wave pulses (act as either amplitude or phase gratings) is achieved using an on-resonant standing wave mask [@TLturlapov05; @Alexey06].

Developed theories of matter-wave Talbot-Lau effect (TLE) usually simplify the analysis by making particular assumptions on the coherence properties of input matter-waves. Closely related to the spatial (beam) Talbot-Lau setup with amplitude transmission gratings, in the first approach  [@KimbleTLTheory95; @ZeilingerTLTheory02; @ClauserInftheory92] the atom flux through each opening of the first grating are treated essentially as individual point sources, from which the Fresnel diffraction on the image plane is calculated. An incoherent sum of the contribution from all the openings at the $1^{st}$ grating gives the final interference pattern. Instead of incoherent summation of point sources, the second approach [@AIBerman; @Periodic02; @Resonantsplitter99] assumes the input atoms as an incoherent sum of plane waves. However, a general theory of Talbot-Lau interferometry applicable to matter-waves with arbitrary initial spatial coherence hasn’t been presented in the literature.

The approach to TLE in this work is motivated by an obvious link between the Weyl function \[Eq. (\[weyldefine\])\] and the time-domain matter-wave TLE due to a sequence of standing wave pulses. In the following we consider a single atom picture with atomic motion characterized by a density 