Polychromatic partial coherence: space-time filtering and Fourier transform

The transfer of the partial coherence by an optical system is studied, within the framework of a polychromatic light. The method relies on the fundamental fact that the coherence is transformed by a linear filter univocally connected to the filter acting on the electric field. It results a particular relationship of structure between the transformations assumed by the field and the coherence: space-time filtering as much as spatial Fourier transform, which are successively analysed in the case of transfer by direct diffraction. The results obtained are specified in the particular case of a narrow-band radiation or yet an incoherent object; which allows, among others, to situate Zernike theorem in a quite general context.