A phase space description of the fractional Talbot effect, occurring in a
one–dimensional Fresnel diffraction from a periodic grating, is
presented. Using the phase space formalism a compact summation formula for the
Wigner function at rational multiples of the Talbot distance is derived. The
summation formula shows that the fractional Talbot image in the phase space is
generated by a finite sum of spatially displaced Wigner functions of the source
©1998 Optical Society of America
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