The Fresnel diffraction of periodic objects at rational fractions of the Talbot distance is described in terms of the Wigner distribution function (WDF). The analysis provides a heuristic model for understanding the formation of the diffraction patterns as well as for evaluating the complex amplitude at any fractional Talbot plane. Furthermore, certain symmetry properties of the Fresnel-diffracted wave field can be derived directly from the WDF. Additionally, a discussion is given on how periodic signals and information about the phase are encoded in the WDF.
© 1996 Optical Society of America
Original Manuscript: January 13, 1995
Revised Manuscript: July 5, 1995
Manuscript Accepted: July 13, 1995
Published: January 1, 1996
Markus Testorf and Jorge Ojeda-Castañeda, "Fractional Talbot effect: analysis in phase space," J. Opt. Soc. Am. A 13, 119-125 (1996)