Space-temporal analysis of ultra-short light pulse propagation in aberrated optical systems

The field amplitude associated with ultra-short light pulses is analyzed using the phase-space formalism of the Wigner distribution function (WDF). By properly modifying the diffraction integral to take into account the dispersion effects (up to the second order), we derive a two-dimensional WDF associated with a reduced pupil function, from which the on-axis irradiance is obtained for varying time and defocus. The behavior of the optical system can be visualized as a three-dimensional irradiance display in a combined space-temporal domain. In order to illustrate this approach, we show some results for the case of an optical imaging system suffering from spherical aberration.