the diffraction pattern as the reciprocal lattice

Here is the pay-off that makes the whole reciprocal-lattice idea worth learning: a diffraction pattern is not a coded riddle you have to decrypt — it is a direct photograph of the crystal's reciprocal lattice. Each spot on the film or detector is one reciprocal lattice point made visible. Where crystallographers once seemed to be doing something magical, they are really just reading a picture of the reciprocal lattice off the detector.

The connection is exact, spot for spot. A reflection appears when a reciprocal lattice point touches the Ewald sphere, and its position on the detector maps back to the position of that point in reciprocal space. So the pattern of spots reproduces the pattern of the reciprocal lattice, and their brightnesses reproduce its weights. Different experiments give you different slices or projections of the same reciprocal lattice: a selected-area electron diffraction pattern in a TEM shows a nearly flat planar SECTION through the reciprocal lattice (because the electron Ewald sphere is almost flat), so you literally see a grid of dots that IS a layer of reciprocal points. A single-crystal X-ray experiment, by rotating the crystal, sweeps the Ewald sphere through many points and builds up the full three-dimensional reciprocal lattice one frame at a time. A powder pattern takes all crystal orientations at once, which spins every reciprocal point into a sphere, so the three-dimensional reciprocal lattice collapses onto a one-dimensional set of rings at radii |g_hkl| = 1/d_hkl.

This is exactly why learning to think in reciprocal space pays off: once you see a diffraction pattern AS the reciprocal lattice, indexing the spots is just naming reciprocal points, symmetry in the pattern is the symmetry of the reciprocal lattice, and the spacing of the spots reads off the cell dimensions by the inverse-size rule. One honest qualification: the picture is the WEIGHTED reciprocal lattice, complicated by which points happen to sit on the Ewald sphere and, for strongly interacting probes like electrons, by dynamical (multiple) scattering that redistributes intensity. The GEOMETRY of the spots is a faithful map of the reciprocal lattice; the INTENSITIES need more care.