We have studied statistically the formation of Talbot images of a grating with random fluctuations in the spatial domain. A detailed theoretical analysis is done for a one-dimensional rectangular grating with random fluctuations obeying a gaussian random process. It has been revealed that, when the standard deviation of fluctuations is approximately beyond 30% of the period of the rectangular grating, the image observed at the Talbot image plane preserves no longer any periodic structure. This result is experimentally confirmed from measurements of the visibility of the Talbot images.
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