Hologram Simulator: How Holograms Are Recorded and Played Back
A free hologram simulator: record the interference fringes of a reference beam and object points live, play the hologram back with real wave optics to see the virtual image, the twin and parallax, explore coherence, compare transmission, reflection, rainbow and embossed holograms and Pepper's ghost, and compute a phase hologram of your own drawing.
A hologram is a photograph of interference. Laser light is split in two: the reference beam goes straight to the plate, the object beam lights the object, and each point of the object sends out a spherical wave. Where the two beams meet on the plate they add up or cancel, making a pattern of very fine fringes. The fringes store both the brightness and the direction (phase) of the light from the object. Drag the object points; the fringe pattern on the plate is computed live from \(I = |R + O_1 + O_2 + \dots|^2\).
Light the developed plate with the same reference beam and the fringes act like a very complicated diffraction grating. Out of the plate come three waves: the zero order (the reference going straight on), the virtual image (an exact copy of the object's light: you see the object behind the plate, in 3D) and the twin or real image. This tab does the whole thing numerically on a small plate: it records the hologram, lights it, and propagates the light with the angular-spectrum method (FFT). Move the focus to look at different depths; move the camera across the plate to see parallax.
Fringes only form if the two beams are coherent: if the light that went the long way still keeps step with the light that went the short way. Real light comes in wave trains about one coherence length long, \(L_c = \lambda^2 / \Delta\lambda\). When the path difference grows past that, the fringe contrast fades to nothing. That is why holograms need lasers, and why the object's depth is limited.
Typical light sources
Ballpark figures: real lasers vary a lot. The deepest scene you can record is about half the coherence length, because light reaching the back of the object travels farther than light reaching the front (and the reference path is matched to the middle).
Every true hologram records interference fringes, but the way the beams meet decides what you need to see it: a laser, a lamp, or just daylight. Pick a type.
The types side by side
| Type | Beams when recording | Lit by | Colour | Parallax | Examples |
|---|---|---|---|---|---|
| In-line (Gabor, 1948) | One beam: the light that misses the object is the reference | Laser | Laser colour | Some; the twin image is in the way | Electron and X-ray holography, particle holography |
| Off-axis transmission (Leith-Upatnieks, 1962) | Both on the same side, at an angle | Laser from behind | Laser colour (white light smears into a rainbow) | Full: left-right and up-down | Museum and lab holograms, holographic interferometry |
| Reflection (Denisyuk, 1962) | From opposite sides | A small white lamp from the front | Picked by the layers (Bragg): one colour | Full | Display holograms, Lippmann photographs |
| Rainbow (Benton, 1968) | Same side, through a slit (a hologram of a hologram) | White light from behind (or mirror-backed) | Changes with eye height | Left-right only | Credit cards, book covers |
| Embossed | A rainbow master copied as a surface relief | Daylight, reflected off a metal coat | Rainbow colours | Left-right, often just a few views | Banknotes, passports, stickers |
| Computer-generated | None: the fringes are calculated | Laser | Laser colour | As designed | Laser projectors, optical tweezers, AR glasses |
| Pepper's ghost (not a hologram) | None: a sheet of glass reflects a hidden lit figure or screen | Its own light | Any | None: a flat picture | Stage "holograms", museum ghosts, teleprompters |
You do not need an object to make a hologram: a computer can work out the fringes. Draw a picture on the left pad. The Gerchberg-Saxton algorithm then searches for a phase-only hologram (it changes only the delay of the light, not its brightness, like a liquid-crystal display used in laser projectors) whose far-field light pattern is your picture. It jumps between the hologram and the picture, keeping the phase it found and putting back what it knows each time.
How holograms work
A normal photograph records only how bright the light was at each point. A hologram also records the light's phase: how far along its wave cycle it was. Film can only record brightness, so Dennis Gabor's trick (1948) was to add a second, simple wave, the reference, and record the interference of the two. The bright and dark fringes encode the phase: where the object's light was in step with the reference, the film is exposed; where it was out of step, it is not. Lighting the developed film with the reference again diffracts the light back into a copy of the object's wave, so you see the object in full 3D, with parallax, focus and depth, as if it were still there.
In the playback equation the middle term \(|R|^2 O\) is the object's own wave (the virtual image), the last term is its mirror twin (the real image, which focuses in front of the plate) and the first is the zero order. Gabor's in-line holograms had all three on top of each other. Emmett Leith and Juris Upatnieks (1962) tilted the reference beam so the three leave the plate in different directions: the start of practical holography.
Things to try
- Recording: zoom in until single fringes show, then change the reference angle: a steeper angle packs the fringes closer (λ / sin θ). Holographic film has to resolve thousands of lines per millimetre.
- Recording: choose the red LED as the light source. The fringes vanish unless the reference path matches the object path to within a few tens of micrometres.
- Playback: focus on each point in turn: only one is sharp at a time, because the image really is 3D. Then turn on the camera opening and move it: near and far points shift against each other (parallax).
- Playback: set the reference angle to 0°. Now the twin image and the zero order sit on top of the picture and the spectrum filter cannot separate them: Gabor's twin-image problem.
- Reflection hologram: tilt it and the colour moves toward blue; shrink the emulsion and a red-recorded hologram plays back green.
- Computer-generated: switch to 2 phase steps and watch the upside-down twin appear.
Things people ask
- Are stage "holograms" of singers real holograms? No. They are Pepper's ghost: a sheet of glass or foil reflects a bright video screen hidden below the stage. It is a flat picture with no recorded fringes and no true depth.
- Why are credit-card holograms rainbow-coloured? They are embossed rainbow holograms: thin surface ridges that act as a diffraction grating, so each colour leaves at a different angle. Benton's slit trick throws away up-down parallax so that each colour makes a sharp image at its own eye height.
- Why can a reflection hologram be seen with a lamp? Its fringes are layers through the depth of the emulsion, spaced about half a wavelength apart. Like the scales of a butterfly, they reflect only the colour that fits the spacing (Bragg's law), so the hologram picks its own narrow band out of white light.
- If I cut a hologram in half, do I lose half the picture? No: every part of the plate received light from every point of the object. You get the whole scene through a smaller window, with less parallax and a little less sharpness (try a small camera opening in the Playback tab).
- What is modelled here? Scalar waves in the paraxial and non-paraxial (angular spectrum) sense, a film whose transmission is proportional to the light it received, and a partially coherent source with a Gaussian spectrum. Not modelled: polarisation, film grain and non-linearity, the thickness of transmission holograms (except in the reflection-hologram section, which uses Kogelnik's coupled-wave formula).
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