An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile resulting from the scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. Analytic asymptotic expressions are obtained for the Fourier components of the atomic wave function following scattering. It is shown that, owing to the scattering into two groups of momentum states rather than two distinct momentum components, the corresponding spatial density profiles differ significantly from pure sinusoids.having period /2n . The prototype LABS consists of a V potentialoff of which atoms scatter. The function f (t), normalized such that ͐ Ϫ/2 /2 f (t)dtϭ1, describes the potential experienced by an atom in its rest frame ͓tϭx/u, where u is the projection of the atom velocity along the beam propagation direction (x axis͒ and is the pulse duration in the atomic rest frame͔ ͓11͔. It is assumed throughout this paper that the temporal width is sufficiently small to allow the atom-field interaction to be considered in an impulse ͑Raman-Nath͒ approximation. A sufficient condition for the Raman-Nath approximation to hold iswhere m is the atomic mass.In the past several years, a number of methods have been proposed for using counterpropagating optical fields to create PHYSICAL REVIEW A, VOLUME 64, 063612