Wavefront reconstruction · object + reference beams interfere · fringe recording & replay
A hologram does not store a picture — it stores a wavefront. During recording, light from the object (the object beam) and a clean tilted reference beam overlap on a photographic plate. Because both come from the same coherent laser they interfere, and the plate records the intensity I = |E_obj + E_ref|² = I_obj + I_ref + 2√(I_obj·I_ref)·cos(Δφ). That final cross term is the magic: it encodes the phase difference Δφ between the two beams as a microscopic fringe pattern, so both amplitude and phase of the object wave are frozen into the plate.
The fringe spacing depends only on the angle between the beams: Λ = λ / (2·sin(θ/2)). A larger reference angle packs the fringes more tightly (higher spatial frequency), which is why holographic film must resolve thousands of line-pairs per millimetre.
During replay the plate is illuminated with the reference beam alone. The fringes act as a diffraction grating and split the light into three orders: the 0th order (undiffracted reference), the +1 order which reconstructs the original diverging object wavefront — seen as a virtual image behind the plate — and the −1 order, the phase-conjugate that converges to a real image in front of the plate. Reconstructing the wavefront, not a flat image, is what gives holograms their full three-dimensional parallax.