M. Testorf et J. Ojedacastaneda, FRACTIONAL TALBOT EFFECT - ANALYSIS IN PHASE-SPACE, Journal of the Optical Society of America. A, Optics, image science,and vision., 13(1), 1996, pp. 119-125
The Fresnel diffraction of periodic objects at rational fractions of t
he Talbot distance is described in terms of the Wigner distribution fu
nction (WDF). The analysis provides a heuristic model for understandin
g the formation of the diffraction patterns as well as for evaluating
the complex amplitude at any fractional Talbot plane. Furthermore, cer
tain symmetry properties of the Fresnel-diffracted wave field can be d
erived directly from the WDF. Additionally, a discussion is given on h
ow periodic signals and information about the phase are encoded in the
WDF. (C) 1996 Optical Society of America