Experimental and numerical investigation of the effect of the spatial coherence of incident light on the Talbot and Lau self-images.

Using binary gratings as test objects, we quantitatively investigate the formation and visibility of the Talbot and Lau self-images under partially coherent illumination generated by a secondary Gaussian Schell-model source. The spatial coherence of the illuminating field is controlled through continuous variation of the source size, resulting in different fringe distributions in both regimes. Although the spatial coherence length varies according to a Lorentzian function with the source size, the visibility of the Talbot self-images exhibits an approximately Gaussian dependence, decreasing to 0.5 when the coherence length at the grating plane becomes nearly twice the grating pitch. In the Lau regime, the self-images remain sharp and clearly visible over a broad range of low-coherence illumination, as long as the coherence length remains below approximately twice the pitch of the first grating. However, when the coherence length becomes comparable to the grating pitch yet much smaller than the transverse width of the incident light field, the illumination becomes locally coherent over individual grating periods. Consequently, Fresnel diffraction features produced by the gratings appear within the main Lau self-image on the CCD plane, superimpose on the Lau fringes, and degrade their regular structure.