Phases of Talbot patterns in angular self-imaging.

The original Talbot (self-imaging) effect is observed in the vicinity of a grating of slits shined with a plane wave, and results in periodic images of the initial diffraction pattern (integer Talbot effect) and the appearance of images with a periodicity reduced by an integer factor (fractional Talbot effect). Most of the studies on Talbot effect so far have focused on the distribution of the intensity of the diffracted light. However, the phases of the Talbot images, obtained in both the integer and fractional self-imaging cases, can be calculated in a closed form and display interesting auto-correlation properties. This paper reports what is, to the best of our knowledge, the first experimental investigation of the phases of Talbot images beyond the integer self-imaging case. We address the problem of experimental measurement of the phases of the Talbot images in the equivalent frame of the angular Talbot effect, a recently reported manifestation of the Talbot effect in the far field. The phases of the Talbot images are measured by far-field holography, and the obtained results are in excellent agreement with theoretical calculations. They also suggest the possibility of using the scheme for a precise "fractional ruler" aimed at distances' measurements.