Partial coherence formulation of grating self-imaging with any illumination

Abstract

On the basis of the partial coherence theory, a uniform formulation for the self-imaging is established, which can be used for both continuous and temporal illuminations with any kind of spectra. The formulation includes the cross mutual spectral density, the time diffractive intensity distribution and the averaged diffractive intensity distribution of grating at the self-imaging distances, and the last two variables are deduced in terms of the cross mutual spectral density. The self-imaging effect of different illuminations is then studied with a numerical stimulation, such as the continuous illumination with a polychromatic light source, and the ultra-short laser pulses with or without frequency chirp. It is interesting to find that the ultra-short pulse laser illumination and the polychromatic continuous illumination have the similar average intensity distribution of self-imaging, so that the self-imaging effect may be helpful for the study of the temporal and spectral characteristics of ultra-short laser pulses. An experiment with a polychromatic continuous light illumination (LED) is given, the results are the same as the predicted.