limited by a field stop, an aperture stop inside of the real optical system (aberration vignetting) and a stop outside of it (natural vignetting). It is shown that each of these 2D-stops can be replaced by a virtual 4D-phase stop, and the result stop for 4D-phase result stops is their intersection. In case of an axially-symmetrical optical system with circular stop openings all phase stops are solids of revolution and can be fully characterized by their meridional cross sections in a 3D-space, which can be easily drawn.