Periodic nanostructures fabricated by atom lithography using standing-wave light field can be applied for nanometrology. Atom-optical properties of 3D standing-wave light field are studied with particle optics model.The initial condition of each trajectory is stochastically selected with Monte-Carlo method, where the effects of isotope, longitudinal velocity distribution and transverse Gaussian divergence are systematically evaluated. 3D nanostructures with varying laser powers are presented,which shows the effect of longitudinal Gaussian distribution of the light field. The effect of elliptical standing wave is also discussed. It is shown that well-defined nano-grating lines appear in 87% of the substrate and full width at half maximum (FWHM) obtained at the center of Gaussian laser beam is 31 nm when the laser power is 40 mW. Good results can be obtained when the shape of the cross section of the standing wave is round.