  We study the diffraction of atoms and weakly-bound three-atomic molecules
from a transmission grating at non-normal incidence. Due to the thickness of
the grating bars the slits are partially shadowed. Therefore, the projected
slit width decreases more strongly with the angle of incidence than the
projected period, increasing, in principle, the experimental resolution. The
shadowing, however, requires a revision of the theory of atom diffraction. We
derive an expression in the style of the Kirchhoff integral of optics and show
that the diffraction pattern exhibits a characteristic asymmetry which must be
accounted for when comparing with experimental data. We then analyze the
diffraction of weakly bound trimers and show that their finite size manifests
itself in a further reduction of the slit width by (3/4)<r> where <r> is the
average bond length. The improved resolution at non-normal incidence may in
particular allow to discern, by means of their bond lengths, between the small
ground state of the helium trimer (<r>=1 nm, Barletta and Kievsky, Phys. Rev. A
64, 042514 (2001)) and its predicted Efimov-type excited state (<r>=8 nm,
ibid.), and in this way to experimentally prove the existence of this
long-sought Efimov state.
