Optical systems under broad-band illumination: Analysis based on a wigner distribution function approach

Abstract

The irradiance produced by an optical imaging system suffering from aberrations under broad-band illumination is analysed in the phase-space domain of the Wigner distribution function associated with a modified one-dimensional pupil aperture. To this end, a coordinate transformation is employed in such a way that the varying irradiance along different paths in the image space can be derived from different slices of the Wigner distribution function, which involve both the defocus distance and the dispersion properties of the optical system. The method is illustrated by comparing the axial irradiance distribution for different primary aberrations. Also, the irradiance along parabolic paths is obtained in order to analyse the coma effect.