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Diffraction-interference patterns of parametric down-converted photons through a transmission grating by both one- and two-photon detection schemes are presented. The measured patterns are explained by the Fourier analysis of the two-photon wave packet, considering the quantum spatial correlation between the constituent photons. Spatial diffraction-interference patterns were recorded by a two-photon detector consisting of two avalanche photodiodes. For comparison, diffraction-interference patterns of Ti:sapphire laser are also observed using the same apparatus (a uncorrelated case).