Retrieving the Talbot length of arbitrary 2D gratings

The Talbot effect has been revived in many fields of modern optics. As a key number of self-imaging, the fundamental Talbot length plays a crucial role in many applications. However, the inspection of the Talbot carpet for determining the Talbot length is applicable only if the 2D field distribution behind the grating is represented by a 1D cross section. In this Letter, we show an effective way to overcome this limitation to explore the self-imaging of gratings with complex 2D periodicities. For that purpose, the near-field diffraction is analyzed using the Pearson correlation coefficient of the intensity distribution in Fourier space. We report results on linear, ring, and spiral gratings.