Talbot Images of an Array Source with Correlated Phase Fluctuation Using the Propagation Law of a Gaussian Beam

Talbot images of a two-dimensional array source such as a surface-emitting array laser are investigated with the help of the propagation law of a Gaussian beam. The effect of the phase fluctuation existing between the elements of the source on the formation of Talbot images is revealed by computer simulation. In the study, the correlation extent of the phase fluctuation is taken into consideration together with its magnitude (standard deviation), and Talbot images of good quality are found to be formed when the correlation extent is larger than the extent of the diffraction of a Gaussian beam in the observation plane. It is further shown that the contrast of Talbot images is governed, in a statistical sense, not by the magnitude of the phase itself but by the phase-fluctuation slope in the array source.