The grid points (delta functions) are exaggerated for clarity. Note that the Fourier transform of a grid is a grid with reciprocal directions and spacings. This is the origin of the reciprocal lattice.
A crystal, and its Fourier Transform:
Finally, we build up a crystal by convoluting the molecule with the grid. The result is a crystal structure. The Fourier transform of the crystal is thus the product of the molecular transform and the reciprocal lattice.