for the matter-waves. Time-domain interferometry using optical standing wave pulses with laser-cooled atoms were pioneered by the authors of ref. [@TLCahn97]. In that experiment, off-resonant standing wave pulses act as thin phase gratings to an atomic cloud. After each standing wave pulse the atoms bunch to the potential minima of the standing wave to form a density grating. The density grating washes out due to velocity spreading of atoms. However, with two successive standing wave pulses separated by time $T_{12}$ applied to atoms, the atomic density grating revives around time $t=T_{12}+T_{23}$ if $T_{23}=T_{12}$ and more generally if $T_{23}=N T_{12}$, where $N$ is an integer. The contrast of the revived density grating is a periodic function of $T_{12}$, similar to the spatial Lau effect. The revived atomic density grating is probed using a Bragg-scattering of a probe light to induce a grating echo [@gratingechoOrigin], and the interferometry based on this setup is referred as a time-domain grating echo interferometer [@GradientefTL06]. Experiments and the theory of the interferometry were further developed in ref. [@Periodic02] that generalizes the technique to include multiple standing wave pulses. Recently a direct spatial image of sub-wavelength spatial interference pattern due to the Lau effect after two standing 