Holography

What a hologram actually records

A camera measures only the intensity of light — the time-averaged square of the field amplitude. In doing so it throws away the phase, the part of the wave that encodes which direction the light came from and how far it travelled. That is why a photograph is flat: the depth information is gone the instant the sensor squares the field.

Holography keeps the phase. The trick is interference. If you overlap the light scattered from an object — the object beam O(x,y) — with a clean reference beam R(x,y) derived from the same laser, the field at the plate is O + R and the recorded intensity is:

I = |O + R|²
  = |O|² + |R|² + O·R* + O*·R

The first two terms are just the brightness of each beam alone. The crucial part is the two cross terms O·R* and O*·R: because they involve the product of the two waves, they depend on the phase difference between object and reference. Wherever the two waves arrive in step the fringe is bright; wherever they arrive out of step it is dark. The phase of the object wave has been converted into a pattern of light and dark fringes — a quantity a plate can record.

Reconstruction — diffracting the wavefront back

Develop the plate and you have a transmittance t ∝ I: a fantastically complicated diffraction grating. Now shine just the reference beam R through it. The transmitted field is t·R, which expands to four terms:

t·R ∝ (|O|² + |R|²)·R   +   |R|²·O   +   R²·O*
        (zero order)        (virtual)     (conjugate)

The middle term is the prize. With a plane reference, |R|² is a constant, so this term is proportional to O — the original object wavefront, exactly reconstructed. Light leaves the plate as if it were still scattering off the object that is no longer there. Your eye focuses it just as it would the real thing, so you see a 3D virtual image floating behind the plate, complete with parallax: move your head and you look around foreground objects.

The other terms are the undiffracted zero order (the reference passing straight through, slightly attenuated) and the conjugate term R²·O*, which forms a distorted real image on the opposite side. Off-axis recording — tilting the reference, as Leith and Upatnieks did in 1962 — angularly separates these three so the bright zero order and the twin image no longer wash out the wanted image. This off-axis geometry is what made high-quality holograms possible.

Fringe geometry and why film must be so fine

Two plane waves crossing at an angle θ make straight fringes. Their spacing is

d = λ / (2 sin(θ/2))

For green laser light (λ ≈ 532 nm) crossing at θ = 30°, that is d ≈ 1.03 µm — about 970 lines per millimetre. Increase the angle to record more depth and the fringes get finer still; reflection holograms with beams from opposite sides (θ ≈ 180°) pack over 5000 lines/mm, with Bragg planes spaced about λ/2 ≈ 0.27 µm through the emulsion. This is why holographic film (Agfa 8E75, Slavich PFG-03M, photopolymers) has ultrafine grain and almost no "speed": it must resolve detail finer than a wavelength of light, and you pay for that resolution with long exposures on a vibration-isolated table.

Quantity	Photograph	Hologram
What is stored	Intensity |O|² only	Intensity and phase (via fringes)
Image dimensionality	2D, single viewpoint	3D, full parallax within the aperture
Light source needed	Any illumination	Coherent (laser) to record; laser or white light to view
Resolution of medium	~5–50 lines/mm	1000–5000+ lines/mm
Effect of cutting in half	Lose half the picture	Whole scene survives, with less parallax
Focusing on the medium	In-focus image sits on the film	Plate looks like noise; image floats in space

Coherence — the laser's role

For the fringes to be stable across the whole plate, the object and reference beams must keep a fixed phase relationship everywhere. The relevant scale is the coherence length

L_c ≈ λ² / Δλ ≈ c / Δν

where Δλ (or Δν) is the spectral width of the source. A single-longitudinal-mode HeNe laser at 632.8 nm with Δν ≈ 1 MHz has a coherence length of order hundreds of metres; even a multimode HeNe gives tens of centimetres — comfortably larger than a tabletop scene. By contrast, a filtered mercury lamp has Δλ of a few nanometres, giving L_c of only tens of micrometres. That is exactly why Gabor's 1948 holograms (using a mercury arc and an electron-beam analogue) worked only for thin, transparent objects, and why holography exploded after the laser arrived in 1960. The path difference between object and reference must stay well within L_c, which also means the optical table cannot move by more than ~λ/4 during the exposure — vibration isolation is essential.

Types of hologram

• Transmission hologram. Object and reference hit the emulsion from the same side; fringes run roughly perpendicular to the plate. Viewed with laser light passing through it. Off-axis Leith–Upatnieks geometry separates the images cleanly.
• Reflection / Denisyuk hologram. Beams come from opposite sides, recording Bragg planes through the emulsion thickness. The thick stack of planes acts as a wavelength-selective mirror, so it reconstructs in ordinary white light, picking out only the recording colour. A single-beam Denisyuk setup is the simplest hologram to make at home.
• Rainbow (Benton) hologram. Sacrifices vertical parallax for white-light viewing in transmission; the embossed version is the silvery security hologram on credit cards and banknotes, mass-produced by stamping the surface relief.
• Volume / thick holograms. When the emulsion is many wavelengths thick, the Bragg condition makes them highly angle- and wavelength-selective, enabling many holograms to be multiplexed in one crystal — the basis of holographic data storage.

Where holography shows up

• Security. Embossed rainbow holograms on banknotes, passports, and credit cards — hard to copy because they encode a microscopic surface-relief grating.
• Holographic interferometry. Overlay two holograms of an object taken at different times; sub-wavelength deformations show up as fringe shifts, used for non-destructive testing of tyres, turbine blades, and aircraft panels.
• Data storage. Volume holograms multiplex thousands of pages of data in a single photorefractive crystal, read out by angle- or wavelength-selective Bragg diffraction.
• Head-up and head-mounted displays. Holographic optical elements act as transparent, wavelength-selective combiners in aircraft HUDs and AR glasses.
• Diffractive optics. Computer-generated holograms (CGH) fabricate custom wavefronts for laser beam shaping, lithography masks, and optical tweezers.
• Microscopy. Digital holographic microscopy reconstructs phase numerically to image transparent cells without staining.
• Art and display. Museum-quality reflection holograms and pulsed-laser portraits that capture moving subjects in a nanosecond exposure.

What is NOT a hologram

• Pepper's-ghost "holograms." Stage illusions and concert "holograms" reflect a flat 2D video off an angled transparent sheet. There is no interference, no recorded phase, and no real parallax — it is a clever mirror trick, not holography.
• Lenticular and parallax-barrier 3D. These show a handful of discrete views with a microlens or slit array; they are autostereoscopic displays, not wavefront reconstruction.
• Volumetric and light-field displays. Genuinely 3D, but they synthesise the image by other means rather than diffracting a stored interference pattern.

Common misconceptions

• "A hologram is a 3D photo." It is a recorded interference pattern. To the naked eye an unilluminated transmission hologram looks like grey noise; the image only appears under correct illumination.
• "You just need a bright light." You need a coherent light source. Brightness without coherence (a flashlamp) records no stable fringes.
• "Each spot on the plate stores one spot of the image." Information about every object point is spread across the whole plate, which is why a fragment still shows the entire scene.
• "Holograms only work with the original color." Reflection holograms reconstruct in white light, selecting their recording wavelength via Bragg selection; rainbow holograms even sweep through colours with viewing angle.
• "The image sits on the film." The reconstructed virtual image floats in space behind (or the real image in front of) the plate; focusing your camera on the plate itself shows only fringes.