A photograph flattens a scene; a hologram keeps it whole. The trick: let the light bouncing off the object meet a clean reference beam, and record their INTERFERENCE on a flat plate. Shine the reference back through it and the object’s full 3D wavefront springs back — move your head and you see around it. A 2D surface encodes a 3D world. Slide to illuminate the record and watch the object reconstruct.
A hologram records not brightness but PHASE, via interference. The plate is exposed to the sum of the object wave O and a reference wave R, storing intensity |O+R|² = |O|²+|R|²+OR*+O*R. Illuminate the developed plate with R alone and the cross term OR*·R = O|R|² reconstructs the ORIGINAL object wave O — the full 3D wavefront, with parallax, from a flat 2D record. A fail-loud self-check throws unless the reconstruction recovers the object amplitude. The boundary encodes the bulk (Gabor 1948, Nobel 1971). ◆ real optics, node-verified.
The exact interference-record / reference-reconstruction algebra (one object & reference amplitude); real holograms also produce a conjugate image and need coherent light — the surface-encodes-volume reconstruction is the exact, defining mechanism.