Coherent-mode representation of self-imaging optical fields

The coherent-mode representation is a fundamental tool that helps us understand the processes of producing and propagating optical fields. In this work, such representation for self-imaging phenomena under partially coherent illumination is presented within the frame of partial coherence theory in the space-frequency domain. Additionally, it is shown that the well-known Talbot and Lau effects are particular cases included in this new formalism. When complete coherence of the field is considered, the general expression for coherent self-imaging of optical fields is obtained (Talbot effect for both linear and circular gratings are presented); on the other hand, when an incoherent superposition of an infinite number of modes are considered, the expression to describe the Lau effect is obtained.