Polychromatic merit functions in terms of the Wigner distribution function

A method for the calculation of the axial illuminance and chromaticity as polychromatic merit functions of optical imaging systems is presented. We show that the Wigner distribution function of the pupil of the system allows us to obtain all the monochromatic components needed for the calculation of these parameters. From this single phase-space representation, the merit functions can be obtained in a polar fashion for a variable spherical and longitudinal chromatic aberrations. Numerical examples for an axially apodizing filter are shown.