Synthesis of filters for specified axial irradiance by use of phase-space tomography

A procedure for designing pupil filters for applications where specified axial responses are required is developed. The method is based on the mathematical relationship between the axial impulse response of a system and de Wigner distribution function (WDF) associated to its pupil function. The desired axial irradiance, which can also have a predefined behavior depending on spherical aberration, is used to obtain this WDF by tomographic reconstruction. The synthetic pupil is retrieved from this distribution.